on the sportsmax zone and I can't tell you that within the last 15 minutes the Caribbean has won its first medal at the World Indoor Track and Field Championship in Glasgow Scotland the Jamaican sprinter Akeem Blake getting bronze in the 60 meters one to finish for the USA the fast starting Christian Coleman winning ahead of the fast closing Noah Lyles so Coleman wins gold Lyles gets silver and Akeem Blake the Jamaican is in the bronze medal position this on day one of the three-day World Indoor Track and Field Championship in Glasgow Scotland we're gonna talk some cricket now because the region's best women's players well kind of because Hayley Matthews isn't there well they'll be back in action on Monday when cricket West Indies the CGU United Super 50 Cup bowls off the T20 blaze is set to start later this month on the 17th of March to be precise. St Kitts and Nevis will host the tournament across three venues Warner Park Connery Cricket Centre and St Paul Sports Complex today we'll be taking a closer look at the six teams and their chances of winning the title the Leewards cricket guru Vernon Springer-Schedule to join us shortly let's start by looking at some of the team rosters the defending champions in the CG Super 50 Barbados they'll be without as I just mentioned their inspirational leader and West Indies captain Hayley Matthews who is in India playing in the WPL and we'll look to at the beaten finalist last year Jamaica who will be led by the former West Indies captain Stefani Taylor. So here's the Barbados lineup Kaysia Knight who will captain the team Alia Alene, Shanika Bruce, Asavi Calender, Zalea Campbell, Jamila Connell, Naijani Khumberbatch, Erin Deem, Kylia Elliot, Ellison Gordon, Tiana Herbert-Meyers, Trisha and Holder, Kishona Knight and Alicia Scantlebury for the strong Barbados team bears we said they are the defending champions the Jamaican team is being led by Stefani Taylor, Rashada Williams, Janelle Henryn, Natasha McLean, all West Indies players Abigail Bryce, Vanessa Watts, Nisha and Waysum there's John L. Dears, Kate Wilmot, Nicole Campbell, Chadyn Nationals with West Indies player Jessica Garcia, Selina White and Kanisha Ferron, the Jamaica lineup there for the CG United Super 50 Club and the T20 Blaze tournaments that are coming up in this month and being played in St. Kitts and Neves. So I know you get excited about women's cricket Mariah partly because your sister Karishma is involved and a top player for TNT and a top player for the West Indies as well. We just went through the Barbados and Jamaica lineups two of the stronger teams that are expected to do well in the tournament. Yeah and Barbados will be without Haley Matthews as you said but Lance I still think despite being without their regular captain Kaysia Knight steps in and I think she will do a great job they have a very strong squadron paper and I think you know Barbados will put up a really good defense even without their skipper so nothing for the Barbados fans to be too worried about. I know the Red Force Divas they got to St. Kitts and Neves earlier today. They're already there you know they're settled and everything and they're just looking forward to see if they can snatch a title as well. I think it's a very very open competition Lance and what I want to zone in on is the Red Force Divas bringing in two youngsters. I had Brianna Harichur on in case you missed it. She's 15 years old but when you speak to her Lance you know she's very very mature. She's very level headed and she's looking forward to make a mark in this tournament. They will be under the leadership of Brittany Cooper saying that they'll be no Anissa Muhammad this year so I think a lot of the teams will be looking a bit different but for me it makes the competition even more exciting because youngsters a different skipper a lot to look forward to. Yeah all right we know how Vernon Springer as we said the Leeward Islands cricket guru. We just went through Vernon as you join us on the show. The rosters for the defending champions Barbados and Jamaica being led by the experienced Afane Taylor with quite a few West Indies players on her roster and the Barbados lineup also looks pretty strong based on the international experience of many of those those players involved. Vernon do you consider Jamaica and the Barbados teams to be among the tournament favorites. Well I think all teams are favorites. I mean this competition Barbados without their captain Haley Matthews that is going to be she's going to be surely missed because you're talking about batting and if you've looked over the years of the cricket West Indies women's tournament the Super 50 or the T20 the bowling for most of the teams have been able to hold their own. What has been the major concern is the batting. So when you look at the Barbados team they're going to be led by a new captain Tysian Knight who is at age 32 wiki keeper. I'm still looking to try and prove something at this level and she would have to really step up now and fill the shoes now of her captain Haley Matthews. Garner you can't count out Garner. You are showing Campbell who is the captain. The most experienced player some 108 ODIs for the West Indies 125 T20s. So they'll be looking for a Sherwin Fraser in the fastballing lineup. I'm looking forward to see how well she will be able to shape shape up Jamaica on paper. You're talking about under the most experienced women's cricketers in the world. Stephanie Taylor 154 ODIs 117 T20s over 5,000 runs for the West Indies seven centuries. She is no mean feat but and Chanel Henry who I thought was the fastest emerging all around the coming in. So you've got to keep your eye on Jamaica Natasha McLean. You know she's a veteran. She can be able to upstage the apocat. Trinidad and Tobago know Anisa Mohammed.  So their batting will be led by a couple of youngsters there. So they'll be under some pressure. Winwood Islands and Leeward Islands when you match up. In fact the Winwood Islands went to think it's a new this early and participated in some warm up games against the Leeward Islands. They played and they'll come in a willow park in Nevis and a water park under the lights. So when was the fast emerging. They have their captain Afifletcher. You know Afifletcher is known for taking wickets. But I want to see she's she's beginning some runs in some warm up matches as well Vernon because she's I think she's batting in the middle order or maybe in the top. I think she's batted four or five a couple of matches I've seen from the scorecards from the from the from the winwords. Let's let's quickly look at the Ghana and Leeward Islands squads and let's assess them. You just referenced a couple of things about those two teams. But let's look at the rosters there and get some more in depth comments from you on Ghana and the Leewards. Well I did mention about Ghana. I said you can't talk to me and come back to captain. I'm looking forward to see Sherry and Fraser. Young fastballer and even down to Sineta Griman. But the Leewards. The exciting news is that Tanisha Bickney Hector has returned to the lineup after missing the tournament last year. You have a new captain Amanda Edwards who in the tournament last year scored 189 runs with a high score of 74. One of the first players to score half century for the Leeward Islands women's team. She replaced Sunelah Willett was really not come to the party as yet. But the emerging Jen Jazeera Clarkston the young 17 year old she turned 18 in the Stampern ship on the 12th of March is an exciting time for joined by some young players in Kimberley Anthony and Sherry and Moses. Now Tanya Martin is a little medium baseballer who had a stint in England a couple of seasons ago. So she should be looking exciting. But the news here is that Renice Boyce from Chilling Island Tobago will also be part of the Leeward Islands set up this year. Yeah. I see that along with a US based player Shibani Bhaskar. Can you talk to us a little bit about that. Well Shibani has played when she was the US captain played a couple of seasons. Missed the last two seasons. So she's in. We also have a Canadian international also being part of the Leeward Islands lineup. So plenty plenty to look for at home. All everything set matches at Warner Park Connery and St. Paul's complex. As you heard the teams are going to be staying at the Marriott hotel so everybody is really excited and ready to go. And it could be a chance for us now to see some new stars because there's no danger that in. I don't know if Stephanie Taylor will be going on maybe after this World Cup. So there's a chance now to be able for some young players to put their hand up and say well hey listen we want to be able to carry this flag for women's cricket. Yeah. All right. You just referenced the warm up matches that the windwards have been playing against the Leewards because they arrived there a full week ahead the windwards. And from what I've seen I think they've played well in almost all of the matches that they have played. We're going to look now at the Trinidad and Tobago and Windward Allen squads and just talk a little bit a little bit more about them because we've already touched on on on what they may have to offer. But the Trinidad and Tobago team will be led by Brittany Cooper. She's she's captain of the team. Yeah. Karishma Ramirak that's Mariah sister is the vice captain. Chanel saw Samara Ramna. Janabi Joseph. Leon Kirby very experienced player. Corbina Alexander also experienced Kanisha Isaac Brianna Haricharan and Katie Jazz Mitchell. Selina Neil, Shanice Pascal, Shalini Samaru and Steffi Sugrim and Mariah you spoke with Haricharan earlier on your in case you missed it show and you're very impressed with how articulate and how business like she appears to be going into the tournament. Yeah. And what stood out for me is one she attends a very prestigious school in Trinidad and Tobago which is St. Augustine Girls High School. When you know like a young girl is attending one of those schools you know she's brilliant. Second thing is she plays national tennis as well land. So I think you know just those two things that I say speaks for itself. It speaks volume. Yeah. Then you know if you listen to the interview which will be aired this weekend she has plans already like you know she really wants to represent the West Indies senior team. So she goes into this Super 50 and T20 with that in the back of her mind knowing that she's gotten this opportunity to of course leave her mark. So I was speaking to my sister about her you know pre interview and she was also telling me she can bat a bit. So she's a good bowler. She's very agile on the field. She can give you some runs. I think she is forced to be reckoned with. Yeah. And Vernon I reckon that Anisa Mohammed's retirement has left a bit of a hole for TNT based on how long she's been there. But the TNT squad looks solid and there are some young talented players in there. Well you will always Anisa Mohammed will be surely missed in terms of leadership. It's like a Leon Johnson out of a guy and a happy eagle squad because Anisa Mohammed came in crucial tournaments for Trinidad and Tobago and even picking up wickets and came and batted well just like Afri Fletcher who will come into this tournament with some experience. But my major concern very quickly lands is in terms of preparation and how the franchises how regional boards are treating women's cricket. And if we go back to even Guyana. Guyana had like about maybe three four county games before they selected their team. It's not everybody sounds like they're organized like a Trinidad and Tobago. The Winwood Islands had a competition in terms of the Leeward Islands. They didn't have a competition so they had to muster up like 26 girls to camp in Nevis. So in terms of how we are preparing women's cricketers. We have a lot of young players coming through. But I think there needs to be more focus on women's cricket. We have to really find some some coaches who are going to dedicate themselves to the women's game. So even the West Indies are organizing West Indies team tours. When the girls go back to their territories. I don't think they have organized coaches who are willing to take them to that next level. And that is a problem which we have to deal with. Yeah. Before we look at the Winwoods team I just want to point out that I saw the departure function for the Jamaica team leaving for the tournament. And the Jamaica Cricket Association actually held a send off function for them which was never done before. And the general narrative coming from the Jamaica Cricket Association was that they were trying to establish some more equity with the cricket and ensure that the women get as much attention as the men. So that certainly was a good sign. The Winwoods squad as you mentioned Vernon will be led by Affi Fletcher. And their squad has been reasonably well prepared. They actually had a Winwood Islands tournament in I think it was Grenada before they selected their team. So they should be match sharp. Affi Fletcher captains this team. Tracey Byron, Nerissa Crafton, Malika Edward, Pearl Etienne, Ornisha Fontaine, Amia Gilbert, Janelia Glasgow, Kimon Homer, Zeta James, Keanna Joseph, Namia Marsala. There is Karina Noel and Selena Ross as well. So a couple of West Indies players or players with West Indies experience in this setup, including the 41-year-old Pearl Etienne, who you would know well, Vernon. And the Winwoods team, I think from a preparation standpoint, appears to me to be one of the teams that had the kind of practice and not only match practice but camping experience. That should put them in good stead for this tournament. Well, you can take your eyes off of the Winwood Islands cricket board. They have really invested in women's cricket. In fact, they have a psychologist as part of the team and they build up for this camp coming to think it's a Nevis pretty early was an indication. In fact, it might have been even more interesting because Trinidad and Tobago, just because of flights, they were also due to get in early. So you'd have had a triangular tournament with Trinidad and Tobago, the Winwoods and the Leeward Islands. So in terms of preparation, Lance, you hit the nail on the head. I think out of all of the teams, the Winwood Islands will be the most maybe prepared team coming out of a competition at the preseason camp just before and then they got to think it's a Nevis a week more earlier. But you know, Lance and all of us, the game is played on the day and the ball is round. So we're looking forward for some exciting, it's 15 games in the Fiji United Super 50 and 15 more games in the T20 players. And let's hope that we can be able to have some great weather and some great cricket. Yeah. Oh, Verna, we'll be talking to you during the week as the tournament starts off on Monday with the opening games. And that runs through, I think onto the 13th of March and then the T20 play starts on the 17th. But we'll be paying a lot of attention to this women's tournament, both the 50 over and the T20. So, Verna, and thanks for linking with us and we'll be in touch again next week, I'm sure. Yeah. All right, God bless you. Yeah, looking forward to you guys. Looking forward to this tournament, Mariah. Yeah. Hope it's going to be good and the competition will be great. And some new players, as the West Indus tries to rebuild its international team, get some new promising players performing in this in this tournament. We go to break. We'll be back with more on the Sports Mag Zone after.


Čutvo je trest o izbranju. Jaz stawim števi izbranje v plašku, appelj vznečati tu krušanje, imaš nekaj ali pri našega naživama. Stavim števi izbranje na konstativendi. Danes zelo. Tudi, da post kalim u vih, gledaj se o izbranje, da je viljene izbranje takv. Jebeni neko izolajte izbranje, naših, nača na stran. Let's try to build up some big families of examples. So the first type of examples I want to discuss are surfaces of revolution. Revolution actually in geometry means rotation. These are not angry surfaces. So what does it mean? It means you take a curve in some plane and let's suppose, for example, we start, and actually here I switch from our usual notation. So let's take a curve in the xz plane. Let's take a, it doesn't matter, let's take a planar curve, whatever the plane is, by changing name to the coordinates, you call them x and z. Now that means that in the x, but still I remember that there is a third one, y. So if I pick a curve, that means it lies on the plane of the blackboard in my picture, and I suppose I'm taking a curve which does not touch the z axis. For example, again, if you want to find an axis, it's enough to find a line which is not crossing this curve. Being in this plane, it means that for some choice of parameter, this curve can be parameterized in the following way. It is a function f of u, usually I call them t, the parameter on a curve, but of course this will be the first parameter in the two parameters of a surface. So now I prefer to call it u. Now it lies in the y equal to zero plane in the xz plane, so it's f zero, and then for some other function, g of u, don't be confused with the names of the coefficients of the second fundamental form. These are just two functions. It's impossible to make confusion. Now what do I want to do? On this I just assume, sorry, otherwise I have to keep on being careful about, let me call it v, the parameter on the curve, which is rotating. Now the only thing I am assuming here is that f is a positive function, just to avoid some problems. And suppose that this parameter lives in some interval, closed or open, doesn't really matter, and let's call it ab. In principle it could be the whole line r or a subinterval. Now to each point of this curve we make a rotation. We have already seen an example of this type. When we construct the torus of revolution we have taken a circle here and rotate every point. So basically now I drop the assumption into the circle and I just do it in general. So for each fixed value of the parameter v, meaning for each point here, I want to add the circle of radius, this distance, in the horizontal plane. And I want to do it for every point. That means I'm certainly going to make a disaster, but something like this. I want to build this object here. How do I do it analytically? How can I parameterize something like this? For any point, so that means how can I construct some kind of map whose image, from some domain of R2 whose image is something like this. I add another parameter, of course u, and then I will try to think where this u will live. So, such that, for example, u will be the parameter on the circle. I'm perfectly able to parameterize the circle. And actually the only thing I have to do is to put a cos. You see? This is by brute force. The image of that thing is by brute force what I drew here. Now, where does this parameter live? You see, for u equal to zero, I get the old curve f0g. For example, for u equal to pi over 2, I get another profile because this becomes zero, this becomes f, and this is still g. So that means I'm moving, when u, for example, is increasing, I'm rotating in this direction and then I get the same profile, but now in the yz plane, I mean, whatever, so the curve in this plane here. It has the same shape, but it's on a different plane. And as long as I move u, I keep on rotating this profile around. Now, if I want to cover the whole surface because the geometric I said I want to add for every point of this curve the whole circle. Am I able to do it in this way? The key point is a hole. Well, a local chart has to be defined on an open set because, of course, what is the circle? The circle would be cos u sine u with u between zero and 2 pi. But if I add the extremes of the interval, as I should, if I want geometrically the image to be the whole circle, the circle is not open. On the other hand, if I enlarge the interval, I say, well, but okay, who cares? Let's take u to be any real number. But that means I'm keeping on going around and around and around and around, many-time periodically around the z-axis. But then that would be good geometrically but not analytically because x fails to be injective and it's one of the properties of a local chart to be a one-to-one map on its image. Because sometimes the two things are fighting. I want a one-to-one map and I want it to be defined on an interval, on an open set. That's impossible. If it's open, I'm missing one point. If it's one-to-one, I'm touching one point more than once. So I'm dead. Here I have to take. I'm forced, if I want this to be a local chart, I force this to be defined on zero-to-pi, for example, open. So now our domain u, remember we always draw this picture, x and some domain u, how does it look? So this is u and this is v here is zero-to-pi and here you have an ab, whatever that is, and so basically this is defined over the rectangle, the open rectangle, and this is going to be my u in the general theory. But this is not enough to cover the whole surface. So that means that this type of surfaces must be covered by at least I have to add another map. In fact, which points are not covered? If I make this choice, the points which are not covered are exactly the ones I started with, so strange enough. I'm losing exactly this profile, but this profile is lost. So I need to add another map which covers these points, if I want to prove that this is a regular surface. How do I do it? Well, and that's the point. Now we are old enough to be able to cheat without being cheated yourself. Because I add another map which looks exactly like this, but now u does not lie here, but lies, for example, in any interval which contains zero. So basically it would be the same x, but I look at it twice, once it's defined on this rectangle, and another time is defined, and I would call it u1, if you want. And then I define it on another rectangle which covers also this, which was the part which was missing in my surface, and I call it u2. But if this is the story, I just remember it, and I stop writing it. So I will always say, I take a surface revolution and the chart like this. Then if I want to make global considerations, I know that I have to take into account this phenomenon. Now, I can also assume a curve parameterized by arc length. I mean, if it was a regular curve, there is no arm, every regular curve is parameterized by arc length. So I start with an equation, a differential equation relating f and g. Of course, the tangent vector would be f prime. Of course, when I put prime, it means the derivative with respect to the only variable, which is v. So the tangent vector would be the vector f prime, zero g prime. The square root of f prime squared plus g prime squared. And then parameterized by arc length means the norm of this, so the square root of this is equal to one. So I drop the square root and I say, I start with a couple of functions, a pair of functions, which satisfies something like this. OK? Very well. So let's see what is the curve. What are the curve at first? The curve, everything we did up to now in this specific type of example. You see, it's a very flexible type of example, because the curve is general. OK? Now, as long as, of course, so here I don't prove that x satisfies all the properties of the local chart. I leave it up to you. But here, of course, the only key point is this curve does not touch the z-axis, because those will be points where it becomes a mess, a rotation. Everywhere else, there is no problem. OK? Now, of course, you will need also this. OK? Because I never said, if I start with a curve, for example, I never said that the curve is parameterized in a way that the map is injective. But if I parameterize with arc length, I'm done. For example, in this direction, but these are all very simple considerations and now I leave them to you. Now, let's compute everything. Well, as usual, stop thinking and write.  And in fact, just to be quick, f and g are always functions of v. OK, I don't repeat it. So, f of v, I don't write.     Then what else, n. And now, remember, these are the moments where sometimes you have to switch on the brain. Because of course I'm going to write n on one of these charts. So, nobody has told me that this surface is orientable. So, on the part covered by one chart, of course it's orientable. And I can define the usual n. So, x u, x v, divided by its norm. So, let's do it since I wrote it. I wrote them almost in line. So, this is what?  Now, of course, the chance of making a mistake is very high. So, please double check.   And then this divided by its norm. I don't even like it. I'll put them. I'll put it at the end. Sorry?  Yes. In fact, for once let's put what should be as a denominator. Because, of course, I switched the brain off a bit too early. You see, this is a multiple of f. So, since I'm going to normalize, this is irrelevant. I mean, I take this out because I have to take the unit normal in this direction. I don't care. I take it out. I remove it and then below there will be as a denominator there will be just what. In fact, let's write it because it's curious. It's this squared. So, cos squared g prime plus sine squared g prime. So, g prime squared plus f prime squared. But it's the only thing I know, actually. So, in fact, there is no denominator. OK? So, the parameterized by arc length here becomes nice. Well, but actually you should be able. I go on with the exercise in some sense under this assumption. But actually often we will deal with example. I mean, when I give you a curve and I rotate it, maybe this thing is not satisfied. So, remember how to adjust things. I mean, don't take the formula that we are going to get for granted for any curve. OK? In this case, we can go on in this way. So, remember this holds on the part of the surface covered by this chart. OK? Well, but actually, since we raised the problem, let's solve it immediately. So, this vector field, of course, is born on the image of X. OK? Now, the point is, does it extend differentiably to the points which are not covered? So, in this specific case I know that X touches the whole surface minus this curve. So, at every point I have a normal vector. OK? At every point minus this curve. So, I can ask, if I go to the limit here, is this an extendable to a differentiable object? And I can see it immediately. Of course, this is not a general vector. That's not what you do in general. Because, of course, if you have a surface which is covered by many charts extending from one chart to the other it's OK. But, I mean, here the point is that the whole surface is covered by two and the points which are missing in one are a closed subset. OK? So, what does it mean? The limit as u tends to 0 or u tends to 2 pi. OK? On one side or the other. Is this vector field extendable in a differentiable way? Yes. It's already written here which is the extension. OK? This formula, of course, makes perfectly sense when u is defined over the whole R. OK? So, this one extends and this is orientable. OK? Now, we probably have everything to start computing first and second fundamental form. What is e?  So, it's f squared.  G is what? It's a scalar product between these two.  Sorry, capital F. OK? And then capital G. Let me write it here, so I save a bit of space.  So, it's f prime squared plus G prime squared. So, again, it's 1. But here, please, remember, the curve is not parameterized by arc length. If you use this formula, it's a disaster. If it's parameterized by arc length, it's 1.   So, that's minus cos squared fG prime minus sine squared fG prime. So, it's fG prime plus 0. So, it's minus fG prime. OK? Little f in the sense of the second fundamental form it's X u v n.  So, f is equal to 0 and little g is this one times this. F double prime G prime plus sine squared. So, it's f double prime G prime minus f prime G double prime. OK? So, if I ask you which are the principal curvatures be careful because now this looks like already a diagonal matrix. The coefficients of the second fundamental form. So, what we have to do remember in the in our notation of the proof is to compute the matrix A. OK? So, since this one will come in as a renormalization so the matrix once I know this which are simple to compute I compute the matrix associated to minus dn. So, we have to the standard basis to remember eG sorry eF fG to the minus 1 eF fG OK? So, then I compute it in my particular case I substitute here what I found and this becomes f squared 0 0 1 inverse times minus fG prime 0 0 and this expression of second order f double prime G prime minus f prime G double prime OK?  Now, you can say that these are the principal curvature so you see there is a scaling factor which comes in so the difference between the eigenvalues of this square is this object here being diagonal it means just it's renormalizing OK? Now, I don't really know which one is smaller than the other depending on the functions f and G OK? Now, because I should say now k1 is equal to this and k2 is equal to that or maybe it's the other way round I don't know but these two are k1 and k2 at the corresponding points and the Gauss curvature is the product of these two OK? And the mean curvature is what it should OK? Now, of course, this is different from what I got in my notes so where did I make this experiment? So, ten seconds to find either a mistake here or a mistake there OK? As a sub-exercise is to double-check if everything is correct now I don't have time to find what? That's already a good... Sorry, you are right OK, OK, OK divided by f squared everything No, this is dividing by f squared only this one. OK, very good So, the exercise is done and these are the two principal curvatures Now, the only thing you can argue is if... Do we know anything about this function here? Well, not much, but certainly can be simplified a bit so just let me double-check if now OK, so now we are in perfect shape Now, is this function something that we can simplify in some sense, yes remember you have this equation here OK, so I can take the derivative of this and I get an extra, a new equation of second order because here there are second derivatives coming in and which of course are which is what? I mean, of course here I would get twice, twice and zero so the two I drop it immediately so this becomes f prime f double prime so that equation if I differentiate it, I get f prime plus f double prime plus g prime g double prime is equal to zero OK but that means so, for example, the Gauss curvature which was the product, so this implies so k was independently of this equation was just the product of these two, no? So it was here there is nothing interesting to be discovered f double prime g prime minus f prime g double prime but here now I can make a substitution and here, OK, I leave it to you it's just f double prime over f you see, well it's just taking here you have g prime g double prime you take it out of this equation you put it back and you see what's going on OK now because, of course, this is a simple expression that you can analyze so, for example, when what does it mean, it's positive or negative so, right, we need to well, but independently I mean, remember the geometric interpretation we gave that's why we wrote the geometric interpretation of elliptic points and hyperbolic points in words to avoid exactly so the interpretation by saying if I cut with the tangent plane the surface lies on one side or it crosses the tangent plane this is a way to say independently of the choice of n OK that's why instead of saying the formula we wrote all this dissertation in English OK so, for example, it's clear that this point should be an elliptic point and, in fact, all the points rotating rotating, you see, in fact first observation, this function now, let's go back to this depends only on v the Gauss curvature depends only on v and not on u which it's a good check it had to be like this OK, meaning if some point has some property then every point on the circle has the same property points on the same circle are, of course, absolutely the same OK, so if something holds here it has to hold over the whole circle and this point should be clearly elliptic OK why, for example, this point should be hyperbolic in one direction of rotation which turns left and one direction of the curve which turns right meaning if I cut with a tangent plane I cross it OK and so on and where it's zero F is a positive function in any case it's a denominator but I mean this is positive so the only way this is zero is where F double prime is zero and so on the other direction here are zero OK that's it that's a nice family of examples you see the remark I made about the orientability of this type of surface you can now play use it also here this formula hold on the part of the surface which is covered by this map X where X is defined with this bounce so now if I ask you how much is this Gauss curvature here in principle you should not be answering you should shut up and repeat the computation with the other chart but being the chart given by the same function just defined on a different interval the final formula will be the same so in fact this formula holds globally this is an accident of this specific situation of course there is nothing general here it's a strange type of surfaces which are not covered by one chart but by many charts for example two but somehow the analytic expression is the same so whatever I compute holds globally very well now just as a specific example in fact you know one example of this of course well the torus we did it you have a question? but you need to speak much louder I mean I am used to two years old kids so the average tone of the voice is above shouting right but I remember mentioning to you this problem when we made the computation in fact one of you came in my office and the question is there is a discrepancy between this and what we did in class when we proved this formula for representing first, second fundamental form and the matrix associated with this now there was a problem there there was a minus one missing or for some funny reason you switch N because of course you have this freedom and you decide that instead of N you use minus N so if you go back there and you try to be a bit more precise than what I was you should, if I remember there is a minus there missing right now specific case the torus of revolution so you can apply the sphere is of course another example let the whole sphere with this trick because you want a curve which does not touch the axis of revolution so if you want to draw the sphere as a surface of revolution you are bound to take this curve of course the profile of half a circle but without the north pole and the south pole and now this problem of the north pole and south pole and we faced here it's another problem so if I take another chart of this form I will never cover the north pole and the south pole ok so the sphere minus two antipodal points you can put it into this picture if you want to curve of course you can play another game just for the accident that the sphere so many symmetries of course the sphere is also the surface of revolution ok so in some sense it is a surface globally you can define it as a surface of revolution or you do another in fact more interesting trick is that you analyze what happens to this picture when the curve touches the axis of revolution because really what we feared is this kind of situation for example if you rotate something like this certainly you are not getting a regular surface this is kind of casps ok these points are clearly bad but so this shows you that there is a problem even if of course there is a bigger problem if the curve crosses the axis but even if it doesn't cross there is a problem but if the curve touches the axis of revolution with a velocity orthogonal then the problem disappears at least at first order so here the problem is smoothness ok so c1 you just require that this is orthogonal if you want more you require more conditions ok so it's not that if the curve touches you are dead there are extra conditions in the case of this sphere all these extra conditions are satisfied but if you rotate this profile you still get a regular surface ok anyway another specific example famous specific example of surface of revolution since it's important for another special lecture I would like to give you later I guess in fact Thursday probably well we have seen for example the elliptic paraboloid for example of surface of revolution one not every elliptic paraboloid because elliptic paraboloids could have ellipses as sections the one we studied in a previous example had exactly a circle as section in that case it's a surface of revolution ok now there is a very famous surface in this family which is called the catenoid oh what is the catenoid the catenoid is what you get by rotating so remember our choices were the two functions f and g little f and little g which gives the curve and then everything becomes automatic so in this case I write you directly the map x of v there is no point in putting another parameter times cos u hyperbolic cosine of v sin u u v a v ok so basically this a is totally relevant it's just one parameter a shrinking parameter so suppose it's just a positive number you see in this case I've chosen g to be this function and f is a cos cos ok how does it look in the so you see in particular besides dividing by a which is not important you can think of it as a graph of a function so forget now the u so meaning we are looking at the curve a cos v 0 a v so you see the x component is a graph over the z component ok so if I draw it if this is the z axis I think of it and this is the x axis I think of it as a graph in this direction ok it's a graph over z which gives me some x and what is the function which I should draw cos ok but cos I know it's something like this actually here parameters are so v is any real number I should always be careful about so where everything is defined and u is between 0 and 2 pi for one chart minus pi pi for another chart ok so if I draw the whole thing I get something which looks like a parabola in fact this curve if you put it in the standard picture as a famous name it's called a catenary so the curve itself in fact the curve itself was very famous you know why have you ever discovered this curve in bridge sorry in bridge meaning you have even studied some kind of static or dynamics of buildings that's the place where it was born in fact it looks like especially if you put it the other way around upside down it looks like an arc so that's exactly the shape of an arc but it's also in fact that's kind of second step the first step when it was born it was born in late 17th century to solve one of the most simplest problem actually so the calculus of variations I mean mathematical physics call it how you want it was born by looking at very simple problem if you look back still enough to create differentiable calculus pick two points and pick a wire is this long enough I don't want to take my belt as a wire otherwise this lecture becomes too informal pick a wire a long wire and take two points hold it at two points at the same height now there is gravity there is a force in nature and there is a resistance on the wire along the wire there is a resistance because of course it has some kind of tension so which is the shape of the wire you know mathematics or mathematical physics was born through letters through challenges in the old times they didn't have matzinet or email or publishing journals so the way think somebody made a discovery and wrote to everybody famous in mathematics saying I am the best mathematician alive because I know how to solve this problem are you able to solve this problem too actually this happened historically many time many important discoveries were actually done in this way because of course if nobody could in a reasonable amount of time answer back that really meant that this guy was one of the best and so some king some prince son I would hire him or her well at those time her was very rare but was hire him and cover him with gold because of course for a prince or a king to have the best mathematician alive at those time it was important now nobody cares so so what happened with this curve so this was the challenge that Galileo made to everybody I can be slightly me yesterday evening I was not able to double check what I'm saying but I'm not sure if Galileo was the one answering or the one challenging take a nice book of history of mathematics and you will find the real truth but if I'm wrong I'm slightly wrong and he said oh I know the solution in fact he wrote it in a book and the solution is the parabola Galileo was already Galileo Galileo is the best the parabola for many years this was considered the solution and then somebody came up and said ok Galileo is Galileo is very good relativity Jupiter whatever you want but I keep on finding something else not the parabola in fact I find the catenary which the name is really catenary in Latin means the shape of a wire ok so then discussions no you are wrong no Galileo this is the truth the catenary was born in this way so it is one of the most famous by Galileo now at those time they didn't know what hyperbolic cosine was ok it was one of these we will see in 20 minutes another famous example of this phenomenon ok but now you have everything now I erase the formula but now they are easy because you see g is essentially the identity times a so g prime is a g double prime is 0 f is this so f prime is a sinh so you don't switch sine and double prime is you put everything together so I don't repeat the computation and in fact I tell you also the mean curvature which I didn't write because it's that long formula all the letters e f and g capital and lower and h turns out to be 0 identically 0 k turns out to be minus in fact minus it's ok because this is kind of a convex function so every point you expect every point to be hyperbolic because you see at every point the tangent plane will have one direction going one way and one direction going in the opposite way so it will cross the surface at every point so every point should be hyperbolic so it should be minus something and the something is simple it's just a squared kosh squared kosh 4 v this is just by substituting substituting substituting with care because in this case this is not a principally a parameterization by arc length of the catenary f prime squared plus g prime squared is not one so you have to take the formula corrected with the right denominators remember there was this denominator at some point was one and now it's not one ok so another example another famous example again this was born in the same way this time was not Galileo to make the mistake you take another famous curve arising in nature the problem is this one it has many strange famous name but basically suppose there is a donkey here connected with a wire to a stone here ok so this is a donkey in mathematics and now the donkey starts moving or the ox depends which animal you prefer starts moving in this way at uniform speed so that's a very standard situation you have something on your back but you move orthogonally you start moving orthogonally and this is the trajectory of this object ok well you expect it to be something like this ok more or less well let's put names to the more or less and I take this curve here and now instead of doing I rotate it in this direction actually it's a nice exercising calculus so describe the differential equation so this object this curve will be described by two functions F and G it's a curve in the plane so which kind of differential equation does it have to satisfy to be the solution to this problem of course here the constraint is that this wire has no fixed norm I mean it's a piece of wood it's not a spring it's not elastic ok so I can tell you directly the end of the story so X of UV in this case actually by changing names to the coordinates I will keep on using the same notation of course it's enough to call now this Z and this X ok I don't care and this becomes Kosh AV sine U and then G I should put here G of V ok but G of V I gave you just implicitly the definition so this is the integral between 0 and V of 1 minus A squared sine hyperbolic sine squared of AT everything to the power one half and don't be surprised that this looks like the norm of a vector just the way it arises dt ok now in this case this curve is parameterized by arc length I mean this is the convenience of this in some sense you do you it's more difficult to draw but analytically simple because G prime of course is this function if I take f prime is this f is this so f prime squared plus G prime squared so I throw away this half and I get one by the standard identities of hyperbolic functions ok Kosh minus sine is equal 1 ok so here on this example you can really apply the formula without being careful of the denominators I was mentioning in the case of the catanoid and this becomes interestingly enough very interesting thing is the gauss curvature also in this case you are expected to be negative just by looking at the picture ok but actually the little surprise is that it's a constant ok it's a surface of negative constant curvature ok of course this is non-compact so it's not contradicting anything in fact you might wonder whether there is a theorem saying in the non-compact case that this is the only possibility now this actually I forgot to tell you the name of the curve the name of the curve is the tractrix this is of the curve in fact the surface I don't think it has a famous name by itself it's the revolution of the tractrix ok of course Italians call it the dinis surface but I suspect it's just nationalistic I mean the implicit function theorem in Italy is dinis theorem so nobody knows outside Italy I suspect that even in this case this is not the official name please there was a question no anyway if you have a favorite book of history of mathematics this was the curve not the surface the curve was at the center of another of this discussion ok in this case I think it was Newton solving the problem I think Newton was challenged by somebody that I don't remember and he came up with the explicit parameterization of this curve now ok so this is enough as general theory and specific examples of surfaces of revolution in the last half an hour I'd like to talk to you about the other famous big family of surfaces which will help us making geometric considerations about the Gauss curvature and these are called ruled surfaces in some sense you would like to say that the ruled surface is a surface which has the property that for every point there is a straight line passing through this point contained on the surface it's covered by lines by straight lines ok so how do we get kind of a more formal definition of this fact so first let me define what is a one parameter family so one parameter this is just don't make a big effort to remember these things these are just to speed up later one parameter family of straight lines is a pair alpha of t w of t is a correspondence let me write everything even though it's quite clear it's a correspondence that assigns to each time t in some interval i ok a point in some sense a map which defines for any t a point alpha of t in r3 and the vector w of t the only thing in trivialities I want this vector to be always non-zero otherwise everything becomes really stupid ok and of course so basically these two in some sense alpha and w are vector fields but in some sense I'm thinking of alpha as a point and w as a vector ok there are two vectors in r3 and of course in a differentiable we have to be differentiable way ok so what do I do with something like this if I have a one parameter family of lines of course that means so I'm thinking so you see if I want to draw I should draw basically two curves in r3 in some sense I want them to interact in the following way for each time t I want to think at alpha as kind of the base point a passing point and w as the directional vector of a straight line ok so I would really like to think of alpha as the base point and w a vector pointed here and I want to consider the whole line through alpha with this direction ok this is the way I want to use alpha and w well what does it mean that if I have something like this I look at so what is this curve this line what are the points covered by this line well for any t so now this will be x will be a function of t and v I look at v w of t so that's the way so for each t if I let v varying on r I'm parameterizing exactly this line ok so now v is any real number so t varies where it should but v I can take it any real number so I take the whole straight line so the image is not like this so the image is called a ruled surface because really has a set it has the property I was telling you at the beginning so as a set the image of this map has the property that there is a point and the vector in fact for every point of the image of this do you have a little geometric intuition when alpha is moving in some way in time also w is moving in time so w for the same t was here when alpha is here maybe w is here and when alpha is here maybe w is here and so that means I'm keeping on adding these lines so this object as a set this is the property I was telling you because now give me any point of this set it has to be on one of these lines so ok that's it give me a set and so that means through this point there is one straight line all contained in this set by definition now these lines so let me give a name even though I don't think I'm going to use it so for each t I have a special line this really so it is the line alpha of t plus v w of t meaning now I think of t as fixed and v moving is called so this line the line is called or the family of this line is called a ruling of this surface alpha and that's it we don't give a name to w in some sense it's the family of directions of the rulings so examples because now we have to be much more careful than before at the first step well of course example 0 so do you know rule surface which rule surfaces do you know that's already example 2 probably for example 0 is the plane but that's already very interesting now it's 0 plus it's 0.1 because suppose it's exactly the plane of the blackboard ok why do you tell me that this is a ruled surface well you have to produce me alpha w and tell me that the plane is the image of an axle you said 2 axes what does it mean 2 axes that's what I heard if you tell me something obvious I have to say well probably ok but what is alpha when you define it as 2 axes what is alpha x and w so so first proposal use cartesian coordinates in that case we tend to say alpha of t is something like t0 I guess ok so the point on the x axes now use the other coordinate as direction so that means w of t is what it's constant it's 0.1 now it is true that every point of course is of the plane is of the form alpha plus v x t equal to x v equal to y ok, one possibility by the way I saw hand waving showing me circles or in fact somebody doing like this which was the most mysterious to me you are not looking at me anymore but you did something like that I don't understand what does it mean well in some sense for example polar coordinates is another obvious choice alpha of t is equal to a point for example in a unit circle but you don't care of any radius cos t sin t now I'm thinking parametra is the plane using in some sense polar coordinates that means I move it here and of course every time I'm here I take the line in the same direction so in this case w of t is again cos t sin t it's the point itself 0 0 as alpha of t sorry, what does it mean oh, that's another interesting proposal alpha of t is equal to 0 0 so your colleague is saying why move the point stay still in the origin and move the vector in the same way and move the vector again in fact this is even more polar coordinates in some sense the plane was 0 0.0 plus the example but it's already telling you that maybe there is absolutely no canonical way in fact why one should be better than the others no, there is nothing better than the other here but there is no canonical way to given a set which has the geometric property to actually write down alpha in w so this was already a good so do you know other examples? so in the case of the cylinder and I think by the cylinder you mean the one constructed over the circle and then you add vertical lines ok, now we are immediately going to generalize this but in this case why this should be a ruled surface in this language again you can pick alpha of t to be the circle and now w of t is always the vertical one sorry, now it's a space curve so for example in the z equal to 0 plane and this is 0 0 1 at every point of this I add the vertical line so this is of the same length in fact let me give you a general definition of cylinder now because now it's clear that the circle has nothing interesting in fact suppose you have a planar curve alpha of t suppose alpha of t is contained in some p so you start with a curve in a plane wherever it is w of t is constant so what's really going on here now the plane might be anything you have a curve in a plane so maybe this plane will have a normal vector but I'm not even taking the normal direction so you see how many accidents there are in this example I'm taking the circle and the normal to the plane why I build a general cylinder there would be something for which there is a curve in a plane and one direction maybe but the point is at every point of this curve you need to take the same direction so even on the circle why taking the orthogonal cylinder somehow you can take something like this and we still call it a cylinder we call and direction whatever the vector w so this would be a general cylinder but then of course there is another obvious family of ruled surfaces which are cones in some sense the plane is everything the plane is a cylinder it's a pathological cylinder if you want in this picture here you see that it's a cylinder it could be constant and outside the plane of course that's a very pathological situation but why not cones cones are what how do I define in this language cones so it's a ruled surface where again alpha of t is contained in some plane p which remember is not required by the general definition of ruled surface so you start with a special curve mainly a planar curve and the rulings all pass through a given point p0 so what does it mean not now well ok there would be the kind of pathological situation but let's try to avoid a little bit pathologies too much ok so of course what is this point this point is the vertex of the cone but you see again I'm not drawing I mean it's a clear generalization of the standard picture because I mean of course the standard picture is this ok so alpha would be for example one of these sections for example and w would be the vector which makes it going to the vertex at every point or you can be even smarter you can take this section alpha is constant and w is rotating in this circle here that defines the same object ok that's another way to put it very well so these are kind of general families so cones and cylinders let's see the most famous ruled surface besides this which is one of the quadrics so it's something defined by a degree 2 polynomial in R3 so we are at example 3 example 3 ok example 3 hyperboloid of revolution one sheet hyperboloid remember to pronounce it with a long e ok now what is the surface s so it's something you want it has to be of revolution so there has to be remember the trick of classifying quadrics is by cutting with planes and seeing which kind of conic first you classify conics then you pass to quadrics and you say ok so it has to be of revolution so one of these sections must be a circle otherwise there is nothing rotating hyperboloid of one sheet means the other sections another of this section is an hyperbola and the third section one two and three it's another hyperbola so two hyperbola and the circle that means the equation is like this x squared plus y squared minus z squared is equal to one geometrikally well geometrikally it looks like this I should have first drawn something like this this is of course a surface which is very popular in Italy because we tend to see it in fact in Italy it has an Italian name it's called the spaghetti shape now because one minute of cooking class how do you cook spaghetti properly first you boil the water first without putting the spaghetti inside ok, don't do that you boil the water you take a bunch of spaghetti you put them as a cylinder that's easy now if you are not Italian you throw them in the water and then they get stuck and you throw them away if you are Italian you put them in a cylinder hands in this way and you twist one way one direction up and one direction below and then you put them in the water and they don't become they don't glue now or anglosaxons which are clearly much less fantasy people they have a very sad life ok because that's the typical shape of a being of the treasure in your office ok, having said that now the spaghetti picture besides having one minute of relax was good to see the two rulings so this surface it's a regular surface you prove it by regular value inverse image of regular value I don't know you are old enough the two spaghetti the spaghetti gets in a position where you can see that there is one family of lines somehow going around in one direction and at the same time so this is special now besides jokes because it has two independent rulings ok, you see this line belongs to a family which really rotates goes around and when you are back here really it's again this one and this spaghetti when you rotate it goes around in a line because of course spaghetti are not flexible and gets back here to the same line so that means you can write it down independently as in two ways with the same alpha of course I'm taking alpha to be this section one of this section ok how do I do that now let's do mathematically this picture well, a simple way it's to parametrize this surface in this form it's cos s minus v sin s this is one of the two rulings actually sin s plus v cos s v ok ok, it's simple that this satisfies this equation and then you have to prove also the other way around that for every point here there is an smv for which is of this form if I take this squared plus this squared minus this squared it's automatic if I haven't done mistakes it's automatic so of course I can split now once I write it in this form sin s zero and this actually will be my alpha in the z equal to zero plane plus v something which will be my w and in this case is minus sin s cos s one ok so this is one of the two in fact the other one is just by switching ok, so this is alpha and this is w now what is special about this now of course s has become t well an interesting thing is of course that w, if you look at it is really the derivative of alpha plus a constant so here there is the accident here is that w is alpha prime plus the vector zero zero one now if I didn't add this it would be funny, you have now suppose we are in the plane and we don't like what otherwise the picture becomes too messy ok, I'm taking a circle because alpha is a circle if I take w to be alpha prime without this of course this is still a vector in the same plane and what vector is it it is the tangent vector remember before we ok, so and of course that's why I'm saying switch and so on now of course if I think of the surface in principle I could use this alpha in this w and what do I get a disaster which actually makes me because which object would be the image of alpha plus v w the whole plane minus a disk I mean I cannot hit any point inside the disk in fact in more than one way in general ok so really the image of the map here would be not even a surface so big warning because now we are unfortunately it has become too late and now we are going to make the theory I mean our old theory applied to this case but here the problem starts immediately the image of X is often not a regular surface for any sorts of reasons one is this kind of monster for example but another one is that clearly where it's written that X is injective remember X of TV if I really hope that this is a local parameterization at least for a piece I mean it's alpha plus t plus v w alpha of t plus v w of t but how can I hope that this is injective so why this should not be equal to alpha of s plus u w of s for some choices of tv and su but this is in general going to be completely false think of the cone for example it's already here the cone is the prototype situation where if every line passes through the same point this map is orthogonal to be injective for example so we have to do something but this something will come on Thursday now questions the other thing which other thing sorry either you start speaking very loud I'm going to ignore all the questions is it wrong? let's double check it x squared so that's cos squared plus v squared sin squared minus twice the minus twice I throw it away immediately the minus twice goes away so this is cos squared plus sin squared so this is the one and I throw it away here so let's see if everything else disappears everything else is here is what? it's v plus v squared sin squared plus v squared cos squared so it's plus v squared minus v squared how do I prove the other inclusion because actually this is a twin if I want to say that s is equal to the image of x of course what I just checked is that the image of x lies here so the objection of your colleague is how do I prove the other way in general it's actually tough but now fortunately one of these coordinates is already z ok if one of these coordinates I mean if you know I mean this gives you the hint so call z so this object is this one so I call v z or by brute force so if you give me this in x, y, z I need to tell you I need to find s and v for which ok so how do I get v because I take the z and I call it v now the problem is how do I find s ok but now it's easy again because give me a point here what is s s basically is projected down here you have a circle and call s if you want the angle or minus the angle or pi minus the angle whatever you want but essentially the angle of this point with respect to the direction if you want this to be cos s s will be the angle with respect to the x axis because for s equal to zero I want to find x the x axis so s will be the angle with respect to the x axis so now I define you v and s and this by construction so now I have to check that with my choice of v and s x of sv is equal to exactly to the point you gave me are you with me? the feeling I lost you so you ask me give me a point x0, y0, z0 I need to prove you that this is x of sum s0, v0 ok of course this on s how do I do it? I tell you v0 by definition I define v0 to be z0 I define s0 to be the angle between the point x0, y0 in the z equal to zero plane so I take the point that you gave me I put it down here and I look at the angle with respect to the x axis and I call it s0 now I know it's true but now I have to check that this is s0 and this v0 this is true but this has to be true I mean now by the way I construct that's not v0


Yeah girl Jenna, people have been tweeting this at me nonstop because back a while ago I did some hot glue crafts from 5 minute crafts. Who by the way can we talk about how they have 50 million subscribers? Do you know how many hours it took me to make that hat in those shoes on this channel that has the audacity to call themselves 5 minute crafts? Nothing on this channel, permit? We're in this for the long haul bud, it's not going to take 5 minutes, we already know it's a lie. There's many videos of people doing things like this on the internet where they see these terrible life hacks and or crafts and then they actually do one. But people were tweeting this jean chair at me nonstop because you know I will make it! What makes me genuinely angry about this is that this craft assumes that you have four identical pairs of jeans. On top of that this person is adhering them together with staples which I don't know if you've ever been like 8 years old before but you can't just staple everything together. It doesn't work. I know for a fact that this is not really going to work and they never really show you how they make this center part stay together. They show you how they close the legs and staple them next to one another. But like assuming you follow these instructions you should just have an empty hole right here and then she sits in it and it's like a chair. I don't know about you but I've stuffed a pillow or like made something with stuffing before. We bought 30 pounds to have this have structure to be a chair and I bought four pairs of jeans from TJ Maxx because it was the only place I could think of that realistically had four similar pairs of jeans that weren't expensive as hell. Like who is this craft for? Who is this chair for? Only person I can think of that this chair is for. Who else would spend money to actually make this? It's just me! I desperately want to know who runs this channel. I just want to talk. I just want to talk. You have 50 million subscribers. Who are you? Who is filming these? Are they going to be at VidCon? Like can I go meet them? Who are these actors in these crafts? Where do they film? Here? Russia? Where are they? Is there any dialogue or is it all just music? No it's all just music and DIYs and I think when I made the video doing the hot glue crafts I think they had like 20 million subscribers or something. They've effectively doubled their subscribers in like a year and a half. They upload like a thousand videos a day. This must be a very large production. I honestly selfishly want to know who thought of that because I feel like we would get along. The jean chair? Yes!  I'm going to make it. I've got four pairs of jeans. One is the size smaller than the others because you can't just find mad jeans that are the same without spending a fortune and 30 pounds of batting in a stapler. So let's do it. I have so many questions. How are they staying curved? How are they standing up? I think... They let me get it pressed into a corner. Yeah I think that the shape of the chair is contingent on it being against a corner. Yeah if you put that thing on an open floor it would collapse. Right? What's going to happen when we get to the middle? How are we going to make it all stay together?  I know we shouldn't make it but I'm going to make it because you guys asked me to and honestly that's all it takes at this point so let's go. This is the best I could do. Who just has four of the same pair of jeans that they're willing to turn into a jean chair? This much money you could buy a chair. Even if it wasn't the dumbest and ugliest thing ever literally no one I've ever known has four pairs of jeans period let alone ones that they don't want. I have two pairs of jeans. I have like... And I resent both of them for being uncomfortable. I wear leggings. So what was the first step? She staples the ends of the pants. I think she staples the ends and just starts filling them up. For those of you that are out here getting bamboozled by five minute crafts let me just show you really quick just in case you were watching that video genuinely being like hmm I got some jeans in a stapler let me show you. Hello. Five minute crafts. How are you allowed to just post make believe things onto the internet?  Look at that. Look at this side. So many staples. Yeah well can we talk about the fact that this chair is going to be sharp? Hello. Like when you sit on it you're sitting on all those staples it's going to hurt. There's like open staples in the chair. It's not for kids. It's not for anyone. Unless they do like one row of staples that's not going to work. It's going to fall apart. I'm getting hot and angry. I'm like in a bad mood. Don't touch it. It's very delicate. I love how they show when they're doing the stuffing too. They're just like putting a little bit in there and being like Tiki these jeans have stuffing in them. Like you have to do a lot. Girls it's not going to hold its shape at all. Are the videos even five minutes? No. Nothing is five minutes. Where do they get the number of five then? Probably started off with something simple and turned into just absolute madness like the rest of YouTube. Damn those legs thick.  This channel lies non-stop. It's toxic. It's time to stop. Where in five minutes crafts do you see this? Huh? You just got this laying around the house really quick. Just stuffed four pairs of your identical jeans. Yeah, I got 30 pounds of polyfill. I said no one but to win fabrics. Can you move? All right. That's one pair. What are you doing? It just like it feels so wrong to take a pair of jeans and staple them. I think this chair would go really nice in our house just in general. You know, like it could really go in any room. It's just a tasteful chair. Craftsmanship. It's so beautiful. That's my phone. Why did you put that in there? Did you check the pockets? You always got to check the pockets. Why would I check the pockets? Well, who knows? Can I check? Wait.  It's taking me longer to stuff these than I anticipated. Like my back hurts. They thick. I think they need to have like some give or else they won't bend. But they don't tell you that.  Come here, sit. Sit. Come here, like sit. All right. Well, maybe we're on to something. Here's the second pair of jeans. Oh, you did two? Wait, this one's way thicker. Damn, this one's done. Well, I didn't want to use two. Damn, she got quads in all the right places. This one's like already falling apart at the end. Look at that. This is garbage. Yeah. Are you kidding me? This is not going to stay. Well, all four pants are stuffed. This is like the weirdest murder scene ever. According to five minute crafts, I should just be able to staple it together like this and on the ends and have an incredible chair. I don't think that's going to work, but I'm just going to do it how they said to do it, which is just staple them all together. So the video shows a person coming in and just doing a little of this. It's coming apart already. Julie, stop. I just stapled that. Like knowing that that exists.  I need staples. Whoa, they're in this pocket. Here you go. How's it working? Is it going really well with the stapler on denim? It's hard enough as it is to sew denim. Do you need the other one? Yeah. Okay, here. Unfortunately I do. Will you move that so I can... I'm like getting dumber from doing this.  This is what I think hell looks like. I was trying to add up exactly how much all of this cost to us. So each pair of jeans was like $20. So 20, 40, 60, 80. That 20 pound polyfill was $60. And then if you don't have a stapler or staples, that might be some more. But that's like $140 this cost to make. If you didn't have this laying around, which no one does. No one does, but also $20 for jeans is damn cheap. And this still costs $140. So no, no, no, no, no, no, no, no. Stop it.  Oh, no. So they just like went like this. See, this isn't the part that I'm worried about.  How? How? How am I supposed to get my... Oh. I know what you do right there. It's so sharp. I'm going to cut myself. What? What do you do right there? Put a chair. This is the ugliest thing I've ever seen. Yeah, Julian. It's ugly.  It's infuriating. It makes me so angry. That's why it belongs in my house. You know? It's dark out.  Maybe we should do this up against like a corner like it's positioned. So it's easier. We've made it to the point where this absolutely has to be in a corner in order to work. So we had to push it into this corner before we could finish stapling it because they keep ripping apart because it's not a chair.  Just as we suspected though, like how does this all connect? How? They didn't give you any way to connect those in the center. Shit. This is like it's really getting up there with one of the more frustrating things I think I've ever done. I can't. It's like it's testing me. What goes there? What goes there? Staples literally everywhere. Everything keeps coming apart. No one's even sat in it one single time. How can they just post this on the internet? This is a fraud. This is a lie. Oh my god. Should we go get an upholstery stapler? No, that's not the craft. The craft isn't things that make sense.  What's that one doing? If you made them all touch, it wouldn't be an open chair. It would be a closed circle. Mathematically, it makes no sense. Oh, Jenna's gonna lose it. There, that's the money staple right there. Okay, so I think it's ready. We did it. It's beautiful. The craftsmanship. All right, your chair's done. Congrats. I don't think I've ever been more angry. I hate it. It doesn't work. I haven't even sat in it, but like it's gonna fall apart. If we like breathe on it right now, it's gonna fall apart.  And it costs $140 to make. And you know what? Just really quick, I'm gonna flash some chairs across the screen right now. Here are some chairs that cost less than this chair that aren't terrible. It's still going. I could just, I could keep going. Basically every chair ever. What do you say? Should I sit in it? It looks like a molding baseball glove. It is so unbelievably the opposite of like being thrifty or creative. I'm gonna sit in it. And the second I sit in it, it's gonna fall apart. But I'm also going to get staples everywhere. They're everywhere. I know how many staples with this. I stapled it. What? I've never seen you in a physically relaxed position less relaxed than you are right now. You know what? I'm so mad. Why?  There's no bottom. Like it's ripping and it's not sewn together. But like if you sewed this, it's honestly kind of sick. The only flaw in this chair is that it was stapled. Because if it was sewn, it'd be kind of fun. Why did they have to staple it? There's a lot of staples. So you guys be very careful. Okay. What do you guys think? You like the chair? Well, it was not five minutes. It was $140, which I will never get back. Don't sabotage me like this. You watched me toil over the creation of this chair. No. My chair. But for where I will sit now. It looks like you're spreading your legs. You think I should just pack this whole thing in a box and mail it to Sophia and I guard? Yeah. She would like it. Yeah. Or actually maybe what we could do with it. We'll fit. Yeah. I was going to say burn it, but I don't think I'll fit. Do you want to sit in it? It can't handle this butt. Just have a seat right there. Just have a seat right there. Okay, Mr. Hansen. Okay. I get it. Oh, no. Julian. No, no, no. It has a foot rest. You're doing that on purpose. No, no, no. You said sit in it. You're doing it. It has a foot rest. Julian. Oh, that's nice. I'm going to actually pass out for a bit.  Julian. What did I do? I was offering for you to try it.  Can you give me your honest opinion? Yeah. No, it's really comfortable. There's maybe 30% of my body that's touching it. The rest of my body is touching the floor. Why would you do that? What do you mean? Why would you just destroy it? I thought it was my turn. Was this not what I was supposed to do? Ah, stapled. Just went into my back. You deserve a staple to get back. Look how you're sitting on it. That's not how it was intended.  Does your computer log in here, YouTube channel, Julian?  Hell, yeah, it is. Don't subscribe to Five It. What are you doing? Why are you sabotaging me? Actually, I have an idea. What if we moved it over here? Oh. What? I was just trying to move the chair. Sorry. I'll do it right this time. Let's move it over here. Oh. Oh no. Oh no. What? Move the chair to a better spot so we can appreciate it and live long with it. It looks great. Because I hated the chair a lot. But this is like a living sculpture that I think we should keep. This is an actual piece of art. I have a great idea. Welcome to my fancy home. This is a new set of pieces. Beautiful art.  Ah. It goes with the vibe, which is fancy, beautiful, fancy people. I didn't appreciate it as a chair, but I appreciate it as art. Because I am an artsy person. What are you doing? Oh my god. We had a pretty good time here today. It was really hard and frustrating. Listen, okay? You have to sew denim or nothing at all. You can't just staple denim. You know what I'm saying? Well, this is what you all wanted to see from me. I hope you're happy with yourselves. This was very frustrating, very annoying. It was $140. It wasn't worth it. It didn't work. Man, I honestly had a bad time the entire time. Oh my god. It's kind of sick. Make sure you subscribe to my channel. I put on an episode Wednesday slash Thursday. Honestly, I never say stuff like this.


Hello and welcome to NewsClick. Today we have with us Professor Madhura Swaminathan and we'll be discussing what is the impact of the lockdown and particularly on the sections which were already at the margins and whether the recent financial package which is being touted as this great bonanza for the people doesn't really help the sections which are most affected by the lockdown. Madhura, good to have you with us but of course not on a very happy occasion. You have written about this lockdown and its impact and the kind of measures that you think should be taken. Now, coming to the first question that I have, what is the impact particularly on the sections which already have a bad record in terms of malnutrition, hunger and so on. We know that India has one of the highest stunting in the world amongst young children. So what do you think is the impact of this lockdown that has been there on them? Thank you, Praveen. I think it's very important to start with the fact that even before Covid, India has a record. We hold the world record for undernourished people. So in terms of children, in terms of adults, in terms of women, particularly pregnant women, various criteria which we take, whether it's anthropometric criteria like weight for age or body mass index or even absolute intake of calories and proteins. In fact, if you take average intake of calorie and protein before Covid, average Indian consume less than the recommended dietary allowance. So we started with a situation of very high levels of malnutrition and food security and there's no doubt that there's been a huge increase in the last two months. So we don't have any numbers to estimate the increase but I can give you the kind of numbers that people are talking about globally. For every one percentage decline in GDP, they're talking about a number. According to a study of wider, there will be, if there's 20% contraction in world GDP, there will be another 400 million poor people. So this is the kind of ratio between decline in GDP and increase in poverty. So we don't have the numbers for India because we don't know as yet how much is a decline in income. But I think it's visible to all of us that because of the lockdown for almost two months now, majority of Indians have lost their livelihoods and their incomes have collapsed to zero. So given that what we have in the packages announced so far by the central government is really minuscule or the pathetic is what I can say. Mathur, you were talking about the malnourishment in India, particularly among the younger population, zero to five years, children and so on. How do we compare in global terms? You said we have one of the worst records. In terms of the absolute number of malnourished, India has the world's highest number of malnourished children. But some say that may not be the correct comparison because we are a population of over 1.3, 1.4 billion. But even in terms of the proportion of children who are malnourished, India has numbers which are very similar to Sub-Saharan Africa. The latest number we have is for 2015-16, which suggests that 36% for more than one third of children below five are malnourished on the wait for age criterion. So while we claim to be one of the growing economies, we certainly have a far better per capita income than Sub-Saharan Africa. Our figures being low also then shows the sharpness of the divide in terms of poverty in this country. Absolutely. So even though there has been a slow decline in the incidence of poverty over the last sort of 10-15 years, our absolute measure of poverty is so low that it's not ensuring a nutritious diet even for those who are above, just above the poverty line. And I'd like to bring in one figure here that in 2017-18, the consumer expenditure survey data was not released, but there was a leak which suggested that in absolute value, the average consumption had come down from 2011. So I think before the COVID crisis hit us, we were in a situation of worsening income and poverty, worsening unemployment. And this has come as a sort of double burden on that situation. So already growing inequality, now a huge hit on their income. This is the way and the fact that at least 100 million migrant workers in the cities and towns, a lot of them going back. So you'll see a huge hit on their incomes and therefore on the poverty levels as well as nutritional levels. Absolutely. So one is that 90% or so of our workforce is in the informal sector and a very large majority of them are casual workers or workers in small self-employed businesses who have had zero income. Although the rural areas have not been as badly affected economically in the sense that agriculture has continued, agriculture, fisheries, daring, all these have been called essential activities. But our studies show that for the poor households in rural areas, particularly for manual worker households, almost 40 to 50% of their annual income comes from the migrant workers' income. So the gaps of the migrant worker income is affecting him or her in the city, but is also having immediate repercussion on the family in the village. So we talk about rural India being somehow protected from the virus as it were, but it has not been protected from the economic collapse. So that is very much going to affect not only the urban areas, but also the rural areas. Particularly now the migrant population going back, at least 40 million by reports are already either going back or on the way back. So this is going to make the things much worse. Coming back to what the government should or has not done. Let's look at this 20 lakh crore so-called stimulus that's been talked about. Others have said it's really not a stimulus. But thinking, okay, there is this amount of money which the government is saying it's going to spend. Is any of it already significant part of it going to the section which needs it most? You know, I've only read what others have estimated, but they're saying in real terms, if you take away all the loans and all the role of the RBI and the banks, probably the fiscal stimulus is at most 1% of GDP. Not 10% of the GDP. Not 10% but let's focus on what's going for food security. There are two components to that. One is the cash transfer or cash income because as I said, you don't just eat plain rice or plain chapatis. You need fuel, you need spices, you need to buy some things to go with it. So the collapse of the cash income among households has not been replaced. There's been a, you know, a piton of 500 rupees for those in Jandhan, Yojana and so on. So the amount of income transfer that is required is at least 5000 or 7000 rupees per month for a rural or urban poor household. In fact Sri Lanka has given 5000 Sri Lankans to about 5.5 billion households already. So other countries are doing it, even other developing countries. If we don't want to compare ourselves with the UK or the US or Europe, there has to be a cash transfer for 2-3 months till the economic activity returns. The second is the food component. Now India has a long and history and well established public distribution system. And I think that in a sense we have an opportunity, we have the network of ration shops more than, you know, something like 5 lakh ration shops in the country, network of dealers, network of storage points, food corporation of India go down. So we have this whole network ready which other countries may not have. This is the time to really say we are going to make food distribution universal and we are going to give adequate quantity and quality of food. So I think that's what needs to be done and has not been done. So when you talk about quality of food, not just quantity. You're really talking about not just rice or wheat and not just for instance dals, but also other supplementary foods or essential foods in that sense, like for instance protein intake, eggs, other things. Is that what you think we should add? Yeah, I'm referring to dals also because as I said the latest in data we had showed that the average Indian was consuming less than 60 gram of protein, which is the daily protein requirement. So even if we take half that protein requirement to be given, you require both pulses and eggs and milk and other products. So I think that what is easy to do to start with is to start distributing pulses, oil, salt, sugar, spices, etc. with the rations. And to add, maybe the easiest would be to add it through the school meals or through the school distribution system, add fruit, vegetables, milk and eggs. If we can give one cooked, I mean hot, nutritious meal to all the children, as well as open it out from that school center to the elderly, to pregnant women and others who are vulnerable. If we can give one balanced and nutritious meal, I think that will make a big difference and this is the time to start. Again, we have a network of, we have a school meal program which is near universal. It was closed down for the last two months and in many states as we know the quality of food given is poor. But I think that can be ramped up when you have a system already in place. Then using it becomes much easier. Scaling it up or using it much easier. So I think to start something new at this stage, people will say we are in a crisis and you want something new. But we have a ration network, we have a school meal and I see this network at every village level, at every ward level. So we can improve the quality of food being given there, I think relatively easy. Kerala has continued to supply meals to the school children and reaching their homes to get the school children the meals which they were supposed to get in the schools. So has any other government taken such measures? As of now, I don't think so because the argument that has been used by most governments is of distancing. What they call social distancing but what I think we should call physical distancing. Again, I think that we are now two months down and the lockdown is being relaxed. So when we are talking today, I think people are queuing up for bus tickets, people are queuing up for rations. To have a queue to collect food in a village school or in a ward school, in a public school is something that can be done with appropriate water for hand washing and so on. So I think that this should be started immediately by all state governments. I want to add that the state governments, Kerala is doing a remarkable job but Kerala as much as any other state government is hugely short of resources now. So the central government has to take the responsibility in terms of funding this better quality of food or in terms of funding. That was really my next question that given the fact that the states do not have the resources that this would really demand particularly if you want a school based nutrition program. It would really need transfer to the center, Exchequer, which at the moment not only it's not forthcoming but even what the states are supposed to get is not coming to them. So we really have a double hit on the states. So what is the kind of transfer, scale of transfers we are talking about in this case with the center should do the states. So let me just go back a minute that even at the peak of our distribution through the Russian system, the food subsidy of the government of India has never exceeded 1% of GDP. Now we're all talking about this package being 1% but just think of it. We are talking about reaching 800 to 900 million people. If we say that we're taking two thirds of our population as a severely food insecure to reach 900 million or a billion. How is 1% of GDP adequate? So I mean, is this what we allocate for 80% of our population? We give them only 1% of our GDP. So I think that even if we can and remember that when we are procuring fruit and vegetable, one of the worst hit agriculture is right now. The horticulture and fisheries and so on who's going to perishable products who have not been able to store it where the system of minimum support price doesn't exist. So if we procure fruit, vegetable, milk and so on and distribute it at a subsidized rate through schools, we're actually also supporting the economy and it's coming back. So the subsidy, I say I have not done the calculation, but I think if we add another 1% of GDP. So we said 2% of GDP for food security. I think that would be quite a substantive sum of money to ensure this. And what it will do is really put cash in the hands of the people who are the growers. So in that sense, it will be a double benefit economically. Absolutely. The meat industry, I know Kerala has even given fish and meat as part of some of their school meals. So that's very desirable, but at least eggs, which is a little easier to transport and so on. So I think that the meat industry is in a doldrum, old trees in a very bad shape. So this could actually become part of the revival of these industries. But as you know, the Hindutva lobby, particularly in this country is also part of the understanding, has an understanding that vegetarianism is Hinduism while other, if we're a non-vegetarian, it's somehow being anti-Hindu, if not anti-national. So we have that problem as well in the country. And there's also been a scare because of this zoonotic disease. People think there has been a scaremongering about consumption. But I think the protein deficiency in India is, of course, one part of it is because there is so little animal protein in the diets of people and that's because they can't afford it. They can only afford meat or fish or mutton or something once a month or once a year. So this is a time when we could see this as a way of actually improving, not just controlling the deterioration that is happening, but improving the nutrition of large masses. And one point I want to make here is that for children, particularly young children, even two months of a poor diet is something that's going to have a long-term effect on their health, on chronic diseases, on their cognitive development. So we really have to address this very quickly. You've written about the crisis in the UK during the war and the rationing the dead, adding proteins to it. And actually their health figures improved during the war in spite of all the deprivations that supposedly they faced. That's right, life expectancy for males, that two who were being killed in the war, and the mortality, life expectancy increase and mortality decrease was most rapid in the 1940s. If you take the whole 1900 to 1950 period in the UK, and this is because of equal distribution. A more equitable distribution. Yeah, equitable distribution. And I think if you look at the quantity of food and vegetable India is producing, if you look at the stocks of food grain, we have the quantity. So basically we have the ability in terms of production. It is just the distribution and the support the government needs to do, which is lacking. And the fact that even under the conditions of crisis, we are not thinking in this direction at all. And that's what is really, what shall we say, the crisis of our conscience in this particular case. World over now, there are a lot of estimates coming out that poverty is going to increase, food insecurity is going to increase, all the global organizations have already indicated that. And I think if we don't do something, I think it will be unconscionable that we are going to have a major increase, a worsening of nutrition and food security in this country after a slow but steady improvement. So I think that not that we have much to talk about, we were in a bad situation, but I think this is going to be a major, as you said, unconscionable reversal. Thank you very much, Mandura, for being with us. We'll be in touch on this and other issues. This is all the time we have for Newsclick today. Do keep watching Newsclick and visit our website.