We have enslaved a hot chain rule to recover this formula here, so what we are trying to do is find the wave functions that represent the states of well defined orbital angular momentum. I explain what the strategy is for doing that and that strategy involves knowing what Ies â oes oedd yr waith cyfrindwyr sy'n golygu'r gwahanol a judacesio Cyfrindwyr yn y reliant am gyfrindwyr. Yn rhai fawr hwnneud ar gweithio ar y cyfrindwyr sunshine, yn ddyloch i fynd i ffordd gylir gael tua cyfrindwyr sy'n gylir gael tua cyfrindwyr sy'n gylir gael tua cyfrindwyr. Mae'n meddwl am y dyma'i ddau cyfrindwyr wedi gweld bethent i fynd y rai sy'n cerddoedd gael eu bobl mae'n gael môl yn gweld ar y peirwyr mewn gwaddodol. We are now in a position to find these wave functions. Let's call it a psi lm. This will be some function of r, theta, and phi, because we are looking at this in spherical polar coordinates. So this of course is r, theta, and phi lm. Now the radial dependence of this wave function is going to be completely unspecified because we are only going to require, all we're going to require is that lz on lm is equal to m lm. This thing has got to be an eigenfunction of this operator with the eigenvalue m, which we now know to be an integer.  We're not going to direct, and we will find, we haven't yet calculated this operator, what l squared looks like is a differential operator, we will get to that. But it will also turn out to involve only derivatives with respect to theta and phi. So these operators, none of them involve anything about radius, and so this function is an arbitrary function of radius and all we're going to be able to discover is what its angular dependence is by imposing these requirements here. OK, so what can we say? We can say, first of all, this equation is going to imply, put into the position representation, it says that minus i d by d phi of psi is equal to m of psi, which we, of course, immediately recognise is telling us that psi at r theta and phi is equal to e to the i m phi times of psi at r theta and nothing, if you see what I mean, and nothing, and nothing, and nothing. So there's some kind of a constant here, right? This thing doesn't depend on phi. If you differentiate this with respect to phi, you bring down an i m, the i's make another minus sign that cancels this, and you end up with m times whatever it is. So what we know is, this should have its subscripts, I suppose, so what we know is that psi l m is equal to some function of r in theta times e to the i m phi. I guess we kind of already knew that. Now we're going to, oops, and we're going to, well, yeah, we're now going to impose the condition that l plus on a psi l l is equal to naught, because this operator would create a state in which m, we've put here the value of m equal to l, which is its largest value. This would try and make a value make m even bigger than l. We know that's not possible, so we have this equal zero. So copying down what that is, this equation is the position representation e to the i phi, sorry, e to the, yes, e to the i phi, d by d theta plus i cotangent theta d by d phi, operating on e to the i l phi times this function k, which depends on r and theta, especially it depends on theta, the r dependence we don't care about, it depends on how much loperate is here with respect to r. So this term looks only at that and brings us down an i l, right? So what's that, sorry, this is going to be equal to zero. So we get two terms, we're getting at this d by d theta term looks only at that. So we discover that dk by d theta minus cot theta, sorry, l cot theta, we're bringing down an i l k equals naught. Then there's a factor of e to the something or other phi which we can cancel away, it's not interesting. So here we have, this is a linear first-order differential equation, the friendliest kind of differential equation, so we solve it with an integrating factor. The integrating factor is e to the integral of this here, e to the integral of minus l, oops, minus l cot theta d theta, but I think that the integral of cot theta d theta is log sin theta, so this becomes e to the minus l log sin theta or e to the log of sin to the minus l theta or simply sin to the minus l theta, that is the integrating factor of this equation. In other words the equation states that d by d theta of the integrating factor which is sin to the minus l theta times the function is equal to naught, in other words this thing is equal to a constant, in other words k is equal to a constant, she's obviously going to be some kind of normalising constant times sin to the l theta, and we have discovered this constant in principle depends on r. You can have any r dependence you like, so what we've discovered is that psi ll is any function of r you like times sin to the l theta e to the i l phi. This is an important kind of result.  Remember these ladder operators come with square root e normalising factors, that was the case in harmonic oscillator, that's the case also with the angular momentum operators, operating on a psi ll, which we now know what it is, sin to the l theta e to the i l phi times the unspecified function of radius, and this l minus, that's roughly speaking put in what it is, no maybe we do it on the next board because we want to be able to see those magic formulae, right, there they are. This tells me that upside l minus 1 is equal to, I think this is just a square root of 2l, so it's function of radius over the square root of 2l, all being well, times e to the minus i phi times, there's probably an overall minus sign coming from that formulae at the top there, d by d theta minus i cot theta d by d phi working on the function we first thought of, which is sin to the l theta e to the i l phi and what are we going to get? This d by d phi will again bring down an l etc, and then this exponential will take one off that, so we'll end up with something that goes like e to the i l minus 1 phi, this will differentiate sin to the l and produce l, sin to the l minus 1 times a cosine, this cotangent multiplying that because this is cos over sin will again produce me a cos times sin to the l minus 1, so the whole thing is going to be minus, unspecified function of radius over the square root of 2l, times, everything is going to go like e to the minus i l minus 1 phi and then from here we're going to get an l, from here differentiating that we're going to get an l, well there's going to be a factor sorry, of sin to the l minus 1 theta cos theta and how many of them, from here we'll have an l and from here we will have, we're going to bring down an l, well a minus sorry an i l, they will cancel so I think it'll be plus another l of the same, same stuff, so you see that we have something like the square, minus the square root of l over 2, whatever your unspecified function of radius was, e to the minus i l minus 1 phi, times sin l minus 1 cosine theta and we could now apply l minus to this again and get the next in sequence, right? We're not going to do it because life gets very boring, l minus 2, but it's just a matter of differentiating, well the thing to pick up is that when we do this next, when we differentiate this, this thing is going to become more complicated because we're going to be doing a derivative of this with respect to theta, so we will get a term that goes like sin to the l minus 2 times cos squared and then differentiating this we'll get our sin to the l back, so we'll get two different terms and then when we differentiate again to get psi, so this is going to be an amount of, this will, this will, it's going to be amount of sin l minus 2 times cosine squared, differentiating this we'll get sin to the l minus 2 and then we'll get a cosine which goes on to that and we will also have, from differentiating this, plus an amount, call it b of sin to the l theta, so there'll be two terms and it'll all be times e to the minus l minus 2 phi and when we differentiate this again in order to get psi l minus 2 it'll get more Byzantine and it'll generate me an l sin to the l minus 3 times cos cubed, this will get back what we had here and so on and so forth, you get more terms, you get a longer thing coming in front of the exponential. So what are these things actually turning out to be?  Yep, this should have been a plus, e to the i m phi. So this thing, I think you may have met this in Professor Essler's lectures, this is an associated Legendre function and probably derived from Solution in Series by using Frobenius' method, I'm not sure. Is that right? But fundamentally, I don't think this is very helpful knowing this is an associated Legendre function, I think it's much more helpful knowing how to do it this way. The normalisation factors take care of themselves if we put in these square root animals and we start with this thing correctly normalised. How do we normalise this traditionally?  So the y l ms are correctly normalised, so if you mod square them and integrate them over the sphere, they come to one. The p l ms have a daft normalisation and that's why I don't think you should bother with p l ms.  Historically they've been defined in a bad way. The y l ms are things to go on, but the y l m is actually one of these functions of cos theta times e to the i m phi. So it has a very simple phi dependence, this animal here. So now let's just summarise what we have. So these things, y l m, theta and phi are the wave functions, essentially they're the wave functions theta phi l m. They're the wave functions belonging to states of well-defined orbital angular momentum.   So if you have an electron, here's the nucleus, if you have an electron in orbit around the nucleus, it seems reasonable to say that it's reasonable to ask what does the system look like, what does the wave function of the electron look like if the electron has well-defined orbital angular momentum? The answer is that its wave function is going to be a function of r, which we'll see, we'll tell you how much it's oscillating in radius as it goes round and round, times one of these y l m things. So these y l m things should give us, we should be able to understand them in terms of orbits at some level. So let's address ourselves to that. What can we understand about these mathematical functions y l m in terms of what we understand intuitively about how an electron should go in an orbit around its nucleus? So the place to start is not when l is large, because when l is large is when we're approaching the classical regime for which we have some grip, and the pictures at the top here, these are contour maps of the real part of y l m. So y l m is an inherently complex thing, right?  So by focusing on the real part of that complex function we've got that p l m times cos m phi. And these ones at the top are all for l equals 15, this is for m equals 15, this is for some intermediate one, m equals 7 and this is for m equals 2. So what's the physical interpretation of these? This thing, and y l m is a function on the sphere, right? It assigns a complex number to each point on the sphere. So the real part is a real number on the sphere and what's being plotted here are contours of constant value of this real number on the sphere. So you have to imagine that these are pictures of spheres. So what do we see here is that around the equator we have, so dotted contours mean negative values of the real part and full contours mean positive values of the real part. So the large values of the real part are around the equator here and that's apparent from this maths because we know that this is y l l for l equals 15 so in fact it's sine to the 15th theta e to the 15i5, right? That's what this thing here is and if sine theta is 1 on the equator and less than 1 everywhere else if you take a number that's less than 1 and raise it to the 15th power you have quite a small number. So you were expecting that the number gets small quickly as we go away from the equator. That makes exactly what we expect on physical grounds because the state l equals 15, m equals 15 means you've got 15 units of angular momentum broadly speaking and they're all of them parallel to the z axis. So this thing is an electron that's orbiting in a plane, classically, if you're orbiting in a plane the equatorial plane that was perpendicular to the z axis. So where do you expect to find the particle? Do you expect to find the particle in the equator where does the wave function peak in aptitude in the equator and nowhere else? Why is it segmented like this? Like an orange, right? We have sort of waves going around the equator here. It's big, small, big, small, big, small. That makes perfect sense because the change in the... because p, the momentum is minus i h bar d by d position, right? So if you have something with a large momentum it's to do with a large gradient or a large rate of change of the wave function. Now the amplitude of the wave function does not change one i ota as you go around the equator because this thing has amplitude which is sine to the 15th power of theta. So it's completely constant at one around the equator but the phase of this wave function is changing like crazy as you go around the equator because it's e to the 15 i phi. And that is expressing the fact, according to this, that the momentum of the particle is directed tangentially around the equator. It's rushing around the equator, it's in the equator and it's rushing around the equator. What else would you expect? That's exactly what should be the case. So let's go now to this case which is, oops, I lost it, the extreme right one, m equals 2. So we've still got sine, sorry, we've still got l equals 15 but we have m equals 2 so we've got a particle which has 15 units of angular momentum but only two of them are parallel to the z axis. So classically what this amounts to is that here's our sort of notional sphere and you think that the orbital plane classically would be tilted like this, well even more so, sort of like this-ish, very highly inclined so that the spin axis of the orbit was pointing almost in the xy plane. So what we're expecting is that the motion is mostly from the northern hemisphere down into the southern hemisphere and back up again. So we expect the contours on which the phase of the wave function changes rapidly. Oh, fiddle sticks this. So annoying. The direction in which the phase varies should be from north to south and lo and behold it is. So now instead of having an orange peel plan we have sort of rings going around almost on which the phase is. And if indeed we put m equal to zero we would have a wave function which had no variation as you went around the sphere. It would all be variation as you go from the northern hemisphere to the southern hemisphere which corresponds to the fact that the particle is moving this way. Now this particle has most of its angular momentum in the xy plane but the thing is because we know the angular momentum in the z direction and Lz does not commute with Lx we do not know how much angular momentum it has in the x direction. Most of its angular momentum is in the x and y directions but we don't know whether it's positive or negative. So that means that we cannot in this picture see an orbital plane. The probability of finding the particle is sort of large all the way down here and all the way down there and if m was zero and the angular momentum vector were exactly in the xy plane we would have absolutely no variation in probability to find the particle as we went around and around the sphere. When in fact even now we have no probability to go around and around the sphere. So what this thing is is a function of theta times e to the i to phi. So the phase is varying as we go around the sphere but in fact the amplitude is not varying as we go around the sphere. The amplitude to find the particle is constant as you go around the sphere on small circles. That is associated with the fact that we do not know we are not allowed to know it is forbidden to us to know which way this angular momentum vector is pointing. But where are we most likely to find the particle? Are we likely to find the particle most likely in a given patch on the equator or most likely to find it on the pole? Well this wave function is largest at the poles the north pole and the south pole because it is going around this particle is going around over the poles in a plane which is of unknown orientation. So there is great uncertainty there are many places where it could cross the equator but what we are sure of is it goes close to the pole. So that's why the probability there is a sort of crowding of the imagine a bunch of circles for a polar orbit going around the sphere at different orientations they all pass through the pole and there will be a great crowding of the circles near the pole and that generates the high amplitude to find the particle at the pole a relatively low amplitude to find it at the equator but not a vanishing amplitude to find the equator because it does cross the equator twice in each cycle. So this amazingly this is an intermediate case M equals 7L equals 15 this curious mess of squares in which you can see the real part is alternatively positive and negative the contours are dotted and full this represents the situation where the orbital plane in classical physics the orbital plane will be just moderately inclined at 45 degrees or 30 degrees or something to the equator and there is absolutely no orbital plane visible there and this is where we come to a key point that if you want an orbital plane to be visible and after all the orbital plane of the earth is entirely visible and the earth presumably moves according to these principles too we have to have how do we get an orbital plane to emerge the way we get an orbital plane to emerge is by quantum interference between many states that look rather like this and have a patchwork of pluses and minuses if you have several of those patchworks of pluses and minuses you can get the amplitude to cancel most places except in some inclined orbital plane so it's uncertainty in the angular momentum which will generate for you if you want it some degree of certainty in the location of the orbit going around the sphere it's the old uncertainty principle over again so those are the classical this is almost the classical regime up here and of course as the earth goes around the sun its angular momentum is 10 to the 50 hbar or something it's simply I haven't worked it out it's some staggering number so you would have to imagine 10 to the 50 patches here of pluses and minuses or maybe it's 10 to the 50 squared 10 to the 100 patches of pluses and minuses and then you can by taking a number of those maybe you take 10 to the 34 of those with 10 to the 50 patches you'll be able to arrange for exquisite the pixels to cancel everywhere except in some extremely narrow band which is the inclined orbital plane of the earth so atoms don't live in that regime up there of L equals 15 atoms live in this regime, this Tarsan regime down here this is where am I, this is L equals I've lost it, this is L equals 1 and these are the three things for L equals 2 so this is Y11 so that means you've got one unit of angular momentum and well it doesn't actually right because what does L equals 1 mean? L equals 1 means that L squared has answer 1 1 plus 1 equals 2 so the total angular momentum the square root of L squared has answer root 2 which is distinctly bigger than 1 so we've got as much angular momentum along the z axis in this 11 cases we can which means the particle definitely is going around the equator and you can see that it's going around the equator well I can't from this angle but I hope you can in the sense that the thing isn't constant the wave function has gradient as you go around the equator there's a gradient on the other hand there is not a very high probability of finding it in the this is only the real part of the wave function if we would look at the imaginary part of the wave function well how does this one, this one goes like sine theta not like sine to the 15th theta this function here is sine theta times e to the i phi so as you, in the equatorial as you go away from the equatorial plane the amplitude to find the particle falls but only falls like sine theta so it's really quite likely not to be the equatorial plane and that's associated with the fact that though we've done our best to get the angular momentum along the z axis it isn't along the z axis because it's total angular momentum is is 1.4 something times h bar and only one of those units is along the z axis so it's in some sense inevitably inclined and this is the case we have no angular momentum along the z axis so this is the case of polar orbits the amplitude to find the particle is greatest at the two poles smallest at the equator et cetera et cetera et cetera but the whole picture is less clear cut and I won't bore you by talking about these but it's worth thinking about the the n equals 2 case to see to what extent you can make sense of these physical sense of these pictures here okay so now we should address an important topic which is the parity this is practically an important topic the parity of ylm so remember the parity operator p working on a psi makes a state whose amplitude to be at x is minus is the amplitude to be at minus x if you were in the state of psi that's the definition of the parity operator and these states of well-defined angular momentum turns out have well-defined parity that's what we're about to show and what's more the parity is minus 1 to the l so states of different angular momentum have alternating parity some are even parity some are odd parity that's what we want to show okay so what we do now is so this is sort of imagined in Cartesian coordinates we need since our ys are all defined in terms of polar coordinates we need to translate the operation of going from x to minus x into spherical polar coordinates so as x, as we go from x to minus x it's easy to check that what happens is that theta goes to pi minus theta and phi goes to phi plus pi so this reflection action you need a picture really well we can just about show it I suppose I hate three dimensional pictures because it's a three dimensional picture here's theta the spherical polar coordinates theta and what you do what we have to do is take this point and move it down here and what we do is we move this point down to here that's the theta goes to so theta this theta goes to pi minus theta and then having got it down here we rotate it through out of the board and back into the board through pi and phi and that's how we get it down here so these are the changes in polar coordinates that are associated with that now ylll oh yeah well what else can we say when if so theta goes to pi minus theta what does that have to say about sin theta sin theta goes to sin pi minus theta and sin pi minus theta it's easy to check from a variety of arguments is actually equal to sin theta so sin theta doesn't change and e to the i l phi what happens if you add pi to e to the i l phi well you're adding e to the you're getting an extra factor e to the i l pi which is minus one to the l times e to the i l phi is that right ok now ylll is a constant rather a yucky constant so I won't bore you with it times sin we've proved this sin to the l theta e to the i l phi so this thing does not change sin or it doesn't change at all right so we can say now that ylll goes to this doesn't change sin and this one changes sin so it goes to minus one to the l of ylll that's under x goes to minus x so this means the parity of ylll is even if l is even an odd that's a very important result and moreover it generalizes because we have we have that ylll minus one is l minus over some square root that's really boring well it turned out to be 2l so we'll put it in times ylll and what about this what's l minus is lx minus i ly in the position representation what is this this is minus i h bar of y d by d z minus z d by d y plus minus who knows h bar it doesn't much matter the key thing is that we're going to have here a z d by d x minus x d by d z and when we change x to minus x y to minus y and z to minus z these things we get we get a change of sign here and a change of sign here a change of sign here a change of sign there so l minus and also as a matter of fact l plus is unchanged by p the strict mathematical statement is that the parity operator commutes with either of these animals indeed all the angular momentum operators commute with the parity operator basically because they contain products of position positions or if you like ratios of positions whatever they don't change so what that means is that what that means is that this is going to have the same parity as this because if you apply the parity operator to this you're pairing the parity operator to this those can swap in order this turns to minus itself the minus sign can be taken out and therefore we've shown that that leads to the conclusion that this thing has the same parity as this let me just write that argument down perhaps so we have that p l minus sorry p on y l l minus 1 is equal to p l minus upside y l l over some square root that's not interesting is equal to l minus p y l l over the square root which is equal to minus 1 to the l times p times sorry this thing produces y l l so we have l minus y l l over the square root but this is y l l minus 1 so it's equal to minus 1 to the l of y l l minus 1 so we conclude that y l l m has parity minus 1 to the l for all m this is a very important fact because it enables you to set to 0 all sorts of integrals which would otherwise be very tiresome to work out how are we doing there's one other thing so which we've unfortunately lost is it coming back? no what I wanted to do was show you the forms of the y l m the first few you need to have some sense of how they go so y nothing nothing is 1 over the square root of 4 pi y which order they put in so we want y 1 nothing is basically cos theta there happens to be some factor of root 3 over 4 pi y 1 1 is of course sin theta times some normalising factor e to the i phi y 1 minus 1 would be the same thing with a minus sign here so the point is that the y 1s go like cos theta and sin theta and the y 2s go like cos theta sin theta so y 2 nothing is equal to a normalising factor that happens to be 5 over 16 pi that's not so interesting times 3 cos theta minus 1 and y 2 1 is minus the square root of 15 over 32 pi which is not so interesting what's important is it goes like sin 2 theta which can also be written as sin theta cos theta and the other one goes like of course sin squared theta this one has e to the 2i sorry e to the i phi and this has e to the 2i phi so what do we need to remember is that obviously y 0 0 has no angular dependence so the machine has finally come back to life and the correct formula here that's what I wanted to show you the y 1s have a cos or a sin the y 2s have a width well that you can either think they have a strong width of cos 2 theta and sin 2 theta right because cos squared theta is something like a half of 1 plus cos 2 theta so there's a width of this could be a rearrange to involve cos 2 theta here we have a sin 2 theta and this sin squared has a width of cos 2 theta about it because we know that sin squared theta is a half of 1 minus cos 2 theta something like that so we have these double angle formulae and so it would go on if we were looking at y y 3 these things would have dependencies that look like cos 3 theta and sin 3 theta that's the pattern but you don't need to know about the pattern beyond here but these patterns you're expected to be able to sense so that when you're given a function of theta which is made up a linear combination of these things you need to be able to unscramble it and write it as the right linear combination of those ys right the next topic so in preparation for work on atoms we need to get an important formula for how kinetic energy can be expressed in terms of l squared and this finally obliges us to face up to the tedium of calculating what l squared is what differential operator represents l squared in the position representation so we start by observing that l squared can be written as l which way around do I want to write it plus minus I want to write it either way but I'm going to do it consistently like this well let's see what we're going to have to add to this to make l squared this is lx plus i ly lx minus i ly what's that going to come to that's going to come to lx squared plus ly squared plus well minus ilx comma ly commutator that's what this thing multiplies up to if we want to get l squared we'd better add here's a good start on l squared let's add lz squared but we need to get rid of this lx comma ly is i lz so we've got here what with this minus sign plus lz we'd better take an lz away in order to square the books so that's what this should be sorry this should be put equal to plus lz squared so what we do now is we write down l plus l minus which we have floating up there in the stratosphere so we have that l squared is equal to e to the i phi d by d theta plus i cotangent theta d by d phi that should operate on l minus which is minus I'll take the minus inside the bracket e to the minus i phi d by d phi d theta sorry this minus sign was up there outside the bracket I think plus because I've propagated the minus inside the bracket i cotangent theta d by d phi so this disgusting mess is that product and then we have to add lz squared this thing is minus lz is minus i d by d phi so with that minus sign we get a plus i d by d phi and this is going to be minus d by d phi squared so the name of the game is to differentiate out this piggy mess and find out what it simplifies to some parts of it are easy we're going to have for example the end of the day we will have terms where this is multiplying this and this is multiplying this and these two exponentials have killed each other off so we will have a term like d2 by d theta squared these i's will generate sorry there'll be a minus d2 by dc minus because one of these has got a minus sign these two will create me a minus cot squared d2 by d phi squared that's the easy part now the mess there's going to be some mess because this differential operator is going to bang into that and generate a minus i times what will kill this off so we'll have a minus i oops oh no but then it's times this so the minus i that we're getting from here will meet this and generate a plus 1 so we have cotangent theta that's this cotangent theta times this bracket so that's the result of this differential operator seeing this when this differential operator sees this bracket or we get actually sorry we get a mixed derivative term we get two terms we get one term that we've already written down and we get a term d2 by d theta d2 by d phi but that is going to be cancelled by a term that comes from here when this differential operator looks at that we'll deal with the differentiation of this in a moment so I'm not going to write down those mixed derivative terms otherwise we have dealt with the action of this on that now what about this one we've got the operation of this on this we've got the operation of this on this I've just said that that's cancelled away what we haven't got is this when that differential operator meets this we get the differential of cot is cusock squared I think so I think what we have is plus i cusock squared theta d by d phi now the sign should be checked at this point because because signs are a pain right I think it must be that the derivative is minus cusock squared both can be taken afterwards right so that's the derivative of this on this and then I claim that these brackets are dealt with and all we have to do is write down the training terms here which is a plus i d by d phi and a minus d by d phi squared now we need to consolidate our various terms we have three terms one two three which are just d by d phi terms and God be praised they all add up to nothing because we have a trig identity which is cot squared minus cusock squared is minus one so we have the cot squared theta minus cusock squared theta is minus one and here's our cot squared there's our cusock squared and I'm missing and this should have had an uh I I I I I we have an I problem right these have to be all no no no I'm not trying to mess with that one I'm not trying to mess with that right I'm going to have a cot squared here with an associated attendant I I've got a cusock squared with an I and I have here a one so let us buy that causes those all to add up to nothing then I also can use this identity to consolidate this double derivative and this double derivative so we have a cot squared and a one and I can trade it in for a cusock squared according to that formula there right so we end up with minus d2 by d theta squared um it's going to be cot squared minus cot squared so it's going to be um we've got a cot squared and a thing they both carry minus signs which means I have to have them on the other side so we get a minus cusock squared according to this I'm slightly worried by this uh so I'm going to end up with a cusock squared d2 by d5 squared and I strongly suspect that sign is wrong but that's what I've honestly got uh so that's this dealt with and the only this is so this has been dealt with this has been dealt with this has been dealt with I think we're all we're all tickity boo we're not are we uh what have I lost to believe this is the easiest way to do it it's hard to believe isn't it but it is it is um this one right so so that remains cot theta db theta thank you so we now consolidate this all being well into 1 over minus 1 over sin theta sin theta d by d theta and this should be I think a minus that sign is wrong a 1 over sin squared theta this has usually written d2 by d5 squared so I've screwed up on the sign there somehow um so when you when you differentiate this we get a cos which cos of a sin is cot so that's this term here we have the double derivative sin et cetera et cetera et cetera and what is this this is r squared times the angular part of del squared not on that note it's time to to leave we're not quite finished with the calculation but that's the important bottom line that l squared is is actually with a minus sign a minus r squared times the angular part of del squared and we'll push that forward into the kinetic energy tomorrow no on Wednesday


Cam Newton who is best known as the star quarterback for the New England Patriots and the current replacement of the GOAT Tom Brady has snagged some pretty luxurious real estate in Beverly Hills and Charlotte. The former includes a lavish party house which Newton was recently accused of damaging. Now Cam Newton has recently put his lux $2.9 million lux condo up for sale in Charlotte but claims he hasn't moved family to Massachusetts just yet. After signing a one-year deal, the star claims that this tenure with the Patriots as a business trip. Wow, look at Cam Go being all business. We'll take a look at Cam Newton's former homes in California in North Carolina, 3,300 square feet of luxury living space. It takes up half of the fifth floor of a building and comes complete with his very own full size Pepsi machine. In these videos we don't reveal any addresses so please do not show up at any private residences because it is not safe for anyone. Cam Newton has enjoyed a very lucrative and successful career in the NFL which has led the star to a $75 million net worth. Through the 2014 season he earned $5.5 million per year thanks to his four-year $22 million contract. In 2015 he signed a five-year contract extension worth $103 million. In his first nine years in the NFL he earned $121 million in base salary alone. Not only was Cam Newton making bank with his salary, he has earned tens of millions off the field from endorsements with companies like Gatorade, Under Armour, Danin, and Beats by Dre. In 2013, Belk Department Stores began selling Newton's line of men's apparel made by Cam Newton and he opened the Fellowship Restaurant Cigar Bar in Atlanta in 2019. Cam has a massive family, including seven children while his ex-girlfriend Kia Proctor is the mother of six of them. He also bears a son that he had with Instagram model Lorena Shaw. So it likely came as no surprise that while Cam was shopping he was looking for digs with tons of square feet. In 2012, Newton paid $1.5 million for a 3,300-square-foot condo and an exclusive Charlotte building called The Trust. He listed the three-bedroom home for $3.2 million in May 2019 and took it off the market a few months later and then re-listed it for $3 million in July 2020. Newton is in pretty elite company as NBA icon Michael Jordan also lives in the building, occupying an entire floor. Here's what's up guys, it's your boy Marlon Palmer and today we're bringing you another house tour here for you on Famous Entertainment and notice 95% of you guys watching are not subscribed so please hit that subscribe button because we post new videos daily. Now we've previously reported on the homes of Birdman and Kylie Jenner so if you'd like to please check those videos out on our channel. If you like these videos please ring that bell for notifications, follow me on Instagram at ThatDooMcFly so we can chat some more and let us know whose house tour is next in the comments down below. Let's get into the video. During Cam's early days with the Carolina Panthers he picked up a sleek spread in Beverly Hills which he paid $123,000 to rent for two months. During Newton's two month stay he racked up over $100,000 in damage. As a result Jared Pover and former professional wrestler Stacy Kebler sued Newton for $270,000 including $180,000 in lost rent while repairs were being made. The modern five-bedroom house eventually went up for sale for a whopping $18.25 million. This dig sits in prime real estate as the gated one-story home sits on half an acre in the Truesdale area. The interior features floor-to-ceiling windows across the living spaces and provide breathtaking views of the city. And if that's not charming enough the interior also flows outside via pivoting walls of glass. The glamorous interior also comes complete with flourishing Calcutta marble walls and white terrazzo floors which give the home a very modern aesthetic. Guests of the family or in this case party can get cozy while a dual-sided see-through fireplace connects to the living room to the dining area.  The master suite also comes complete with a fireplace and dual bathrooms with heated marble floors. Cam Shor loves his fireplaces, oh the glamour. Probably the coolest feature and the best spot of the party was in the backyard that features a small yard and terraces surrounding an infinity pool. This spot features luxurious dining, enchanting views of Beverly Hills and most important, access to the outdoor bar. How about spending a weekend partying in that little house? After looking at the infinity pool I can see why he raged pretty hard. While we know Cam likes to play hard, he also works hard, his numbers don't lie. Shortly after Cam was cut loose in North Carolina, former Panther's quarterback had listed his lux condo in Charlotte, North Carolina for $2.9 million. The three-bedroom, three-and-a-half bathroom features a spacious 3,300 square feet of luxury living space. It takes up half the floor of a building known as The Trust which listing details call the most exclusive address in Uptown, Charlotte. Newton initially snagged this condo through an LLC in April 2012 for $1.6 million. Fun little fact that there are seven units in this building and his neighbor happens to be Michael Jordan. Ever heard of that guy? Oh yeah, you probably have. The condo is absolutely stunning as gleaming hardwood floors cover most of the interior, and exposed ductwork and concrete ceilings give the unit a loft-like vibe. The charming dining room comes complete with an abundance of unique antiques and delightful house plants while features easy access to the kitchen and living area through a sliding glass door. The living area is a treat to get cozy in as it features bright furnishings and an abundance of windows that give off a very airy and roomy ambience. The cute views, massive furnishings, and fireplace deliver a relaxed spot for Cam and his family to unwind.  I mean, why wouldn't you indulge after the big game? The master bedroom comes complete with a large walk-in closet, which is ideal for the star QB as he is known for having quite the closed horse. For those pre-game meals, the spacious kitchen comes complete with all the high-end features and abundance of stainless steel appliances, including a large island and an enormous amount of cabinet space. I mean, when you have seven kids, you probably want to go all out on your cabinet space. Let's be real here. A few more luxurious upscale customizations include a question home automation system, high-end fixtures in the guest bathrooms, and top-of-the-line light fixtures. Probably the coolest feature of the house is the full-size Pepsi machine, which includes an autograph and picture of Newton celebrating after a touchdown and labeled Rookie of the Year 2011. I mean, it's probably easier just to grab a Pepsi from the fridge, but it's just something about getting it from a machine with your face on it that says, I made it. You know, my only question is, does he have to pay to get the Pepsi from his own vending machine? I don't know. While Kevin has kept most of this information of his recent home in Boston private, he made the trip solar and calls it a business trip as he hasn't had any time to explore. Newton said he'd like to have some of his children with him, but the coronavirus pandemic makes it kind of hard and wakes up every morning missing the hell out of his family. All right, so I think we'll bring this house toward to an end here. We got to take a quick look at Cam Newton's home and that luxurious condo in Charlotte, North Carolina with his own Pepsi machine.  After seeing his house, what did you guys think? Was it everything you would expect out of Newton? Personally, I thought the first house was like just a better spot to party that infinity pool definitely did it for me out of Newton's new features. Which were your fave? You guys can go ahead and rate them in the comments down below. Follow me on Instagram at daddoomandfly so we can chat some more. And let us know whose house tour you want to see next in the comments down below. I'll see you guys next time.


Are you between 14 and 18 years old? You like comics and you like to draw? The Seeds in Space competition is for you. The IAEA and the FAO have sent seeds into space to create new varieties of plants that are resistant to climate change. Choose one or more stages of this fascinating project and create a comic panel illustrating the stage you've chosen or a comic strip if you want to illustrate a few steps and send your drawings before 16th April 2023. The winner drawing will be used to inspire a Seed in Space comic book. Also, all nominees will receive a gift. You want to know more? Click on the link. Good luck!


yeah right the next school board meeting is the 15th right next Tuesday um well but but what sevan is talking about are the committee meetings that happen so yeah so like the one related to like the macy's building when would that be there'll be some information about well that that will be discussed most likely we haven't seen the agenda for for next Tuesday that will that will be next week perhaps you know i think the i think the final agreement is going to be signed next week because we're expecting the air quality report friday or monday so the the meeting is tuesday so my guess is that that will be that will be finalized on tuesday and there's always there's always at the very beginning of the meeting the public comment you know you can make any kind of comment you want about any issue involving burlington schools and that's true again with the committee meetings that happen regularly throughout the week like the next de and i is next week isn't it the 22nd and the and the curriculum committee meets the day after the regular um monthly regular monthly board meeting so it's gonna be on the 14th yeah i mean 16th so yeah and and kevin you can make a comment in public comment about anything at any of those meetings cool sounds good does anybody on the school board feel as uncomfortable as a lot of people do about giving don synex nearly 10 million dollars yes really i'm the one with that said you know jimmy is about to evaporate they're moving to pretty much all online i know a lot of patrick they looked into dealer it didn't work out that was that was one of multiple places down in the south end and also i do have to say of course that's a concern but there are two other who are 50 with don who are local so i don't know if you know it's not just don and whoever that was that entity before it's work field two other yeah there were three three other owners with with synex synex owns 50 that's the that's the problem and it was a long and involved negotiations that went on it was not always pleasant i we understand right but anyway synex does not own more than 50 at this point they own effectively 75 percent no that's that's that is in the past there are two there are other people that but their shares are so much smaller no it is oh they own 50 and he owns 50 percent there are three local owners who own 50 percent and synex is the other 50 they own 50 percent of don synex's prior they of of of brookfield's share and synex owned the other part so you add it together they own 50 percent of a share so the math is not actually 50 50 but it's okay we it's a we wait i don't know this this is not something i do i do not know this what are you talking about i don't know i don't even know i've i have lost track of what is part of executive and what is part of known to the public so if i've spoken out of turn accident that is no no that would be whether that is your executive or my executive that is not privy so how do we find how do we get to the bottom of this um i can clear who are there other people aren't max and max and brian have left are they that they can't help me clarify um i will text both of them right now i'm sorry and if i've misunderstood that i'm sorry because as we know with this project there are like constant moving parts and it's hard to you know like kind of um on top of everything that's shifting so quickly but that was kind of my understanding is it was kind of a bit more complicated than like a 50 50 split so well just i will ask i will i it's been presented to us that don is 50 and these vermonters local are 50 so um previously san x was 49 previously san x was 49 and brookfield was 51 i have a question um a little off topic um um steven and jean is building a new high school still on the table the final design for the for the site is still in discussion because the because the uh the readings haven't come back yet we still don't is that that's right janey right it's still up in the air i mean we're going forth with the cost estimates so we have a better idea of what the final decisions will be in terms of re either restructuring or building a new high school whatever i don't think that i don't think we're actually going to be building a new high school but you know the plan to save what's what's worth it saving is still in the works and uh until we know more about about the final soil testing and the cost estimates that are coming in next we won't we won't be able to answer that question and barbara when you say build a new high school that can mean something very different oh yeah one person to the other when somebody says build a new high school sometimes they don't mean actually build it in the spot in the spot where it is right now or it means completely tear down that building and build something new so when you say that what do you mean build it in you know i out of but i say level it build build a state of the art in the same in this in the same location no downtime i would think i would think so i i you know i that i don't know because i don't know what's available what i'm saying is like everybody has a when they ask these questions they have a very i like when i hear that question i have to say give me a clarification of what that actually looks in my mind it's starting from leveling it and starting from scratch that's that's how i think about it i just want to say practically speaking as much as can be salvaged is probably the most financially advantageous but at this point we don't know we could actually work with if we even wanted to work with it so there's that so your idea of getting a shiny new high school might come true out of default we have no idea okay it takes months for the i think that would take we have to actually be animated 70 million is still budgeted for that i think a brand new high school from scratch would take more of the money would take another bond issue but and i know people in the city who would support that but right now we're just trying to figure out what to do with the high school that's there how it's going to be restructured or is it possible to do it even there so we're trying to figure that out right now but in the meantime i'm excited about the kids getting back into the high school the downtown high school because i think there are lots of creative possibilities for pursuing intellectual studies in the heart of the city and you know the whole movement toward place-based learning we have kind of an advantage of being down there so that the high school kids will be there will be at the downtown high school for the next year for sure and uh we will have a fully functioning school in that in that location with all the potential around it just think of the proximity to the theaters down by the lake the lake itself the bike path you know there's so there's so much possibility the church street i think anyway i'm an optimist and i feel optimistic about this decision that had to be made and i think it was i think we're we're at that spot now and i'm i'm kind of happy that we're moving forward in that direction anyway even though we're still waiting until the end of february that means the high school kids have not been in a regular classroom for almost a year in burlington and of course around the state it's the same things going on like genie pointed out earlier it's still a hybrid model we're talking about until we we know what's going to happen with coven it's just a hybrid model but at least they'll be where they need to be and you've read the reports about the damage to educational progress because of this all around the nation so you know our burlington kids are are in a tougher position because of the pcb's have discovered at the site of the high school it's really unfortunate uh but people are dealing with it you know and in heroic ways i think especially those kids who won those presidential scholar's awards they were just unbelievable those kids that when they would you know their their work ethic and their um their drive to be successful and their creative energies they put into their projects it's just unbelievable it's rewarding in that way anyway anyway thank you or any more questions so i don't want to make this meeting go any longer than needs to but all the other buildings you guys have explored this was the only one that had possibility uh building for the old ymca yes you guys are brilliant i know no keep going yeah uh the memorial auditorium yeah how about how about how about exploring eminent domain the mall and the mall in south burlington yeah mall in south burlington jeez there's a the hannah fritz on sylvan road just yeah eminent domain that hole just put the building right there uh yeah good job i wouldn't want it to have to be on the school board right now but thank you thanks for holding it okay is everybody tired enough yet okay that was the best thing ever that we need to leave on that okay amanda what did you say my friend amanda put something in the chat let's see what it is i'll make an appearance i was watching on youtube um but then i couldn't see the chat and so i i was cooking latkes sweet potato latkes are the first time ever it's a mess um but they came out well so um so it was it was on the background it was in the background when jimmy and amanda will you save some for me we have we we um grated a lot of sweet potatoes so we have extras so yeah we're gonna make some tomorrow too okay great so anyway this is the first night of kanaka happy kanaka to those who celebrate mary christmas because we won't see you until january 14 well it's very nice seeing all of you and i miss you so i miss you amanda and i didn't actually know it was on tonight and i was looking up something and i i saw it was live so i just spontaneously turned it on and it was it was a lovely evening you guys so it's the second thursday it's gotta be war two three i don't even know what day it is anymore more days i mean i'm not the only okay good night everybody and thanks again for sticking it out thank you take care


One of the things that I noticed in Bosnia that I was really struck by is people didn't stop caring about the things that people care about every day. So I made friends with this one young woman. She was a Bosnian and she worked on our staff as a translator or something. And she was a soulful person and we became friends and she had great, great sadness in her. But it really wasn't anything to do with the political or military situation that was raging on around us all the time. It was about her profound sense of loneliness that she'd never really felt deeply mirrored in a relationship and she longed for that. And that's where her energies were. That's where her heart was. And I remember being struck by that. It's like we don't stop being human in the midst of these calamities. Of course, as one might expect, I'm spending a lot of time in my practice speaking with people about the disruption in their lives currently. But after a few minutes of talking about how they're managing with this or that, people are still worried about their families. They're worried about their relationships. They want to find love. They want to be understood. They want to find joy. That is all happening just in this different context. But the context doesn't erase those kind of basic human things. I mean, of course, it impacts them. I'm finding that people are facing unique challenges, for example, in their relationships because of the disruption. Or they're facing unique challenges in terms of how they relate to their career plans because of the disruption. But those basic things that we all need, they haven't changed. I would say that I have a similar experience, Lisa, that maybe in the first 5 or 10 minutes, people are doing an update about what they're circling around on the news or some adjustments they had to make. But when we go right to the dream work, I have yet to have a single dream about the coronavirus show up in the practice. People are dreaming about family relationships. They're dreaming about their complexes. Or they're dreaming about this tension of values between two different parts of their psyches. Or they're dreaming about love and longing. And that the full spectrum of the concerns of the soul seem to continue to circle forward despite the outer seeming of things. So the image that comes up for me as I hear you two talk, and I could say my experience in my practice is the same, is of the ocean. And that even when the surface is storm-ridden, choppy, and churning, if you go down 100 feet or 200 feet or however far, there is a deeper layer that remains steady on. That the deeper layers of the psyche are still there and that we access them in our work with individuals. And there's something very deeply reassuring about that and about how the two of you are expressing it, is our depths are still there. They are still speaking to us and they are still concerned with the things that are very deeply human and deeply individual. I absolutely love that image Deb. I think that's perfect that the surface of the ocean can be churning and even churning dangerously. Ships can get capsized and people can get hurt. But if we go deep enough down in the ocean, there's little perhaps changing or even going on and life moves forward as usual in these mysterious places. Jung addressed this tension between what's happening on the surface and what's happening on the deep in the red book. And he introduces the idea of this voice of the spirit of the times versus the voice of the deep or the depths. And as he is negotiating these two values inside of himself, he feels this enormous tension about what is he going to align with. And I think what he comes to is that he needs to be able to hold both. That there is a voice that comes from the top of the ocean and the sailors that are crying out in the tumult of the storm. And at the same time, there's a spirit that comes from the bottom of the ocean that says all is well and all is held and all is sustained. And part of the human experience is to be able to hold both as a way of being fully human. I'm just thinking of this quote from Jung that I think kind of backs up what we're all saying, where he talks about working with people who are dying and watching their dreams. And he concludes that the self, the deep part of the psyche is profoundly uninterested in death, that it sort of is a little bit of a non-event. And again, there's this sense that what's going on in the surface may seem quite tumultuous, but at a deeper level, things are just unfolding as they need to. Well, I think coming back to the idea of the lightning struck tower in Taraki 16, there are many ways of interpreting that. I mean, in this image, if some are familiar, there's a tower on top of a mountain and perhaps it has one or two windows and there's a golden crown at the top. Often there's a lightning bolt that's struck it and you'll see a male and female figure that are falling through the air or ostensibly down into a fertile field. One of the ideas about the top of the tower being exploded off of the structure is the idea that certain events both internal and external depose the power of the ego and its ability to isolate itself from life through constructs of thought and perception and fantasies of limitless power. That events, such as we're experiencing right now, cause the ego to have to feel small and vulnerable and cast out of its certainties. And that's an opportunity for transformation for many of us and a transformation that we might not choose and given the opportunity in an easy way, but it's a transformation that we can find ourselves thrust into perhaps with a willingness to embrace it.


Documentum continues to build around efforts to assist agriculture stickholder communities in implementing strategies to improve livelihoods to enhance climate smart agriculture practices. The focus this time was on the adoption of soil and plant health management systems on smallholder producer farms through farmer-focused community-based education and training, hosted by the Inter-American Institute for Cooperation on Agriculture IECA, and in collaboration with the Canaries Community Improvement Foundation, the CCIF. The training exercise brought together 25 participants for hands-on sessions exploring the basic principles of soil health examination and planting. This project, as I said before, is one that is of great importance. Not only does it seek to improve and build the capacity of the community to address a problem that the community may face in terms of the slippage and loss of soil and its impact on the marine environment, but it also provides an empowerment of community members in green businesses in seeking to use the vertebrae as a green business, establishing opportunities for using it in various different ways that the vertebrae offers so that the community can also achieve some level of income from the vertebrae, not just to address the environmental concern but also the economic and the sustainable livelihoods concern. Done as part of the ecosystem-based adaptation project, which is managed by the Caribbean Biodiversity Fund, IECA has been keen on engaging communities in establishing vertebrae nurseries as a means of bioengineering and for addressing the degradation of slopes around the village of Canaries. The partnership with the Canaries Community Improvement Foundation has been ongoing for the last year and a half. Some people in this crowd will be able to get something out of this workshop and have a fulfilling life by creating their own green business, be it agriculture or the craft work. The Inter-American Institute for Cooperation and Agriculture promises to closely monitor the progress of this project in Canaries and looks forward to providing the required technical expertise to community members who desire to take on the initiative seriously to advance their individual attributes to livelihoods. From the Information Unit of the Ministry of Agriculture, I am Amanda Fee-Clock, reporting.


Welcome back. Now this one is quite like the David and Gulath favour. On one side was Facebook, a company whose market cap is greater than the GDPs of 144 countries, allied with a bunch of big telcos and together they were offering free internet to a billion Indians who could not afford it otherwise. But then it came with a cap yard. Facebook would decide which websites could be accessed on this platform. They even had a massive ad campaign that estimates put at 400 crore rupees. On the other side of course there was a motley group of internet activists, there were entrepreneurs involved in it as well and very often individual voices. Early last week telecom regulator TRAI ruled that no company is going to offer or charge discriminatory tariffs for data on the basis of content.  So what went wrong for Facebook over here? Can the brand really recover from this debacle? We ask the experts in this story. Once the poster boy of a new, free and fearless world of social media, Facebook has been facing flak in India over the past year over its free basics platform. Formerly known as internet.org, the platform would provide free but restricted internet access to almost a billion Indians with the help of a few telecom giants. This later became the centre of a heated battle over net neutrality with internet activists, politicians and the general public all in the fray. But early last week telecom regulator TRAI ruled against differential pricing by telecom companies, effectively putting the brakes on zero rating platforms like free basics. Packets on internet, the pipes should not sort of decide, pipes should be agnostic to the packets. The move has been generally welcomed, especially for internet based services, which could have faced a great struggle for existence otherwise. I think we are one of the leading app players over here in this market with 100 million plus users. And the very reason that I am sitting here and talking to you, and the very reason where 100 million plus users are utilising true colour, is because of one single genesis called net neutrality. So we assume that net neutrality in whatever Abda, it has to be free, it has to be equal and the right of usage and the right to utilise internet should lie in the hands of the users. And I think better sense has prevailed and we are really thankful to TRAI to have taken a very robust stand on this subject, giving equal opportunity to all sets of parties involved in this discussion or the debate and coming to a very good conclusion. Facebook subsequently had to shut down free basics in India, but with 130 million Facebook users, 375 million people online and additionally almost a billion who aren't, India is the biggest growth market for the social network which remains blocked in China. So how badly could this debacle hurt the brand's image in this key market? Well obviously Facebook has put so much effort behind free basics in India. I mean and this is the second time you know the internet or was the first one and now this I think clearly there's for them this takes it's a knock because it was such a public campaign and there was so much investment from you know Zuckaberg downward that obviously there is loss of face involved there is there is a sense of having tried really hard and very visibly having failed. So to that extent Facebook as a brand will today be a little less confident and a little more vulnerable than it was in the past. I think it it's a really strongly entrenched brand it has a relationship it has a very kind of a significant relationship with its Indian users. So I don't think it's in any imminent danger of any kind beyond the fact that it now is a little more vulnerable to its public face I think has become is face's challenges I think today more than it has in the past. What stands out in the debate over net neutrality is the fact that Facebook was being opposed by a motley crew of individuals who took to social media and even Facebook itself to protest against free basics. Facebook in turn launched a massive 360 degree campaign across media one that cost it almost 400 crores. But the move seems to have backfired. So where did Facebook go wrong? Even the digital brands which you know come from a different world which is more democratic where you know the brute you would imagine that you know the brute force of money is not employed but the instinct of large corporations is that when pushed when in doubt you know you eventually throw big advertising at the problem and which is what Facebook did that they threw big money and conventional advertising at a problem that you know whereas they are they are the preeminent digital player in India and in spite of that when it came to the crunch like any other large corporation they threw money at the problem in this case it did. But given that India is a country that has been struggling with connectivity for well over a decade now some feel that the vehement opposition to Facebook free basics was premature and an overreaction while others believe that a wait and watch approach could have cost India dearly. It's quite possible that Facebook would spend a lot of money on free basics and get not much.  We have no evidence for that. I've heard that I've heard it said that well you know what's wrong let's try we could have tried it for one year or five years my point is you're sure you know it's poison we could have tried it for one year or five years then we could have figured out how many died and it's a dead few died or did a lot died then we decided that they should keep it going I mean we know clearly it's poison every experience of the free basics experience around the world has been shown to that it is poisonous and you know the poor 36 countries that are around the world I hope they now change the mind taking the lead from India in terms of banning free basics Egypt has already done so I hope the others follow suit soon that's the first part. The second part that's brought up is you know what it's all the people with internet who have now determined that the poor should not get free internet that's also nonsense it's ridiculous this move is not an anti-poor move it's an you know unless you call Zuckerberg poor and Sunil Bhatti middle poor it's not anti-poor it's basically anti-colonial it's stopping the colonization moves that Ayrton and Zuckerberg were trying it's saying go back with your own legitimate business we're perfectly cool with what you are.


CHAPTER 100. DOWN IN SUFFIC. It need hardly be said that Paul Montague was not long in adjusting his affairs with Heta after the visit which he received from Roger Carberry. Early on the following morning he was once more in Wellbeck Street, taking the brooch with him, and though at first Lady Carberry kept up her opposition, she did it after so weak a fashionist to throw, in fact, very little difficulty in his way. Heta understood perfectly that she was in this matter stronger than her mother, and that she need fear nothing now that Roger Carberry was on her side. I don't know what you mean to live on, Lady Carberry said, threatening future evils in a plaintive tone. Heta repeated, though in other language, the assurance which the young lady made who declared that if her future husband would consent to live on potatoes, she would be quite satisfied with the potato peelings, while Paul made some vague allusion to the satisfactory nature of his final arrangements with the House of Fisker, Montague, and I don't see anything like an income, said Lady Carberry, but I suppose Roger will make it right. He takes everything upon himself, now it seems, but this was before the halcyon day of Mr. Brown's second offer. It was at any rate decided that they were to be married, and the time fixed for the marriage was to be the following spring. When this was finally arranged, Roger Carberry, who had returned to his own home, conceived the idea that it would be well that Heta should pass the autumn, and if possible the winter also, down in Suffolk, so that she might get used to him in the capacity which he now aspired to fill. And with that object he induced Mrs. Yeld, the Bishop's wife, to invite her down to the palace. Heta accepted the invitation and left London before she could hear the tidings of her mother's engagement with Mr. Brown. Roger Carberry had not yielded in this matter, had not brought himself to determine that he would recognize Paul and Heta as acknowledged lovers, without a fierce inward contest. Two convictions had been strong in his mind, both of which were opposed to this recognition. The first telling him that he would be a fitter husband for the girls in Paul Montague, and the second assuring him that Paul had ill-treated him in such a fashion that forgiveness would be both foolish and unmanly. For Roger, though he was a religious man, and one anxious to conform to the spirit of Christianity, would not allow himself to think that an injury should be forgiven unless the man who did the injury repented of his own injustice. As to giving his coat to the thief who had taken his cloak, he told himself that were he and others to be guided by that precept, honest industry would go naked in order that vice and idleness might be comfortably clothed. If anyone stole his cloak he would certainly put that man in prison as soon as possible, and not commence his lenience till the thief should at any rate effect to be sorry for his fault. Now to his thinking Paul Montague had stolen his cloak, and were he Roger to give way in this matter of his love he would be giving Paul his coat also. No. He was bound after some fashion to have Paul put into prison to bring in before a jury and to get a verdict against him so that some sentence of punishment might be at least pronounced. How then could he yield? And Paul Montague had shown himself to be very weak in regard to women. It might be, no doubt it was true, that Mrs. Hurdle's appearance in England had been distressing to him. But still he had gone down with her to Lohstoft as her lover, and to Roger's thinking a man who could do that was quite unfit to be the husband of Hedda Carberry. He himself tell no tales against Montague on that head. Even when pressed to do so he had told no tale. But not the less was his conviction strong that had ought to know the truth and to be induced by that knowledge to reject her younger lover. But then over these convictions there came a third, equally strong, which told him that the girl loved the younger man and did not love him, and that if he loved the girl it was his duty as a man to prove his love by doing what he could to make her happy. As he walked up and down the walk by the moat with his hands clasped behind his back, stopping every now and again to sit on the terrace wall, walking there mile after mile with his mind intent on the one idea, he schools himself to feel that that and that only could be his duty. What did love mean if not that? What could be the devotion which men so often affect to feel if it did not tend to self sacrifice on behalf of the beloved one? A man would incur any danger for a woman, would subject himself to any toil, would even die for her. But if this were done simply with the object of winning her, where was that real love of which sacrifice of self on behalf of another is the truest proof? So by degrees he resolved that the thing must be done. The man, though he had been bad to his friend, was not all bad. He was one who might become good hands. He, Roger, was too firm of purpose and too honest of heart to boy himself up into new hopes by assurances of the man's unfitness. What right had he to think that he could judge of that better than the girl herself? And so, when many, many miles had been walked, he succeeded in conquering his own heart, though in conquering it he crushed it, and in bringing himself to the resolve that the energies of his life should be devoted to the task of making Mrs. Paul Montague a happy woman. We have seen how he acted up to this resolve when last in London, withdrawing at any rate all signs of anger from Paul Montague and behaving with the utmost tenderness to Heta. When he had accomplished that task of conquering his own heart and of assuring himself thoroughly that Heta was to become his rival's wife, he was, I think, more at ease and less troubled in his spirit than he had been during these months in which there had still been doubt. The sort of happiness which he had once pictured to himself could certainly never be his, that he would never marry he was quite sure. Indeed he was prepared to settle Carberry on Heta's eldest boy on condition that such boy should take the old name. He would never have a child whom he could in truth call his own, but if he could induce these people to live at Carberry or to live there for at least a part of the year so that there would be some life in the place he thought that he could awaken himself again and again take an interest in the property. But as a first step to this he must learn to regard himself as an old man, as one who had let life pass by too far for the purposes of his own home and who must therefore devote himself to make happy the homes of others. So thinking of himself and so resolving he had told much of his story to his friend the bishop and as a consequence of those revelations Mrs. Yeld had invited Heta down to the palace. Roger felt that he had still much to say to his cousin before her marriage which could be said in the country much better than in town and he wished to teach her to regard Suffolk as the county to which she should be attached and in which she was to find her home. The day before she came he was over at the palace with the pretense of asking permission to come and see his cousin soon after her arrival. The truth was the idea of talking about Heta to the only friend to whom he had looked for sympathy in his trouble. As to settling your property on her or her children said the bishop, it is quite out of the question. Your lawyer would not allow you to do it. Where would you be if after all you were to marry? I shall never marry. Very likely not, but yet you may. How is a man of your age to speak with certainty of what he will do or what he will not do in that respect? You can make your will doing as you please with your property and the will when made can be revoked. I think you hardly understand just what I feel said Roger and I know very well that I am unable to explain it but I wish to act exactly as I would do if she were my daughter and as if her son, if she had a son, would be my natural heir. But if she were your daughter her son wouldn't be your natural heir as long as there was a probability or even a chance that you might have a son of your own.  If it does properly belong to you it must be better with you than elsewhere. I think very highly of your cousin and I have no reason to think otherwise than well of the gentleman whom she intends to marry. But it is only human nature to suppose that the fact that your property is still at your own disposal should have some effect in producing the more complete observance of your wishes. I did not believe it in the least, my lord, said Roger, somewhat angrily. That is because you are so carried away by enthusiasm at the present moment as to ignore the ordinary rules of life. There are not perhaps many fathers who have regans and gonerals for their daughters but there are very many who may take a lesson from the folly of the old king.  The world, I take it, thinks that the fool was right. The bishop did so far succeed that Roger abandoned the idea of settling his property on Paul Montague's children, but he was not on that account the less resolute in his determination to make himself and his own interests subordinate to those of his cousin. When he came over two days afterwards to see her, he found her in the garden and walked there with her for a couple of hours. Troubles are over now, he said, smiling. You mean about Felix, said Heta and Mama? No, indeed. As to Felix, I think that Lady Carberry has done the best thing in her power. No doubt she has been advised by Mr. Brown and Mr. Brown seems to be a prudent man. And about your mother herself, I hope that she may now be comfortable but I was not alluding to Felix and your mother. I was thinking of you and of myself. But you will never have any troubles. I have had troubles. I mean to speak very freely to you now, dear. I was nearly upset what I suppose people call brokenhearted when I was assured that you certainly would never become my wife. I ought not to have allowed myself to get into such a frame of mind. I should have known that I was too old to have a chance. Oh, Roger, it was not that. Well, that and other things. I should have known it sooner and stronger. I should have been more manly and stronger. After all, though love is a wonderful incident in a man's life, it is not that only that he is here for. I have duties plainly marked out for me and as I should never allow myself to be withdrawn from them by pleasure, so neither should I by sorrow. But it is done now. I have conquered my regrets and I can say with safety that I look forward to your presence in Paul's presence at Carberry I will make him welcome as though he were my brother and you as though you were my daughter. All I ask of you is that you will not be cherry of your presence there. She only answered him by a close pressure on his arm. That is what I wanted to say to you. You will teach yourself to regard me as your best and closest friend as he on whom you have the strongest right to depend of all, except your husband. There is no teaching necessary for that, she said. As a daughter leans on a father I would have you lean on me, Hedda. You will soon come to find that I am very old. I grow old quickly and already feel myself to be removed from everything that is young and foolish. You never were foolish, nor young either, I sometimes think, but now you must promise me this. You will do all that you can to induce him to make Carberry his residence. We have no plans as yet at all, Roger. Then it will be certainly so much easier for you to fall into my plan. Of course she will be married at Carberry. What will Mama say? She will come here and I am sure will enjoy it. That, I regard, is settled. Then, after that, let this be your home so that you should learn really to care about and to love the place. It will be your home, really, you know, some of these days. You will have to be squire of Carberry yourself when I am gone till you have a son old enough to fill that exalted position. With all his love to her and his good will to them both he could not bring himself to say that Paul Montague should be squire of Carberry. Oh, Roger, please do not talk like that. But it is necessary, my dear, I want you to know what my wishes are and if it be possible I would learn what are yours. My mind is quite made up as to my future life. Of course I do not wish to dictate to you and if I did I could not dictate to Mr. Montague. Pray, pray do not call him, Mr. Montague. Well, I will not, to Paul then. There goes the last of my anger. He threw his hands up as though he were scattering his indignation to the air. I would not dictate either to you or to him but it is right that you should know that I hold my property as steward for those who are to come after me and that the satisfaction of my stewardship will be infinitely increased if I find that those for whom I act share the interest which I shall take in the matter. It is the only payment which you and he can make me for my trouble. But Felix, Roger, his brow became a little black as he answered her. To assist her, he said very solemnly, I will not say a word against her brother but on that subject I claim a right to come to a decision on my own judgment. It is a matter in which I have thought much and I may say suffered much. I have ideas, old-fashioned ideas, on the matter which I need not pause to explain to you now. If we are as much together as I hope we shall be, you will no doubt come to understand them. The disposition of a family property, even though it be one so small as mine, is to my thinking a matter which a man should not make in accordance with his own capricious or even with his own affections. He owes a duty to those who live on his land and he owes a duty to his country. And though it may seem fantastic to say so, I think he owes a duty to those who have been before him and who have manifestly wished that the property should be continued in the hands of their descendants. These things are to me very holy. In what I am doing I am in some respects departing from the theory of my life. But I do so under a perfect conviction that by the course I am taking I shall best perform the duties to which I have alluded. I do not think, Heta, that we need say any more about that. He had spoken so seriously that though she did not quite understand all that he had said, she did not venture to dispute his will any further. He did not endeavor to exact from her any promise, but having explained his purposes, kissed her as he would have kissed a daughter and then left her and rode home without going into the house. Soon after that Paul Montague came down to Carberry and the same thing was said to him though in a much less solemn manner. Paul was received quite in the old way, having declared that he would throw all anger behind him and that Paul should be again Paul, he rigidly kept his promise, whatever might be the cost to his own feelings. As to his love for Heta and his old hopes and the disappointment which had so nearly unmanned him, he said not another word to his fortunate rival. Montague knew it all, but there was now no necessity that any allusion should be made to pass misfortunes. Roger indeed made a solemn resolution that to Paul he would never again speak of Heta as the girl whom he himself had loved, though he looked forward to a time, probably many years hence, when he might perhaps remind her of his fidelity. But he spoke much of the land and of the tenants and the laborers of his own farm, of the amount of the income and of the necessity of so living that the income might always be more than sufficient for the wants of the household. When the spring came round, Heta and Paul were married by the bishop at the parish church of Carberry and Roger Carberry gave away the bride. All those who saw the ceremony declared that the squire had not seemed to be so happy for many a long year. John Crumb, who was there with his wife, himself now one of Roger's tenants, having occupied the land which had become vacant by the death of old Daniel Ruggles, declared that the wedding was almost as good fun as his own.  Yes, I be, said John, but not such a fool as to amiss the having of you. No, John, it was I who was the fool then, said Ruby. We'll see about that when the barons born, said John, equally allowed. Then Ruby held her tongue. Mrs. Brown and Mr. Brown were also at Carberry, thus doing great honor to Mr. and Mrs. Paul Montague and showing by their presence that all family feuds were at an end. Sir Felix was not there. Happily up to this time Mr. Septimus Blake had continued to keep that gentleman as one of his Protestant population in the German town. No doubt, not without considerable trouble to himself.


I do not remember when I first heard about the Holocaust. As an Ashkenazi Jew who was born in Ukraine, the Holocaust, its horrors and pain was always a part of our lives. I had the feeling that I was born into this. The narrative that 6 million Jews were murdered just because they were Jewish. I have heard of my mother's brothers who were killed in Poland. The entire family of my grandmother who was executed along with over 32,000 other Jews in Babi Yar in 1941. That was the story of my relatives, my roots, my family. And they had no rights after killing the whole family. They were forced to go to the police station, forced to sit on public chairs in Lita. In the name of God, there were 225,000, but there were 270,000. In your memory, there were 100, 100, 90, and 4% of the Jews who were murdered in the Holocaust. There are people who call for the Holocaust. But there are people who say that it is a war against Ukraine. It is not a war against Ukraine. If you listen carefully, you will hear this. You will see that there is no connection. That is the most correct thing to do. Because in the end, it happened to the Jewish people and we are aware of it. But when we say we are going to the world, it is not going to the Jewish people. It is not going to anyone else. And more than that, I will tell you, this is also our way to deal with two things. In anti-Semites and in extremism. And I think that our message as an Arab community, that we come here and say, we are here to learn, we are here to know and to get to know. And on this way, it is also our way to learn, to get to know and to also pay more attention to us. And that is how we are going to get to know about the extremists and the extremists, that the extremism and the anti-Semites are against us. When I heard about Joseph's visits to Auschwitz, I raised an eyebrow. Why do they need it? They are not Jews. Their family had nothing to do with it. Why do people really need to learn about the Holocaust in our days? After all, many years have passed and almost everyone who witnessed it is no longer alive. In addition, how Holocaust stories and this journey to the concentration camp can bring us, Arabs and Jews, together. Jews from Syria, Jews from Lebanon, Arabs from An-Tarid, Bahrain, An-Tarid. It is very effective, very effective. What they did when they built the country here, they made the bombings. They made the bombings. So they were in this plan. They didn't know what to do. They didn't know what to do. They didn't know what to do. All of this is good and bad. I would like to ask how we look at the future. How we look at it. Because we are coming, we are coming. It is our lives. We need to understand how we are coming together. My career is on the road. On the road. Good morning everyone. Good morning. I am very proud of everyone. It is 4.30 in the morning. I am very proud of all of you. Because the issues we are facing are historical issues. We have never done anything like this. Especially in terms of quantity and quantity. But we are doing a story for today. Dear passengers, once again welcome LL Flight 561 from Ben Gurion Airport Tel Aviv to Warsaw, Poland. This coming Thursday Israel will mark Yom Azikaron, a memorial day in remembrance of the Holocaust and all of those whose voices have been silenced forever. This is the end. I was born on September 29, 1927 in Koushice, Hungary, today Slovakia. My father, Laiush, was alive and he did not work in the Hungarian government. I had two brothers, Magda and Clara, who were musicians and musicians. My parents were sent to the gas station. I was chosen to be a doctor for Dr. Joseph Mengel. I have been used as a model in Jumbaz and Raqqas to stay on the stage of my life in Auschwitz. I am not more like the Arabs. I live in the country. The Jewish people are exposed to injustice. I killed 6 million Jews on the way of Hitler and Nazism. I do not know what they were doing here. I did not know. I did not go to Yad Vashem. I met him. I do not know why. I really know more and more about Auschwitz. Yusuf, what is the word in Arabic? The word is the Nazism. Did you go to Yad Vashem? Yes. The first Holocaust. Of course, this is the first time I have traveled here to Auschwitz. I really liked it. I hope that this trip will be a good one. We will go back to the community. We will go back to what happened. We will not go back to the right things that happened to the people. We will go back to the community from all the ups and downs. We will go back. We will go back to the people who were there. When I was a child, there was a day when I was a child. I was not very understanding what a child was like. People used to tell me simple things but I was not very understanding. They used to tell me more than the necessary things. The first time I heard about the child was when I was 11 years old. We were the first ones to teach things to the children. Why do we, the Arab community, in the Israeli community, have to know about it?  So we have to know who the people we live with what is their history and where they came from and what happened with them so that we can live together. And here we are, almost 80 years later, the delegation of Arabs and Jews arrived in beautiful Krakow to learn about the Holocaust. Nevertheless, what can we learn about the Holocaust after so many years? And surely, the attitude toward Jews here is different today. Am I wrong? I don't know what's going on in this building. I don't know how to get out of here.  But for a while, I will let someone come here and look at the game, at the doll and see how it is done. Of course, there is no other option to think about it. It is clear that it is a Jewish issue. We are here because of the Israeli war.  And we are Arabs who open up to the world as Arabs. It doesn't matter if it's Christian, Christian or Muslim. What is the difference between us? We are the voice that comes to say that there is no racism. There is no doubt that when someone hears about me about Genocide, about Majzara, they don't like it coming back again. So that everyone can get along with the Ukrainian people they feel that they are becoming like Majzara they are becoming like after the mass murder. We can't compare. Even though there is no comparison. Nazis fled Poland in September 1, 1939 and on the 18th, they took all of Poland. No one knew, in one of the Jews they didn't know what was happening to them, what was going on. And what happened to them, they didn't know. Nine kilometers away, nine kilometers from here there was a small Jewish woman called Shvinzitsi. My father, remember the woman, was living there. He had a family, he was a Sandler. He was a woman, she was married for ten years. And two small children, one from Zalman who was four years old and one from Feigale, two years old. His wife, because she was still a member of the First World War she said to my father, Izzak, so you took everything, we didn't come, you continue to live so that you don't have to work. But we were all fine. And so they basically did all the things, all the families. When they entered the village, they didn't find any friends. Only relatives and people, children, would gather. They told everyone to go to their homes and spend them in their lives. Do you want to go to the village? Yes, I want to go to the village. Do you want to go to the village? Yes. We are the only ones. We are the only ones. Even in the lead-up to World War II he was providing intelligence information to the Nazis. So how does someone go from someone who supports and believes and is enjoying his comfortable, wealthy life with Nazis to someone who ends up saving 1200 Jews? But I believe that it started from a personal connection that he had. He started to see what was happening to the Jewish community and at first he started to see that it impacted him negatively financially. His team, his friends, his neighbors started getting taken away. There were 64,000 Jews in Kraków specifically. All of them were expelled to a ghetto first in Poland and only 10% of them survived the war. The majority of the Jews from Kraków, not all Poland, but from Kraków who survived were because of Oskar Schindler. And there is a day for which we went through this journey. The day we arrived at Auschwitz. I see a line of people and everyone spent their money to get in. To enter a place that 80 years ago people were willing to give everything just to stay out of. The atmosphere of the place is indescribable. The order, the systemacity, the efficiency and the perfect symmetry. Every wall, every stone, every part of the complex puts you in a dark mood for one very simple reason. The product of this factory was death. This was a very difficult experience. It's not easy for one person to accept the idea that it's nothing but for the sake of a specific religion or a specific person, just because the Jews went to the Nazism neighborhood that is close to 6 million Jews. There were 40 Jews in Lina Al-Aim. There were 2000 Jews in Lina Al-Aim. It was a struggle for me. There are a lot of other things that are very difficult every day. They really need to understand that the whole world is full of Jews. I'll tell you something. One of us doesn't know, really. There are things that don't exist, and there are people who accept that there are Jews. There are all the things that exist here, and all of humanity, and all of the reverence that exists. And I know there are people who say, look at this, this is the truth. Look at this, the Jews are lying. There's nothing to say. There's nothing to say. Thank you, Dave. You must film at this? Yeah. The documentary will be with them. This is the situation for filming. Just turn it off, please. It wasn't easy at all. It was hard. It was sad and emotional. I saw all these people who have nothing to do with this place, nothing to do with these atrocities, nothing to do with the pain of our people. But each of them cried, felt my pain, and sympathized with the victims, and each said, never again. I don't know how people can live here for a year or two. It's something that's hard to understand. It's something that I don't understand. Again, I learned about it. I know what it's like. I lived it before, but when I got here, I didn't understand how people can live here, and live here. And live here, and live here. They can live here for a year or two. It's something that's hard to understand. It's hard for me to understand. Before we got here, we had to pay the money to come here. We had to pay the money to come and visit the museum in Auschwitz. I remember someone who used to pay money 80 years ago to get away from this place. It was the most exciting, the most genuine, and the most incomprehensible ceremony. Because only in this place can any person, regardless of race, gender, and religion, understand the magnitude of the disaster that was here. This is just the beginning. It's just the beginning that all those who say that the Arab society, the Israeli people, they don't want to be part of this, that we don't give you money, and not two or three. And the next year, it will be more and more. It was there, it was there. All of us together, all the Christians, Muslims and Muslims. That's how it is. No, no, no, no. Listen, let's start. I want to ask you, not here. Let's go, brother. I want to ask you. Not in Poland, Muslims, Muslims, Muslims, Muslims, Muslims, Muslims, Muslims, how much do you have? 2 million. They want to be Palestinians. Yes, I don't know. You don't talk about it. brothers, тます. I give the version, yes, Also, there is one Israeli who is very, very intelligent. he who is intelligent, so I can accept it. I want to say only one thing. I didn't hear you. You're going to speak with your brothers. I don't want to go to the city. The city that wants to be a city, I don't want to go to the city. The city, the city, that's what I wanted. I'm more than willing to go to the city. And I'm here with a lot of people who come here to fight. There are no other people. And I'm saying that the people are willing to go to the city. Who is the leader? Who is the leader? I'm really so touched by what you're saying. Because you went to the trouble to look, to find, and I can see that you want peace. You don't want war. And I'm wondering myself, how is there ever going to be peace in Israel? This, us. What we're doing. You are connected. This is the real Israeli society. This is the truth. This is who we are. Druze, Christians, Muslims, Jews. All of us here together and we are growing up. Now I have to share with you one more thing. We came here as 35 people. Since three days ago, we came to Krakow and we've been in the Jewish quarter. We've been in the Shinsar factory. We came yesterday here for a tour. As I told you, we heard the ceremony in Arabic. Today we're in the match of the living. Since three days ago, we've been getting messages from Arab Israelis, Arab around the world. How can we join you? We want to be here. We want this. Next year, I am telling you, not only are we going to double the number, we're not going to triple it. It's going to be even bigger than that. And that's why how it will happen. It's us. It's this guy, this guy, this guy, this girl. It's us. Well, it really warms my heart to hear that. And I'm really in awe because outside Israel, we all think that Israeli and the Arabs and the Jews, they're at one another's throat and they hate each other. I love you. So I often think, how is there going to be peace? Who is going to do it? And I think that you really give me hope that one day there will be peace. It does my heart good to hear this. And I can just only hope that in future you'll all live in peace. The world is not perfect. We have many disagreements because we see this world in different ways. But what I learned during the journey is that we can try to empathize with the pain of others. Yes, everyone expresses empathy in different ways, whether it's by traveling to Auschwitz or by empathizing with the Ukrainian people or simply being tolerant of people who are different from you.