Now, the last thing we have to discuss is write on Bragg's law. What is Bragg's law? That is the equation of Bragg's law. What is Bragg's law? So, what happens in that? See, Bragg's law is the law we have through which we can find out the interplanar displacing. Interplanar displacing is what? It is the distance between the two layer in a crystal. Crystal has layer-laying structure. Suppose we have a layer 1, 2, 3 and so on we have. So, we must have some distance between these two layer. This distance d, we call it as interplanar displacing. And to find out this d, we use Bragg's law. The relation of Bragg's law is n lambda is equals to 2d sin theta. n lambda is equals to 2d sin theta. With this equation, you can solve all the questions of this. Whatever question they ask, whatever question this equation you can solve. Everything will be given one unknown detail. Use this formula and get the answer. I will discuss that. But how do we get this expression? n lambda is equals to 2d sin theta that we are going to discuss. Now, to find out this interplanar displacing, we use a light of certain wavelength. And that light will be in the order of that interplanar displacing. According to that, generally we choose x-ray because x-ray has penetrating power. So, that can penetrate into the crystal and then reflection. We have a receiver ring. We have a source of x-ray. That receiver receives light which gets reflect from the crystal surface. And then on the base of the image that you get, on the base of that image only, we will find out that beam. So, first of all, to understand this, we have to understand two properties of wave. And that is constructive and destructive. What is constructive? Interference. Properties of wave that is interference. That has two types of interference, constructive and destructive interference. What is constructive interference? When two waves of same phase. Suppose this is wave one and another wave is this. When these two waves combines, why they have same phase? Because you see they have same direction, right? This is the direction of the wave. The same wave, when these two combines, they will give you a net wave whose amplitude, suppose it is A1, this is A2. So, the net wave will have amplitude is equals to A is equals to A1 plus A2 of one. That is what Kea is. So, this is constructive wave. So, it will have to be same. Any multiple of them. That is possible. Basically, you will get, you have to add these two amplitude. When the wave is same, when the phase is same, when the phase is opposite like this, these two opposite phase. When these two combines, if the amplitude is same, then these two cancels also in each other. You will not get any wave. So, this kind of interference, we call it as constructive or destructive interference. What is diffraction? What is diffraction? This is interference, right? Can you see it is a bending of light? See, wave has two properties. Interference and diffraction. Interference, we have discussed constructive. We have the use of this interference only. Diffraction is nothing but the bending of light. It shines. It is an angle. It shines. That is diffraction of light. So, when the light or the, you know, light strikes at any sharp edge, it diffracts. And that, the shiny part when you tilt the blade like this, any shiny use, knife also if you, you know, tilt like this, at some different angle it shines. So, that is bending of light because of bending of light. So, that is diffraction, we call it as interference. We have use of interference here. Two types of interference, destructive and constructive. Now, to get a better image, we need constructive interference because you have nothing here, right? Our source of the wave is same, right? So, you will get obviously same wave you will get with same amplitude. And if the interference is destructive, you won't get anything. Receiver cannot, you know, receive this because you are not getting anything here. But here you are getting the larger amplitude wave, okay? To get the better picture, better image, we must require constructive interference for any experiment, whatever you are doing. So, here also for Bragg's law, or to find out the interference spacing, we require constructive interference or destructive interference, okay? Now, suppose the crystal we have this, this is the layer we have in the crystal. This side we have source of X-ray. Why X-ray we are using? Because it has penetrating power. It can go in a, like, it can go into the crystal action, okay? So, this is the source of X-ray. And this side we use, we take one receiver which can receive the reflected wave from this crystal, okay? So, this is the direction of wave we have in this section, it goes and it reflects, it goes like this. The angle of incident, this angle is theta. Okay? Now, since we require constructive interference, so the phase or the wave that you get here, that wave must have the same phase, okay? Then only we get constructive interference. Suppose this is the wave we have, okay? Same phase, so it should go like this, or then from here it should go like this. So, same phase we have, so here it should be. So, phase should be same, so it should go like this, okay? This one is, suppose we have path A, and this is, we have path B. This distance is the independent spacing, D, okay? Sir, let's see if we can touch it. Isn't it supposed to be like the surface which you should touch and then... Yeah, I am coming to this. Let me explain one point. Obviously, this wave goes like this. Okay. It goes like this, okay? But the point is, we should have here constructive interference. So, phase of the wave must be same. That's why I have problems, okay? Now, can you tell me path A and path B, two different paths we have. Which path the wave has to travel more distance, here B? B, correct? And what is the path difference? This distance is the same? This distance and this distance is same. Path difference is what? From this point to this point, okay?  So, if I ask you what is the path difference? Path difference is nothing but A, P, plus D, B. Isn't it clear? A, P, plus D, B. Okay? What is this distance? It is D. And if this is theta, this one is what? What will be this one? 90 minus theta. What will be this one? Theta. And what will be this one? Theta. 90 minus theta. Okay, let's put theta down. If this is theta, then what is A, P in terms of D? Sine theta is what in this triangle? Sine theta is what? A, P by? O, P. O, P, right? A, P by O, P. So, what is A, P? A, P is D sine theta. Okay? A, P is D sine theta. Similarly, P, P is also D sine theta. Because if it is theta, this is also theta, right? Yeah. Theta? This is 90 minus theta. Take A, P, theta. T minus theta. Sir, O, P and A, P are parallel. No, no, it's not parallel. Okay, we say it's parallel. Okay, it's parallel. It's perpendicular, actually. It's perpendicular. This is perpendicular. I'm saying O, P and A, P. O, P and A, P. O, P and A, P. Yeah. O, P and A, P. O, P and A, P. Then if that is the case, then B, O, P should be 90 minus theta. If they are parallel. You are saying O, P and A, P. Yeah. If they are parallel. It is not parallel. I have just drawn perpendicular from this point to this point. This is the perpendicular. A, P, A, P. O, P should be a parallel. O, A, P is also 90. Okay. This will be 90 minus theta. This angle, this angle. 90 minus theta. See, this is theta. This should be theta. Take that. And this is also theta then? Yeah. This is 90 minus theta? Yeah. This is theta. This is 90 minus theta? This is theta. Since it is theta, this is parallel. A theta, A B theta over here? Yeah. A B theta over here? Yeah. These two angles must be equal. 90 minus 91 is theta. Sir, how can that be possible? That means 90 minus theta, theta. Okay. This is 90 minus theta? A little bit theta. Sir, A, P, B is the right angle. Yeah, A, P, B is right angle. A, P, B is the right angle. A, P, B. Yeah. A, P, B. How can this be equal? I don't know. But you're not assuming all that. No, no. This, the angle of whatever angle we have here, the same angle we should make in its reflection now. So, this angle and this angle must be same. Just like this. Okay. So, this angle is theta. This is 90 minus theta. And with the same angle it reflects. This should be theta. If this is theta, 90 minus theta, this should be theta. Okay. So, theta. Now, if it is theta, then what is P B then? Can you say P B? P B is again D sine theta. D sine theta. So, what is the part difference?  That is 2 D sine theta. You'll get part difference. Now, if the part difference in terms of lambda is N lambda, then this thing is true. Okay. Now, you look at this, the part difference A B that you have. Suppose we have this A B. At point A, the wave is coming from the bottom and it is going from the top. So, at point A, the wave is coming this way and it is going this way. Now, for this thing to be possible, one possibility is what? It may go like this. This is one possibility. Another possibility is what? It forms two ways. Another possibility is what? It forms three ways like this. Okay. It is what? What is this distance? Lambda. What is this difference? Lambda plus lambda. That is 2 lambda. It is 3 lambda and so on. Then we can say the part difference must be an integral multiple of lambda. Okay. And that's why the part difference is N lambda is equals to 2 D. Is it clear? Part difference must be, must be the integral multiple of the wavelength of the light that we are using for this. And that should be equals to 2 D sine theta. Okay. Numerical questions you can solve under this. Mostly they are numerical only. Okay. They will give you the, no, all things will be given. Angle of incident. N is generally N, they like order. First order diffraction is there like that. First, second, whatever order they have written, it means that is the N value given. Okay. And whatever unknown you can find out from this. Sine 54.5, like this also they will give angle. But this value will be given in the question itself. Sine of 54.5 is this. Okay. Must you take care of what is the theta we have taken? Theta is this. Okay. If they have given you this value, then answer will be 90 minus theta. Okay. Sometimes they will give you this angle. Theta is 54.5. Okay. So, 90 minus this is that incident angle. Got it? So, how do you do 80 degrees or 80 degrees? I didn't say it... What is the point is... I didn't say it's 90. But here it is... Yeah, it is 90 also you can see. This is theta, right? So, this angle is this... A b b is 180 minus... 180 minus 2 theta. Depends on theta actually. See, we don't know about this angle. What is this A b b? But we are very sure that this angle should be this. Equal to this. Because if this is theta, this should be 90 minus theta. And the angle with which it is... The angle forms with this vertical line. Same angle it goes at the reflection. Same angle is an angle of incident or angle of reflection. These two angles must be same. That's what the concept is. Theta and theta. Okay.


So in this video, we're going to do a little bit of trigonometry, right triangle trigonometry, but with an Asosceles triangle. It turns out that Asosceles triangles are deeply connected to right triangles as we're going to see in just a second. We'll recall what is an Asosceles triangle. An Asosceles triangle is a triangle with two sides that are congruent to each other. So for this diagram, let's say that if we have this triangle ABC, which is Asosceles, let's say that side length AC is congruent to side length BC. And let's say that both of these congruent sides are congruent or they're equal to 24 centimeters in length. Now with an Asosceles triangle, if we have two congruent sides, then it's also true that we'll have two congruent angles. That is the angles opposite of the two congruent sides and an Asosceles triangle will also be congruent to each other. And let's say that their shared angle measurement is 52 degrees. So angle A and the measure of angle B are both 52 degrees. Okay, so with that in mind, we want to now compute the length of the base and the altitude of this Asosceles triangle. So what do these words even mean for us for a moment? What does altitude for example mean? So an altitude with respect to a triangle is the unique line that connects a vertex to the opposite side of the triangle so that those two lines form a perpendicular angle of a right angle. That is, these two lines are perpendicular. So for example, the altitude of A would look something like this. This is the line that passes through the vertex A and is perpendicular to the opposite side. So we get something like a right angle right here. The altitude of angle B would look something similar. You get something like this. It's the line segment that connects vertex B to the opposite side of B and forms a right angle. That is, these two lines are perpendicular. Now when it comes to an Asosceles triangle, two of the angles are congruent to each other. So you have this third angle. The altitude with respect to that third angle is critical for an Asosceles triangle and you can see it illustrated here on the screen. The reason why this one's so interesting is for the following reasons. You'll notice that with this triangle segment AC is congruent to segment BC because it's an Asosceles triangle. Angle A is congruent to angle B because it's an Asosceles triangle. And likewise, we have that this line segment. Let's say that the point of intersection between the altitude of C with respect to the line segment AB. Let's call that point D. This is known as the foot of the perpendicular line. You'll notice that the line segment CD of course is congruent to itself. I don't know what it is, but it's congruent to itself. And so if you look at the two triangles formed by cutting the Asosceles triangles in half by this altitude, you see one triangle over here ADC. You also see another one over here. You have BCD like so. You see these two triangles. Now these triangles are going to be congruent to each other. You'll notice that angle A and angle B are congruent. Angle C, excuse me, side B and side A are congruent to each other. Of course, the segment CD is congruent to itself. These two angles right here are right angles so they're congruent to each other. And it turns out that this is the bisector of that angle. It cuts it into equal pieces. And the foot is also going to form the midpoint of the line segment AB. So these are congruent to each other as well. So we have these congruent triangles. An Asosceles triangle can be cut into two pieces and those two triangles themselves are right triangles. That's what I meant by Asosceles triangles are very much related to right triangles. Basically, an Asosceles triangle is just a double right triangle. If you take a right triangle like this one over here and you just reflect it over one of its sides, you just form an Asosceles triangle and you have that connection there. So what we need to do is we need to find the base and altitude of this triangle. Why is this significant? Why might we want to care about that? Well, recall that the area of a triangle is one half base times height, which the base is the length of that one of the sides of the triangle. And then the height is then the length of the associated altitude of that side. So if our base here is the line segment AB, then the height of the triangle is the length of its associated altitude. So if we know the base and the altitude, we can compute the area of the triangle. In general, this can be challenging, but finding the area of an right triangle is pretty easy. And then for an Asosceles triangle, well, since it's just two right triangles, we can find the area of an Asosceles triangle fairly easy. So how are we going to do this? So the altitude is the height of the triangle. The base of the triangle is going to be B here. What I'm going to do is introduce a new symbol. We're going to call it X. Little X is the distance between A and D, which A and D, this right here is going to be half of the base. So the base is going to be 2 times X, whatever X turns out to be. Now to find X, what we can do is we can do a right triangle relationship on the triangle ADC. You'll notice that X is the adjacent side with respect to angle A, and we know the hypotenuse 24. And so that tells us that if we take cosine of 24, excuse me, cosine of 52 degrees, this is equal to X over 24. Clearing the denominators, we get that X equals 24 times cosine of 52 degrees. Well, since the base is just 2 times the length of X, that means the base is going to equal 2 times 24, which is 48 times cosine of 52 degrees. Consulting our calculator, we can then compute cosine of 52 degrees in our calculator times that by 48. And we'll get that the base of the triangle is approximately 30 centimeters. You'll notice that there was no instructions on how to round or any significant digits or anything like that. So what I'm going to do is I'm going to match the original style. Since the measurements of the side length of the triangle are given to the nearest centimeter, I'm going to round my answers to the nearest centimeters well. So the base is 30 centimeters. What about the height? We're looking at this right triangle again with respect to angle A, the height is just the opposite side, and we still know the hypotenuse is 24. So if we use the sine ratio this time, sine of 52 degrees, this will equal H over 24. Clear the denominators, we end up with H is equal to 24 times sine of 52 degrees. This is the exact answer. If we use our calculator to approximate the sine of 52 degrees and then times that by 24, make sure you're in degree mode when you do this and round to the nearest centimeter, we'll end up with 19 centimeters as the length of the altitude, the so-called height of the triangle. And so if we have the height and we have the base, then we could find the area of the triangle. We would just take 30 times 19 and divide that by 2. And so we see that the area of the triangle is approximately one half base times height, like I said, is one half 30, which half of 30 is 15 times that by 19, you would end up with 285 square units of area.


Hi everyone, Joe for jaspyscasebreaks.com coming at you with another 2 box break of 2019-2020 Panini Mosaic basketball. This is one of those, uh, those sell-o-pack editions right there which features the pink camo they can see behind Zion. This is random team number three. Big thanks to all of these folks right here for getting into the action. There is an early bird spot, so first 20 sold, have a shot at an extra spot. The early bird catches the worm. For seven times, name on top will get the extra spot. One, two, three, four, five, six, and seven. After seven times, Jesse's time. Congrats to you. Let's grab Jesse's name right there. Congrats. Jesse, you are the early bird that has caught the worm. So now let's see what team you're going to be assigned. It goes to everybody as well, so that's a new dice roll. It randomized it six and a four, ten times for each list. Good luck. One, two, three, tenth and final time. After ten, we got Matthew Shearer all the way down to Colin Sullivan. Ten times for the teams and tenth and final time. After ten, we got the Clippers on top and the Bulls on the bottom after ten. Now trades are allowed. We'll pause the video just for a few moments and allow for a little bit of trading if you want. Trading your own risk, of course. So Matthew Shearer with the Clippers, Oliver with the Hawks, Brian Zeller, you got my Lakers, Nick Coba with the Kings, the Cavs for Jesse, LeBron James has some Cavs cards in there, Derek with the Pistons, Nick Coba with the Rockets, Jesse with the Thunder, Joe with the Trailblazers, Alex with the Heat, Brian with the Wizards, John Samuelson with the Pacers, Rokio with the Nets, we got Derek with the Jazz, Joe Crowell with the Celtics, Jesse with the Grizz, nice. Thanks for Matthew Shearer, Ryan Redmond with the Mavs, Luca Donchage's Worship, Joe Crowell with the Bucks, Derek Holton with the Magic, Golntay Warriors, Zach Paul, Scott with the Sons, Nancy with the Nuggets, and Greg McKinnon. Pelicans. Ryan Redmond Spurs, Brian Zeller with the Hornets, Khan, you have the Raptors, Nancy with the Sixers, Joe Crowell with the T-Wolves, and Colin with the Bulls. Sort by Column B, right here by Teen, and we're going to pause really quick and allow for some trades. Stick around, we'll be right back. All right, welcome back everybody. No deals were done in this, it's all right. Let's see what we can pull out of here. Quick little two box, cello box breaks. Love the mosaic, the pink camo parallels are the cards that we're looking for. It's exclusive to this set. Of course, nice silver, good refractor here and there, I think would also be nice too. Someone was saying Genesis parallels are also available in these retail packs, so a lot to look out for. Good luck everybody. What is this? Cowboys day today? We got a Charles Haley football life, Troy Aitman football life, Emmett Smith football life. Wasn't there a Michael Irving football life? I want to say Cardinals edition of Emmett Smith wasn't too shabby, right? I feel like he had a decent stretch of games with the Cardinals. Anyhow, basketball is coming back, folks. July 31st is the date. I think on my show notes page, I'm going to have to eventually track down all the sports and where they're at and when they're coming back and everything. I think basketball is coming back on the 31st. And is that hub, I think they're all going to be in Orlando. I think there's going to be some teams, I think all the teams will play out the final eight or so games, eight or nine games regular season. I think there's like maybe 18 left, but they'll cancel that. But I think they're playing just under 10 games. No, that noir is going to be our last break of the night, Wayne. That's going to be like a nine o'clock, nine o'clock specific. So maybe three hours from now. A lot of other breaks in between. So I should have screen-charted the schedule for people not to do that. All right. So there's a schedule in the chat right there, everybody. So yeah, sorry, I lost my train of thought, but yeah, it's coming back on the 31st. I think all the teams are playing eight or so games. And then after that, they'll be, if the eight or nine seed in each conference, from my understanding, if they're like within a few games of each other, I think they're going to have a play-in game for that eighth spot, the eighth and final playoff spot. I think it's an interesting way to do things. So that should be pretty interesting. And then it's a normal playoff schedule after that. The usual, what, I think, are they all seven games, seven game series from first round to finals round? But the playoff schedule apparently is going to be exactly the same. Remember veteran commons don't ship unless it's a silver like that Brandon Ingram or any other kind of parallel like that Mosaic James Harden. Veteran commons that do ship are LeBron James, Kobe if any, I don't think he might not be in this at Luka Donchich and Yanis. And these will go to the teams that according to the groupbreakchecklist.com, I think the only one that might be in dispute would be the, they'll go to the usual teams. Carl Malone's going to go to the jazz. Vince Carter goes to the Raptors. And that's the only thing I might need to highlight. I can also check the checklist. Oh, look at this. Luka Donchich silver. The base was going to ship anyway. A silver Luka Donch, it's even nicer. That goes to Ryan Redman and the Mavs. Oh, the East only has nine teams. Derek E is saying, yeah, I thought they shaved down one of the conferences. So, so they'll still do the play in, right? Point is basketball is back. That's going to be nice. There's Hachimura. Well, maybe it's just the West that has the play in just because they have a lot more teams that are in contention for that final eight seed. Nice green LeBron James. That'll go to the Lakers. It'll be for Brian Zeller. But July 31st. So we're in early June now. So I guess that gives players, because players are scattered around the country, if not the world, right? You know, so that gives everybody a chance to come back, do whatever, take care of whatever visa stuff they need to take care of, whatever self-quarantining stuff they need to take care of, whatever, blah, blah, blah, blah, blah. Prepare teams for their staff testing and whatnot. Maybe give them a little bit of a quote, unquote preseason, you know, so players can kind of warm up over the next, so what? Week or two to get everybody back. After two weeks, two, three weeks of some kind of preseason, and then by the end, they'll kind of bring them to the end of July, which sounds like plenty of time, which is good. No, we don't want to restart the season, then next thing you know, Yana tweaks a hamstring and then is out for a month, you know what I mean? That's not good. There's Nikhil Alexander Walker. So from my understanding, game seven of the NBA Finals, this is another buck for Joe Crowell, could be as late, so let's say all the series go seven games and blah, blah, blah, and then the NBA Finals go seven games, the NBA Finals could be October like 12th or something like that. I think that's what I heard, right? That makes sense because basketball playoffs, they definitely do feel like a long time. So yeah, that makes sense, right? July 31st, basically August. August, August, September, regular season playoffs, September, October, yeah, that makes sense. Eric Jay, not happy with the contenders. So stingy on anything lower than a second rounder. If you get a first round, it's like when in the, has it always been like that? Yes. It has, especially contenders draft. Regular contenders by then they kind of figure out, no, regular contenders is like that too, to be honest with you.  Minshew last year jumps out at me. So, yeah, that's always kind of been like that. So all of these pinks of course will ship. These zions or jaw marrants, that's what we want to see. Oh, nothing here. All right. Well, we've got one more box. Let's see what we got. If it goes late, when would the next season slash draft happen? Regular season starts in October. Correct. So I think that pushes the calendar back on everything. So now next season gets interrupted from what I understand. There may be a shortening of games there too, a shortening of regular season games. So I don't think they're going to start the regular season until, well, how long does it, finals usually end in June, right? It doesn't ever hit July. And then June, July, August, September, November, so like three or four months. So if it ends in October, I think they'll probably have the draft in, I don't know if they've figured it out yet, but my guess, my pure speculation is that they'll have the draft sometime in the winter, right? November, December, you know, then they'll do a preseason again in like January. Maybe they start the season with the All-Star game, which is in February. And then maybe you either have a compacted season or a game shortened season. And then you finish the season on time, then the normal playoffs next summer, late spring, early summer, and then knock on wood back to normal. Are they saying start the season on Christmas Day? When are they going to do the draft, Ryan Ruff? Right, for us hobby-wise, yeah, the draft day is going to be important for us. When is that draft day hobby-wise? So it's going to push all sorts of things around. I mean, my guess is that Panini could milk 1920 product for a few more months. I don't know how they're going to approach. I'm sure they're talking about it. Christmas Day would be wild. That means if the NBA finals goes all the way until October 12 or something like that, or they do a draft in, when will they do the draft? Or do they do the draft? When is the draft usually? Isn't it July? June? This month? So maybe, yeah, maybe they do just, they could do the draft now, Derek. College seasons are over. So maybe they do the draft now, but say you're not on a roster until the 2020-2021 season officially starts, which would be kind of crazy. They could be watching their team, which would be kind of weird, right? There could be playoff teams going, oh, if only. But see, well, final seeding, they don't have final seed. That would be the problem. I guess they could do the lottery now, because, right, because the playoff teams, then I don't know. Now I'm confused, because you have to stop to wait for the playoff teams to be over. You can't do until after the playoffs. You've got to figure out where the other teams all land, too. I don't know. Everything gets pushed back. It's weird. So they want to start Christmas scenes a little early. But I think I do remember, Ryan. I do remember them discussing that. But Philip, clients' draft is pushed to October 15. So a few days after the last potential finals game? That's interesting. Vanilla Grill has always talked about restarting. Will we see the outbreaks from these proteins? Probably will, yeah. But I don't think there's going to be fans in stands anyway. So I don't think it's really, it's not going to impact the restarting. I know players are out there, too, but they're going to be testing players. So if someone gets it as a player, then maybe you're just not going to play. It's tied to Rome. Silver for the Suns. That'll be for Scott. So draft is right after the last potential game of the finals. It's going to be a busy time for teams. And then are they going to try to see then that's a good, oh, nice green John Morant. So does that mean Derek is right? What kind of combine or summer league do we have? Are there GMs are going to be watching playoffs and doing scouting all then? Nice green John Morant for the Gris. Jesse Stein, nice. And then have some sort of winter league, winter league, a winter, winter league in Vegas. That'd be nice. I actually traditionally go visit my sister for Christmas in Vegas. She usually has to work during Christmas. Thanksgiving is when the fan gets together, but so I don't know, maybe maybe catch some winter league games. That'd be nice. So Phillip saying November 10th training camp and season tentatively starts December 1st. The situation is fluid. So they're restarting much more quickly than I thought. So Phillip, from what you're hearing, reading, does that mean no, that's basically no, I guess October 15th. So maybe there will be some kind of fall, some kind of fall basketball league for the, for the rookies. Hmm, it'll be interesting. I think the players should be able to handle it though, right? They're already, they've already had like a two month break or something like that. You know, so yeah, players get six weeks. No, I mean, I think, I think the idea is, you know, 90% of the teams are not going to be playing until October, right? Most teams are going to be out. I think that's the idea and they've been, they've already had a couple months off due to the pandemic. So maybe now they're, they're young, they're professional athletes, they should be able to handle it. LeBron's only 36, he should be able to handle it too. I don't know, maybe a lot more load management for LeBron, wherever, wherever he ends up next season. That's a short off season though. That's a lot of work that the GMs will have to do as well. It'll be interesting to see. LeBron can opt out after this season anyway. So I don't know, we'll see.  Do you think he's coming home again? Actually, now I'm curious. Do you guys say, when you go to the popular website to look up contracts, here, I'll drop the link into the chat. How do you say it? Do you say, Spotrack or is it Spotrack? I've never heard anyone actually say it. Yeah, Tony, it's literally the next break after this on the schedule, the World Cup soccer. Or is it just Prism, is it not World Cup? And not anyway, where it says soccer, Tony, on the schedule. All right, so LeBron, so this is 1920. LeBron's player option is after 2021. So he has one more guaranteed year with the Lakers. Then he can opt out if he wants to. So there could be potentially two more, the current year, two more years of LeBron. And then 2022, free agent. There he is, there's LeBron. He heard us talking about him. There's LeBron right there, the Lakers. Pink Camel, exclusive to this set right here, going to Brian Zeller. So it'll be interesting to see. I think that contract brings him to, brings Brony to the end of his, I think that's how he timed it. Because that might be senior year. Kobe White for Colin tried to trade, couldn't trade Mojo. It's pretty solid. And we'll have to look up exactly what year Brony's in, but I think it lines up pretty closely. So yeah, I mean, Lakers are probably hoping they don't have, they're not in a draft position where they're picking Brony, but that could be crazy. If they can get LeBron's kid and then re-sign LeBron like a one year deal or something like that. One or two year deal. All right, that's it ladies and gentlemen. Very nice break. We've got more of these two box, cello pack boxes in the store. So check it out, jaskyscasebreaks.com. I'm Joe. I'll see you and talk more basketball with you next time. Bye bye.


Okay, this is algebraic geometry lecture 11 in which we will discuss quotients of algebraic varieties by groups. So first of all, we just recall for any algebraic variety or any algebraic set, we can go to its coordinate ring. And so the algebraic set will be given by some subset of a to the n. And the coordinate ring will be given by the polynomial ring x1 up to xn, quotient out by the ideal of this algebraic set. The algebraic set is y, i of y is functions vanishing on y. So this can be thought of as the ring of all polynomial functions on the algebraic set y. And this coordinate ring has three properties. First of all, it's an algebra over K. Secondly, it's finitely generated. It's obvious. And third slightly more subtle property is it is no nil potent elements. On the other hand, if you've got an algebra with these three properties, it's finitely generated over K and there's no nil potent elements, then by the strong nil still and that's it corresponds to an algebraic set. The algebraic set it corresponds to isn't quite unique because it depends on your choice of generators. If you choose seven generators, it will be contained in seven dimensional affine space. But somehow if you choose a different collection of generators, the corresponding algebraic sets are essentially isomorphic in some sense in the sense that there are polynomial maps between them that are inverses of each other. Informally, we can think of algebraic sets up to some sort of isomorphism as being more or less equivalent to algebras with these three properties. Technical term is a category of algebraic sets is equivalent to the opposite of the category of coordinate rings. So now we have an application of this. Suppose we have an algebraic set Y acted on by a group G. And the question is, can we form a quotient Y over G where we identify points in Y if they are equivalent under G? Well, actually, this doesn't really work. We can't form a quotient by identifying points of Y under elements of G as we'll see a little bit later in some of the examples. But we would still like to form something that we can count as being a quotient. Well, if you try forming equivalence classes of points of Y under G, you immediately run into problems. For instance, how do we embed this inside some affine space? We said an algebraic set was contained in an affine space. And if you start identifying points inside affine space, it's not all clear how you're going to embed that quotient in affine space. However, if you look at it from the point of view of coordinate rings, this is much easier to do because the functions on Y modulo G should correspond to functions on Y invariant under G. So what we can do is if we've got a group G acting on this algebraic set Y, then G will also act on this ring here, the coordinate ring of Y. And we can look at the ring of invariants where we take the coordinate ring kx1 up to xn, quotient it out by I of Y. And then you quite often denote the invariance of something by putting a superscript G. So this is the invariant ring. And if the invariant ring satisfies these three properties, then it's the coordinate ring of some algebraic set, which it would be reasonable to call the quotient Y over G. Well, let's check these properties. First of all, it's obviously an algebra over k. Secondly, it obviously has no nil potent element. So the problem is, is it finitely generated? And the answer is sometimes it is finitely generated and sometimes it isn't. And in general, it can be quite tricky to work at which. So Hilbert proved that in many cases it was finitely generated and seems to have thought that it was quite likely that it would always be finitely generated. In the 1950s, Nagata actually found an example where this ring of invariants was not finitely generated. So it's actually a fairly tricky problem. Anyway, let's look at a few examples of this. So one example we've all seen. Let's take an to be affine space and G to be the group S permutations. The light has gone off. Anyway, never mind. GN is the symmetric group of permutations of coordinates. So the coordinate ring, we take space of polynomials in n variables, take the invariants under the symmetric group. So this is just the ring of invariant functions. And you know what the ring of invariant functions is. It's generated by the elementary invariant polynomials where e1 is x1 plus plus xn e2 is x1 x2 plus all other things. And so I'm up to en, which is x1 times x2 times xn. Well, this is the coordinate ring of affine space. So we see that if we take affine space and quotient it out by the symmetric group on acting on its coordinates, this is actually isomorphic to affine space again. This example is actually really misleading because the answer is particularly easy. In general, quotients of even affine space by groups are in general very, very complicated. It's only if a group happens to be a reflection group or something very close to a reflection group that you get a really nice answer in general and SN happens to be a reflection group. You have to be a little bit careful about this. For instance, if we take the real line and have the group z modulo 2z acting on it just by taking x goes to minus x. So it sort of identifies points like that. Now if you take the real line and quotient out like that, you might think the quotient is going to be a half closed interval. But in fact, the quotient. So that would be the quotient if you identify points under the group. But you notice this isn't the same as what you get from this construction here. So the quotient under this construction is just the whole real line again. And what's happening is the points here are what you get by identifying 2 and minus 2 say. Whereas you also get some points here which you get by identifying say 2i and minus 2i. So you might think these are complex points, but in fact they count as real points of the quotient for slightly complicated reasons. So the points of the quotient might not be what you expect. Next example, let's look at a special linear group in n variables over k acting on k to the n. Let's take the general linear group. Then the orbits of points here are either the point zero or everything else. So you might think that the quotient is going to have two points. In fact, the quotient only has one point because the only invariant functions, the only invariant polynomials acted on by gln are constants. So here we just get the field k and this is the coordinate ring of a point. So although you might guess that the quotient of k n is two points because you can either take nought or everything else. In fact, if you calculate the quotient by taking invariant polynomials, you only get one point. So the third example is classical invariant theory. Here we take the group G to be SL2 over say the complex numbers and it acts on things called binary context. So if you look at a nx to the n plus a n minus one x to the n minus one y, so nought y to the n. Well, you can act on x and y by SL2 acting on x and y is a x plus b y c x plus d y. And this will transform this quantic into some other quantic and will act on the coefficients a n a n minus one and so on in some rather complicated way. So a nought up to a n is a point in n plus one dimensional affine space. So we can ask what is the quotient of n plus one dimensional affine space modulo SL2c. And the coordinate ring of this will be all polynomials in a n a n minus one that invariant under SL2c. And these are called invariants and finding them as part of classical invariant theory. A simple example if we take a two x squared plus a one x y plus a nought y squared and a typical invariant is the discriminant. Which is a one squared minus four a nought a two or b squared minus four a c in usual notation for quadratic equations. So you have this question is the ring of invariants finitely generated. And this was proved by Paul Gordon in a very complicated proof. So Gordon was known as the king of invariant theory because he was really good at proving finiteness of invariants. Well, Gordon's proof of this was so complicated that people kind of despaired of pushing it any further. In late 19th century, Hilbert found an astonishing way of proving in very great generality that rings of invariants are finitely generated. And we'll describe Hilbert's proof because it's actually remarkably short. By the way, there's a rumor that Gordon is supposed to be very negative about Hilbert's work and said this isn't mathematics, it's theology. It's not at all clear that Gordon really said this and the story that he'll that Gordon didn't like Hilbert's worker, mostly nonsense. Hilbert Gordon thought very highly of Hilbert and even used Hilbert's work and results himself. What he did do was when Hilbert's papers first submitted Gordon was the referee and Gordon quite correctly pointed out there was some gaps in Hilbert's paper. So this might be where this rumor about Gordon comes from. Anyway, in the next lecture we'll be giving Hilbert's proof.


From around the globe, it's theCUBE with digital coverage of IBM Think 2021, brought to you by IBM. Welcome back to IBM Think 2021. And we're going to dig into the intersection of finance and business strategy. My name is Dave Vellante and you're watching theCUBE's continuous coverage of IBM Think and with me is Brian Hoffman who's the Chief Operating Officer of IBM Global Financing. Brian, thanks for coming on theCUBE today. Good morning, great to be here. Good morning. So I think we've heard a lot about the impact of hybrid cloud, AI, digital transformation. And I wonder as a finance person and a former CFO, what do you see and how do you think about some of the key considerations and financials and strategies that are supporting these major projects, right? We got to come to the CFO and say, hey, we want to spend some money and here's the benefit, here's the cost. How can CIOs and their teams work with CFOs to try to really accelerate that digital transformation? Right, great question. And actually that question, I think I might have answered it a little bit differently two years ago, a year ago before the pandemic. I think it's actually changed a little bit with the pandemic. In my experience as a CFO, people would come into me for projects and there was three ways that you could justify it. You could justify short-term immediate, quick payback kind of hitters. You could justify it with improving our efficiency or effectiveness, reducing costs in the long run or making the client experience better or more from a strategic point of view, growing revenue, getting to new clients, improving margins, right? And so the hybrid cloud transformation journey really still addresses those three things. And when we come in, a lot of people focus, like you said, on that third strategic point, but all three of those come into play. And what's really interesting now is as I'm dealing with it and I'm talking to other CFOs, the pandemic is really, if you will, thrown a wrinkle in here, right? So the clients that I'm talking to, the IBM clients, they have to operate their business very differently. And their business models, some of them are changing. Clearly their clients, their business models are changing, they're operating differently as well. So our clients have to react to that and hybrid cloud and that type of a structure really can support that. So there's really an emphasis here now to act with much more speed on this journey to get moving on it, to get there because you have to make these changes and doing those two things in concert really has a ton of business value. Yeah, I mean, the CFOs that I've talked to and the CIOs, it's really kind of industry dependent, right? If you're in airlines or hospitality, it's like, ah, we got to cut costs. A lot of organizations said, okay, we're going to support remote workers, put in VDI or deal with end point security or whatever it was, but we're actually going to double down on our digital transformation. This is, we're going to lean in, this is an opportunity for us to come out stronger. How did you guys approach it in terms of your own internal digital transformation? Yeah, we were working on our digital transformation, you know, a little bit before the pandemic and it kind of followed those three items. When they first started implementing it, they came in and said, hey, if we can move to a cloud platform, our infrastructure savings will be pretty significant. You know, the IT infrastructure savings will be 30 to 40%. So, you know, quick payback CFO types, love that. So, you know, we went forward with that. But then quickly we saw the real benefits of moving to a hybrid cloud strategy. So just as an example, as we were making some of these changes, we found a workflow tool in one of our markets in Europe that was a great tool. And if we wanted to implement that across the business in the old days, you know, we're in 40 countries. We've got 2,500 employees, three lines of business. It would have been very complex because our operating structure is very robust and very complex. And probably would have taken us a year to years to do that. But since we are now on a cloud platform, we got that rolled out, that workflow tool rolled out across our business in months, saving, you know, 20 to 30% of workload being much more efficient in getting to our clients and reacting quickly with them. And in fact, that tool got adopted across IBM because that cloud platform enabled that to happen. And then the great thing, which I didn't even realize at the time, but now thinking more strategically, my IT resource earlier was running at about 50-50. 50 people were working on maintenance, and see kind of things from 50 on development. As we've now transitioned to this cloud, my IT resource is now 70 plus percent dedicated to new development. So now we can go attack new things that really provide customer value. In the pandemic, you know, the first thing you look at is, can we get into more, you know, electronic contracts, e-signatures, things that would provide value to customers anyway, but in the pandemic is like really a significant differentiator for us. So all those things were enabled by that journey that we've been taking. Interesting. I mean, most of the CFI, in fact, every CFO I know of a public company took advantage of cheap debt and improving their balance sheets and liquidity is not the problem today, especially in the tech industry. And at the same time, I'm interested in how companies are using financing. They don't want to necessarily build out data centers, but they do want to fund their digital transformation. So what are you seeing in terms of how your customers are using financing? What's the conversation like? What advice are you giving?  And as we deal with them, financing really helps the return on their investment, right? Aligning the payments of those cash flows for when they're getting the benefits. And we see a real good value in improving the return on those investments and helping, you know, if it's something that's going to go to the board, that really makes a difference to them. So, you know, that's always been a value proposition. It continues to be. The other thing that's helping now, like you said, is even in this environment, people want to accelerate this transition, but it's a big time of uncertainty.  But many of the CFOs are saying, hey, listen, you know, I want to go as fast as I can, help me put together a structure that lets me, you know, get this in place as quick as possible, but not below my budgets, not make me take too much risk in this time of uncertainty, but keeps me moving. And I think that's where financing really comes in as well. And we're kind of talking much more about that value proposition than just, if you will, the improved ROI proposition that we've had all along. I want to talk a little bit more about IBM Global Financing.  But what do people need to know about IBM Global Financing? We actually run three different businesses and we've been transforming our strategy over time. So, you know, right now with IBM being all in on hybrid, we are very focused on helping IBM and IBM's clients on this digital journey, on IBM growing their revenue. You know, we in the past have been more of, if you will, a full service IT financer doing a lot more than just IBM, but we are really focused now on helping IBM. So I think the best thing for IBM clients to know is as you're talking to IBM about the total solution, the total value prop that IBM brings, that financing, that cashflow solution should be embedded in what they're looking at and can provide a lot of value. You know, the second thing I think most people know is we provide financing for IBM's channel. So, you know, distributors, resellers, et cetera. If you're an IBM distributor or reseller, you know about us because just about 100% of IBM's partners use us to provide that working capital financing. You know, we have state-of-the-art platforms where we're just so integrated with them. Again, I don't have to do a sales pitch on that because they don't know us. And the third one just because people might not realize this is we do have, we call it an asset recovery business. It's a pretty small business, you know, it's bringing back equipment that comes off lease or that is used by IBM internally. And while, you know, it's not as well known, I'm pretty proud of it because it really does help with the focus that the world that IBM has on sustainability and reuse and making sure that, you know, we're treating the planet fairly here. So that's a small but powerful piece of our business as well. They're quite broader than leasing mainframes in the 80s. That's for sure.  So how specifically are you helping clients really take advantage of things like hybrid cloud? So yeah, so what we have typically been doing and I can give you a couple of different examples, if you will, for larger clients, what we tend to be doing is helping them, like I said, accelerate their business. So, you know, they're looking to modernize their applications, but they still have a big infrastructure in place. And so they'll run into, you know, budget constraints and, you know, cash is still be careful to be managed. So for them, we are much more typically focused on, you know, if you will, a project-based financing that allows those cash flows to line up with the savings. Again, those are tend to be bigger projects that often go to boards, that return benefit is very important. A little bit different value proposition for more mid-market customers. So, you know, as I was kind of just looking recently, we have a couple of different customers like Forum Engineering or Novi Steel. They're too smaller compared to some of the other customers we use. They are, again, much more focused on how do I conserve and best use my cash immediately? But they want to get this transformation going. So, you know, we provide flexible payment plans to them so they can go at the rate and pace that they need to. They can align up those cash flows with their budgets for their business cycles, et cetera. So, again, we're smaller customers where timing of the cash flow in their business cycle is very important. We provide that benefit as well. You know, I wonder if I could ask you. So, you remember, of course, the early days of public cloud. One of the first tailwinds for public cloud was not the pandemic. The financial crisis of 2007, and a lot of CFOs said, okay, let's shift to an OPEX model. And now, you could always provide financial solutions to customers, but it seems like today, you know, when I talk to clients, it's much more integrated. It's not just public cloud. You can do that for on-premises. And again, you always could do that, but it seems like there's much more simpatico in the way in which you provide that solution. Is that fair? Yeah, absolutely. And this might be a little too finance geeky. I don't know. No, bring it on. If you go back, well, if you go back to the financial crisis and all that, and at that time, a lot of people were looking to financing for, you called it OPEX, but if I was talking about off-balance sheet transaction, right?  First of all, people are seeing through it now much more clearly, but second, you know, the financial disclosures say you kind of have to show that stuff. So that, if you will, window dressing benefit has gone away. So now, which is great for me, we really get to talk about what's the real benefit? What is the real benefit of, you want to make sure that you have known, timed expenditures.  And so, you know, financing under the covers of an integrated solution, and IBM has a lot of those integrated solutions, allows businesses to have that, you know, known timing, known quantities. Most of the benefits that people were looking for from that OPEX cloud model, with that, you know, some of the problems that you have when you try to have to go straight to a public cloud for very, you know, big sensitive businesses, confidential data, et cetera. Right, thanks for that. So, okay, we're basically out of time, but I wonder if you could give us the bumper sticker and key takeaways, maybe you could summarize for our audience. Yeah, for those that know IBM Global Financing or deal with IBM, my view would be in the past, we might have been a little more, you know, out there with our own banner, et cetera. In the future, I think that you should expect to see us very well integrated into anything you're doing. I think our value prop is clear and compelling and will be included in these hybrid cloud transformations to the benefit of our clients. So, that's our objective and we're well on our way there. Great, anywhere I can go for more information? Obviously, IBM.com, you got some resources there, but is there any? Absolutely, .com. There's, I think there's probably a slash financing, but yeah, there's, loaded with information that people need. Excellent, Brian, thanks so much for coming to theCUBE, really great to have you today. I appreciate the time. Yeah, my pleasure. And thank you for watching, everybody, this is Dave Vellante for theCUBE and our coverage of IBM Think 2021, the virtual edition, right back.


Thank you for staying with us. You're still on to the breakfast on plus TV Africa and right now. We'll be looking at the headlines this morning It's time for off the press. Well with me is my co-host Okay, so the first people going to be looking at this morning is the Guardian and the first headline here the major headline here says 1999 constitutions were and here and let's review amendments cost national assembly one billion an hour yearly That's a lot of money. I don't know. Why don't they just jettison this Constitution and get a new one. Everybody has been complaining that the 1999 constitution has a lot of flaws So if you identify them, why are you just picking and choosing every year you find out something that is not good enough for you And you want to change it And I don't know what they do that will cost one billion narrow A constitution one item or two items or not So let's have a constitutional conference if that's the need for us in 2014 or 13 Or thereabouts we had a national conference organized by the then administration of jonathan Where they went to the grassroot and everybody contributed what the fell should change or what should be added or removed or something to the constitution that document was not implemented and To be fair to jonathan. He said he wanted the next administration to look into it See what things can be used and then implemented and the next administration of huharic did nothing about it So that documents that cost nigeria a lot of money is just there lying down It cannot be that the whole of the modern 200 million nigerians didn't know what they were saying So something good could have come out of that but that document is still there So dusted up see what you can do have a constitutional conference change the constitution if you need to Because a lot of people say this constitution came from the time of the military So 1999 till now things have changed things have evolved. Yeah, just go ahead and change it and put the rest of the things that we need to And voilà Everything well for this one. They're saying that they want to do the amendment on state police Just an item. Yes. Well state police value added tax v 80 And electoral reform. So those are the ones they're looking at Well cost one billion But guess what next year again, they might say oh, we want to change this other thing another one billion And based on inflation rates that might even be higher. So I mean have a constitutional conference and then move on That might just work All right, another one here says time to revamp nigeria's criminal justice system Yeah, I think this is this has been a long time coming. We keep crying out about this all the time We need to reform. We need to reform. We need to revamp the justice system because As of right now people don't even trust the justice system Then people say they they lack the credibility that we expect, you know from them But I mean We're still we still sing the same song every single year So when you say time to revamp the justice system, what is actually being done? Do we do anything about it or do we just is it just words that I just You know put out into the air. So it seems like what we're saying something So we're saying something but we're really not doing anything about it Yeah, what what is a crime in nigeria? We need the definitions because sometimes you see some things And it seems as if it's a crime, but you find out it's not a crime And people just do the things they want to do and get away with it What is it if you have laws that you will never implement laws that can never catch anybody? We've seen things that happen You cannot do x y z and then you see the people who are making the laws doing the same x y z and you ask yourself What good are the laws? Let's not let's not even go far Um, I think about two weeks ago or something. We had that issue of the governor of legal state um Arresting the military official who was on a motorcycle driving One way, right? So you see people put these laws, but then they they never uphold it It's just there for the common man. Yeah night in in Lagos. We don't have okada, you know We don't have okada. Yeah, but the policemen use it for okada And if they take you know, they use it as transportation That's what I'm saying.  There are the people who have the jobs that are being paid Uh, maybe the salary may not be big enough But some of these people who were doing the okada work as it is Were graduates without a job. Yeah, and they had to put food on their table regardless. Yeah, so When people were even talking about the governor arresting the person The the the buzz was about the arrest of the person flying one way They were not even talking about the fact that he was using a bike Yeah on a road that should and it was carrying a passenger. Oh, yeah Yeah, and you know most times they they um confiscate these bikes from these young men You know who are riding it because obviously it's it's illegal to ride a bike in Lagos state for instance But guess what they take these bikes and they use it for themselves the bike that that man was driving. I'm not sure it is No, I'm not I'm not sure most times they just you know, they tell you oh, there's been a ban They confiscate it and then they distribute it You know amongst themselves and they start to use it for commercial purposes So the reason why you seized it from someone you take it and you start to use it for that same reason So what are we saying so that tells you when somebody tells you that okay?  I never believe why why they burnt it You know they they they catch someone taking tasks from from our forests in dangerous species Um, they are being killed because they want to transport this thing to other places and make money They say they have seized it and then they have destroyed it They have gone to somewhere they have destroyed the legal refineries that this so it gives you an idea When a common bike will be seized that someone else is using it What is done by uh to those things that they uh the seize And when you hear that we have seen some things that what like two billion naira You begin to ask yourself was it really what two billion there might have been five billion or something It just manufactured the numbers changed the figures. It's a problem. Yeah, but then with our justice um criminal justice system, I think we Yeah, we really we really need to revamp it and let's stop talking. Let's start doing the work All right, um cbn targets 21.4 percent inflation Says naira is undervalued as of right now inflation is about 28.92 percent But cbn is targeting 21.4 percent And says naira is undervalued they should be telling us what is giving rise to the inflation in the first place And how they intend to tackle it. It's not just giving us figures that we are going to do this We're going to do that 21 percent even is still very high So Why can't they bring it to a single digit? It is possible But let them Tell us the things that will be done and let's see how we can key into it as well Or we can contribute also to telling them What really is the problem if i'm a farmer for instance I can tell you the problems that we have as farmers If the other person is a trader who imports from china or germany or anywhere You can tell you the problems that he has so that if you can address that Inflation will have to come down But if you stay stay in a glass house and they're making policies for people Whose experiences you've never had there's a possibility that you don't even their realities is totally different You're totally far far removed from the kind of feelings that your people are feeling so you just Drop numbers and say this and that some things don't work in Nigeria If you say the laws of demand and supply States that if this this this is done Supply will go higher or the demand will go higher. You bring it to Nigeria. It doesn't work So study the Nigerian terrain and not wait wait for imf to come and give you things that you need to do The world bank will come and tell you what to do and you say yes, that's globally acceptable Globally who is global when they talk about the world It's someone that's making that that's saying all of that So that's someone's personal opinion or a group of people That's their own personal opinion But it's the fact that they say Naira is undervalued as of today someone was I saw online on instagram and someone was saying how About 10,000 10,000 pounds is how many million Naira? I think Naira to the pound is about 1700 and something Yeah, yeah the dollar is one one three something. Yeah, I mean I just I feel I feel for businesses who have to deal in effects Because every single day you buy something for this amount And then you want to get something else and that same commodity you want to still get it and it's higher What do you ask yourself? What is this that is not tied to effects in the first place?   What is not influenced by effects? So something fundamentally has to be done about our effects if we want want our economy to grow Because if the Naira keeps going up and some experts have said it keeps going up So it might get to a point where it will be 2000 Naira to a dollar That means it will be like a Zimbabwean dollar now our money That's alarming. It's it's not good. Yeah, let's move over to the next paper All right EFCC probes 347 billion Naira funds. This is punch EFCC probes 347 billion dollar funds someone's foreign firms. So this is a forex scandal I mean, we're just talking about FXM right now 347 billion dollars How do I even do the conversion into Naira? How did how did it get to that amount? What happened? What is what is really going on? This is it a lot. Yeah, but when you say EFCC You know, why are they coming up now? You say EFCC and then you're thinking about whether there's someone there Who is in the bad books of one person or the other who is in power and all that in fact? Let me just take the writer. So he says industrial companies banks gets lion's share on the imifili Social services receive the least forex allocation An anti-corruption agency depends forex scandal probe Detectives may grill five foreign companies next week So Could I sit down? Let's I mean, let's just see let's just see how this develops how the story develops and let's see what happens But I mean properly investigation should be done into this because 347 billion Not Naira dollars That's I can't wrap my head around it. I can't even start to do the calculation. It's that's a lot So let's know what exactly happened. Where did the money go to? Where did the money come from? Where is the money now? How do they accumulate this amount? So these are the questions that we want to ask um All right, another one says FIRS projects 19 trillion revenue 19 trillion Naira revenue in 2024. So this year FIRS is looking to get 19 trillion Naira that's from all the taxes that we pay, right? Yeah, when when when I when you say You're afraid that people may be taxed more experts will tell you that it is not necessarily that they're going to bring New tax is going to make sure that the people who are already taxable Remitting the taxes for instance the companies that are removing money from their staff as tax Money should remit this money because they do not in most cases remit this money to the government and all that But we'll see we're sitting here now You're seeing that you have to do renewal of your car, whatever they were talking about 1000 every year Something that was a one-off is 1000 every year and you tell yourself that oh 1000 is not so much It's just one off and you're paying 1000 and then there are small things Before you know it you're paying That you were supposed to pay So what are they really doing to make sure that money comes into the into the coffers of the nation without necessarily Having to tax people Where is the subsidy money going to are they sincere about how much has been made? Where is the money for all other natural resources that we are mining in this country going to do we have a figure for that All that will give us a lot of money. Where is even the money that is being repatriated from from other places? corrupt Amounts of money that we'll give paid into Coffers of other countries Switzerland and the rest of them Do they even account for it in the time of buhari when abacca lude was repatriated to nigeria It wasn't part of the budget as some of the money that will be used to be spent, you know When it came they did trade that money Trade that money I don't know how Oh god I want to say oh my god, you took him right out of my mouth. I just want to say that but like Hold it in hold it in so well. Yeah Well, let's move over to politics. Um on the assembly screened new deputy governor as ayedati was sacks cabinet What's your thought? I know you have a guy like with the whole undo thing. I'm sure you have more more knowledge on that So no, not really but people like they said and you said that the people expected that the deputy will come from on those central but ayedati were Graciously, I would like to use that word graciously choose someone from The elite governor's place. I think I think that was a good consolidation to the people of the war He might want to test To contest the next time He will choose a deputy maybe from somewhere else, but for now I think it was a good move for him Let the people of our war feel that they're still there in government and they lost a brother But they didn't lose everything even though.  They are suffering These people so it doesn't mean that someone in your religion will necessarily give you a better life Someone from your locality will necessarily give you a better life I don't know if the people of bayals. I will say when jonathan was there. They were better than now or or before then I don't know if the people of dow rap will say they were better. They are better off Because buhari was the president and all that. I don't know what people just see in My person has to be the person that is there And I don't know why it's also connected to why the northerners are saying that you cannot move any department of cbn Or any other thing to lego state. You're depriving the knot. I mean if something is located in your place What does it say does it mean that everybody in that village would be employed because there's further character So wherever it is people from the north south, yes, they have to be represented. So I don't know We have to change that psyche We do all right. Let's move over to the nation and The us6 removal of barriers to investments. So blanking lots to new boys economic policies Nigeria offers compelling opportunities for investors. But then blanking I said that Nigeria must remove the barriers to investment That we have currently what do you think about that? I mean the president goes to different countries Seeking foreign investment Now he has gone on a private visit I do I wonder what that means a private visit is on is he on leave We need a president right here at home and he's going for private visits to France So a private visit is he going to pay his own way to that place? Will he use the money the taxpayers money to go on a private visit? I don't know what it says is globetrotting To make sure that he will Get investors to come into the country and all that then is the is the environment conducive enough For foreign investors to want to come in and stay and thrive Because I mean if I'm putting my money somewhere, I expect profitability. So how is the social Social economic environment in Nigeria as of right now For foreign investors to come in and say, oh, yes, I can come here and I know I'll be profitable my business You know would thrive and whenever the business is no longer profitable and I want to go and I can't leave They handcuffed me Anyway, I think it's just a subtle way that blinkin has used to tell him that conditions are too too Bad in Nigeria and you have to do something about it and we cannot come Even though he said oh blinkin said The biggest economy the largest population he was giving all the good things about Nigeria But after that he said that the economic the barriers have to be removed for investments What are these barriers? I'm sure the presidency And all the people in government and know it but are they ready to do it? Because first of all no matter what you see as an economic expert or anything You have to think about security. The security is not there. So How can I come and invest in a country where there's no security? I can I come and invest in a country where I'm not even sure of the stability of your your currency I'm not sure today. It could be anything to so there is no way I can plan Yes, your currency is stable. The planning is difficult So investment will be very difficult in this place. It will be very difficult And now that companies are leaving What is being done by the government to encourage the companies that are already indigenous companies that are staying here Even the indigenous companies are thinking about leaving to Benet to Ghana to other places and just using Nigeria as the market Why do we even keep looking for foreign investors? Because I remember China had to you know block their borders They had to go through that process of saying, you know what we're shutting out of the world We want to start producing our things and I remember one time they started this whole campaign of Buy buy Niger to grow the Naira. I can't remember how the phrase was coined But it was some was of some sort buy buy Niger to grow the Naira So they got all their costs from outside the country They were going to buy 160 million Naira SUVs The yacht as well that's from outside of the country But yes, how do we promote Nigerian goods because all we do like I mean we're talking about forex now all we do is buy things From outside all we do is imports Are we looking at how to export because that's even how you grow your revenue? So we need to start looking at you know Encouraging the businesses that are here Producing for ourselves at least let's even produce what we use first before we say, okay The standard is good enough for us to export now. Let's try it out because if you never try you never know So we I don't know if I'm capable of producing this This the ceramics of you know to create this mug right now I don't know what the capability of Nigeria is to say, okay Yes, we can produce it and it's good quality that we can use and what we say Oh, this is amazing We start to export that and that brings more revenue into Nigeria So we need to start looking for you know, not just looking for foreign investors The ones that are here from what they encourage them to be able to do better Well, there was this story. I was told a long time ago how someone perfected The yam pounder he invented it in Nigerian because of course they don't pound yam in china or So he did that and was looking for support and all that he never got it Then he sold the patent to somewhere someone else Abroad and then the person produced it and brought it back to Nigeria They don't pound yam in china Now we have yam pounders from other places and we're so happy that it's not from Nigeria and all that Well, there's even that stereotype the moment, you know, that it's not it's Nigerian You're like, I don't want it but you say oh, it's imported. Oh, yes, definitely It has to be of good quality But we can also make things that are of, you know, good quality all Nigerian products are not inferior So I saw I saw a small a young boy hocking or her or her is a vegetable Yeah, so he was hocking or her and he said this or her is from Italy, you know And people were just laughing and they were enjoying it But it just told me the kind of mentality we have so that everything has to come from outside before it's regarded as something that is good enough Yeah It's it's it's a very bad thing for us very bad Okay, um well Let's just take maybe let's just take one more before we wrap the wrap up this segment so Chairs of government share 1.1 trillion Naira from federation account revenue They keep sharing our money I was having a conversation with someone yesterday and I said I feel like Nigeria the money they've collected it They've shared it and everybody's just looping right now and that money is just It's just with some select few the one percent of the one percent Because you hear that they are borrowing money. They are getting money from this a batch of looters call me game Yada yada yada, but then we're not seeing this money How is the tiers of government sharing 1.1 trillion Naira from the federation account revenue yesterday? There was this news that um Oil producing states there was a an amount that was given that the oil producing states have Shared among themselves within a particular time Yet their debt profile is rising even higher and higher and I was just asking myself What is the reason for this when you talk experts will tell you that borrowing is okay So long as you're using it well, but are they using it? Well, and why are they borrowing? Because whatever they are doing I must say whatever they are doing in the states and most of the states that I know Money that they could get from the state itself can do all those things. So what are you borrowing for? We are not seeing any significant improvement in your state because of the money you're borrowing In fact, some of the things are dilapidated. You go to cross river for instance The obudu cattle ranch that used to have wonderful facilities is going down The tinapa project that had so much money pumped into it is going down So every every government comes and they want to have a legacy project And when they have this legacy project the next one that comes there's a continuity And I say government is a continuum. You are just sharing this money and nothing else You go there share it put it in garamos go and then that's the end So government has to show working and yes, I love that show workings You have to win the trust of the people because if I see that There will be quality education the roads will be good security will be good And everything I need health will be good. Then you ask me for tax I will have no problem even if I'm giving you half of my salary because I know that half of my problems are already solved Yeah But I pay tax I still have to be the one to go and scoop Soil from somewhere to come and fill potholes.  So why am I paying tax? Well for you to share Well, this is where we have to wrap it up on this segment. When we can't when we return we'll be looking at a hot topic Please stay with us


Good morning everyone, I'm Stefano Garzarella and I'm software engineer at Red Hat and today we will talk about VSOC, a way to communicate between VHEM and the host with a very minimal configuration. So, it's not working. What happened? Can I continue? Okay, this is the agenda of the talk. First of all, we will have an overview of VSOC and looking also at some use cases. Then we'll take a look of implementation details, looking also at some transports that implement the communication channel between host and guest. We will see some new features such as multiple transport, local communication and network space support. And finally, we'll take a look of tools and languages that support VSOC socket. During the presentation, we'll have some very short demos to understand better on how to use VSOC. VSOC is the acronym of VHEM socket. It allows you to create a communication channel between guest and host using the standard POSIX socket API. And a peer, I mean a guest or a host, is addressed by a context identifier, CID. And we have well-defined CIDs, for example, CID HANY, used for Liston on any CID. It's CID local, it is a new one, and it is used for local communication. And CID host, its value is 2, and it is very useful in the guest to reach the host in any condition. Compared to a network interface where we need to set up IP addresses for both host and guest, with VSOC, the only thing to configure is the CID to assign to VHEM, and this can be configured by the user or automatically by the management tool. Anyway, in the guest, no configuration is needed, and the host can be always reached using the CID host. As we said, an application can use socket API such as bind, Liston, send, receive to create a communication channel between guest and host, and to use VSOC. The address family to use is AFVSOC, and the address family to use is AFVSOC, and the API socket is addressed by a 32-bit context identifier that identifies the VHEMs or the host and the 32-bit port to identify the service. So if you want to adopt an existing TCP application to use VSOC, the only thing to change is the peer addressing using the VSOC address family. Stream socket are supported by heavy transport, and datagram instead is transport-dependent. Now we can talk about some use cases of VSOC. As we saw, network application can be easily adapted, but VSOC is very useful for guest agents or when the hypervisor want to provide some services to the guest. Some real cases that use VSOC are the QEMU guest agent or the Cata container agent. It is used to start a container in a VHEM and control them. Another example is the Android bug bridge. You can use VSOC when you have an Android device emulated in a VHEM and you want to use ADB without configuring network cards or CDL ports. Going into the details under the VSOC core that provides the socket interface to the user application, we have several transport that implement the communication channel between guest and the host. These transports depend on the hypervisor, and we can put them in two different groups. The first one is the guest-to-host transports. They run in the guest and usually they are device drivers. Currently we have WurthIO, VHEMCI and HyperV transport. Another group is the host-to-guest transport. They run in the host and usually they provide the device emulation to the guest. For now we have Vhost and VHEMCI transport. In the QEMU KVM environment we have WurthIO transport running in the guest. And VHOST transport running in the host. Both transports provide the interface to the socket layer through the VSOC core and they use the WurthIOQs to exchange pockets. The VHOST transport provides the internal WurthIOV SOC device emulation to the guest that implements the WurthIOV SOC device driver providing the WurthQs to the host and they use the IOHEMT FD and IQFD to get the ninja events to the guest. Let's try to start a VHEM using LibVirt, QEMU and KVHEM and try to communicate using NCUT. It's a very simple demo. We can start our VHEM with VRT install. We can create our VHEM with VRT install and we can configure the amount of RAM, the number of CPU. But the important thing is this parameter to attach a VSOC device and we are configuring the CAD Assign to this VM. In this case it's 33. Okay, VRT install is using LibVirt to create a QEMU, KVHEM virtual machine and it will configure the parameters that we specify such as the amount of RAM, the number of virtual CPU and it will attach the device that we need such as the block devices for our disk image and the VSOC device configuring the CAD that we assign it to this VM. Now just with the boot. Okay, we can log in. Okay, this is the host-to-guest communication demo. So what we want to do now is to start NCUT in the host listening on port 1234. We use the verbose mode just to see the detail of the connection and we specify dash-vsoc to use the VSOC socket. This is a standard NCUT and now support VSOC. Okay, now what we can do in the guest is to try to connect to the host. So using NCUT as well we need to specify the CAD of the remote peer. In this case is the host and we can use the well-defined CAD too. So the guest can reach the host using the CAD2 in any condition and the port where NCUT is listening. Okay, you have the connection, so I am the guest. Now we can do the opposite, starting NCUT listening on port 1234 in the host guest and we can connect from the host. In this case we need to use the CAD that we assign it to this VM, so 23 and the port where NCUT is listening. So, okay, we have, hey, I am the host. Yeah, we can switch to the slide. Now we can talk about new feature. The first one is multi-transport. So before Linux 5.5, the VSOCore was able to handle only one transport at runtime. So it means that in a nested VM environment we couldn't load both host to guest and guest to host transport together. For this reason we introduced this feature. So starting from Linux 5.5, the VSOCore is able to handle two types of transport loaded at runtime together. The host to guest transport to handle the host part in the communication. So in this case to communicate with L2 and the guest to host transport to handle the guest part in the communication. So in the KVM environment, the L1 guest will load both birthday or transport to communicate with L0 and Vhost transport to communicate with L2. Another feature recently added is the local communication. This can be very useful, for example, to testing and debugging applications that use VSOC without running VMs. Think about CI. It will not be simple, for example, to start a VM, run a synchronized test between host and guest. For this reason we introduced the VSOC loopback. It will be available in Linux 5.6, and we also introduced a new CAD, the CAD local. Its value is one, and can be used to do the local communication on the same host. Anyway, other CADs can be used. For example, if we are inside the guest, we can use the CAD that is assigned to this guest, or if we are on L0 host, we can use CAD host to do the local communication, because we are the lowest layer. We don't have any other VMs under us. Okay, let's take a look at local communication. As we previously done, we can start NCAT listing on port 1234, and this time, still in the host, and try to connect with NCAT using the CAD1, that means, okay, do local communication, and that's it. We are local. And starting the NCAT listing on port 1234, we can do the same thing also using the CAD2, because we are on the L0 host. Okay, this was very fast. Another feature is the network namespace support. It is an experimental feature. The current implementation does not support network namespace. This means that resources such as the CAD allocation are shared between them. I'm currently working on these. I sent some patches upstream with the proof of concept. So the idea is that network namespace support can be useful in the host to partition VMs between different VM monitors or at final generality. And these features allow us also to assign the same CID to VMs running in different network namespace or to run applications listing on the same port but in different network namespace. So for example, in this case, we have two network namespace plus the default one. So we are able to start three different VMs with the same CID and three different applications listing on the same port. The network namespace support can be also useful in an asset-VM environment. For example, to isolate host application and guest application listing on the same port with CID handy. So for example, in this case, we have two applications. One is the guest application that wants to communicate with L0 and this one is a host application that wants to communicate with L2. Oh, sorry. Creating the NetNS1, we are able to... So the application in the NetNS1 can communicate only with L2 and the application in the default network namespace can communicate only with L0. So in this way, they are isolated. Let's take a look on this experimental feature. So this is the network namespace demo. The first thing that we can do is to create a new network namespace. Now, we can start inside this NetNS1 hand-cut listing on port 1234. And now this guest... We started this guest before the creation of NS1. So this is not running in the NetNS1. It's running in the default NetNS1. So if we try to connect to the host, the connection is refused. So what we can do now is to try to create a new VM inside NS1. So this time, we can use QMU directly to create a new VM in the NS1. And the important thing is we want to attach a vhost with sort device. And we are assigning the 33 CID. So it is the same CID. It's just an example to show you that with the NetNSpace support, we are able to have two VMs with the same CID because they are running in two different NetNSpace. Of course, I can assign a different one. Or using libvirt, we can leave to libvirt to automatically choose an available one for us. So now the VM is booting. And... Just wait. Okay, we can log in. Now, what we can do now is to do the same thing. So try to connect to the host using hand-cut. And yeah, we have the connection. Okay. And it works. We can turn off this VM. And now we can talk about tools and languages that support VSOC. Most of them are merged upstream. And these are the useful tools that introduced the VSOC support in the last few years. With these tools, we can dump traffic, statistics. We can test the host-gas communication. We can test block devices using NBD over VSOC. Or we can measure the performance with IPERF. Or we can do very cool things with SOCAT. For example, to concatenate the CPIP SOCAT with VSOC SOCAT. Or to VSOC SOCAT. For the developer's point of view, these are the languages that allow us to develop application using VSOC SOCAT. They mainly provide the binding for the VSOC address family. And this is an example, very simple. We have two Python applications that allow us to communicate between guest and host. On the left we have the client running in the guest. That's one to connect to the server running in the host. We can try them. So this is the Python example demo. So we can start Python in the host and in the guest. Now we need to import the SOCAT module. It is the only module needed. All the VSOC staff are inside this module. At this point we need to create our SOCAT. And we need to use the AF VSOC address family. And we want a stream SOCAT. We can do exactly the same thing also in the guest. And since we want the server in the host, we need to bind this SOCAT to an address. And in this case we are using CID HANI because we want to list them on any CID and port one, two, three, four. Now we can put the SOCAT in the listing mode and we can wait for a connection on the accept system code. At this point in the guest we can connect to the host. So using the connect we can use the VMR to see the host, CID host, or the true value. So it's the same. And the port one, two, three, four. Now we have the connection. So in the host we can wait for some bytes and we can send something from the guest. We send, okay? We receive the data. So we can print the remote CID, this 233. It was the CID that we assigned to this VM. The remote port, it is a random port assigned to the SOCAT by the government. And the data received. So concluding, VSOC is very useful when we need a point-to-point connection between host and guest. Existing TCPIP application can be easily adopted just changing the address family of the... Just changing the address family of the SOCAT so just changing the peer addressing. And more and more tools and languages are supporting VSOC in the last years. And about new features, nested VMs will be supported in Linux 5.5. Look back in Linux 5.6 and hopefully, natural nest space will be available soon. Thanks. And question? Yeah? So you only if the other one is not loaded. So I'm going to say how this works. I mean... No. Sorry? Yeah. It was at the other side. Yeah, VM address C hosts only if host to guest is loaded and guest to host is not loaded. Yeah, this is for local communication. Sorry, the question is... I wrote in the slide that the CID host is supported only if host to guest is loaded and guest to host is not loaded. But it means you can use CID host to do local communication in this case. So only if you are on L0. So if you don't have any host under you, you can use the CID host for local communication. Yeah, it's... Thank you. That's all for that. Okay. Yeah, please. Yeah. Sorry. Can you repeat? Yeah, the question was... Can we map this socket on Unix file, for example, Unix domain file? Yeah. Yeah, you need an app and user space application to do this. But for example, with Socat, you can do it. So, for example... Yeah, exactly. Yeah, you can create a bridge with Socat and use the QMGest agent. Yeah, send the patches to the maintainer is reviewing, but the idea is to have it upstream. Okay. Yeah. If I understood, you mean we can remove the natural cards and use Vsoc? Oh, okay. No. Okay, the question... Yeah, the question is if you have two natural spaces, can we communicate between natural space using Vsoc? Yeah. For now, there is no natural space support, so you can do it. But if we enable the natural space, for now we are not allowing to communicate between two different natural space. So maybe it can be a feature that we can add to do it, or you can use other wave, like Unix domain socket or standard socket. And you have the two hosts connected, for example, with the TCP or... No, for now, you are not able. You need to use a new user space application to do this kind of bridge. And Socat was one of these kind of complications that you can connect two different kind of socket, like one TCP socket and Vsoc. Yeah, it's something... You need a user space application to do the bridge. And what kind of limitation do you mean? Oh, no, there are no limitations. The CAD are 22-bit CAD, so you can start whatever, how many guests you want. It depends on, of course, memory of your machine. Okay, we are run out of time. Thank you very much.