This talk will be an introduction to the Birch-Swinnerson-Dyer conjecture at a roughly graduate student level. So first of all it's named after two people, not three, so Birch is Brian Birch and Swinnerson-Dyer is Peter Swinnerson-Dyer or Professor Sir Peter Swinnerson-Dyer. And the Birch-Swinnerson-Dyer conjecture relates the following two objects. We take the rank of a Mordell group of an elliptic curve and we're going to relate it to the order of zero of the L function at s equals one. So I better start by explaining what all these various things are like what is an elliptic curve, what is the Mordell group and so on. And then I'll say a little bit about Birch and Swinnerson-Dyer's motivation for finding the conjecture and then I'll summarise some of the progress that has been made on it. So let's start by quickly reviewing what an elliptic curve is. So an elliptic curve is roughly an equation of this form, so y squared equals x cubed plus bx plus c. So b and c are fixed constants and we've got a curve like this, so typically an elliptic curve, if you draw it it might look something like this. And the problem here b and c are going to be rational and the problem we want to do, we want to solve is find all rational points. For instance a well-known historical example studied by Fermat is an elliptic curve y squared equals x cubed minus two and this obviously has one rational point five three for example. And if you look at it you see it's really rather a difficult problem to figure out whether or not it has other rational points. One reason for the interest of elliptic curves is that in some sense the simplest curves we don't really understand. So if a curve is degree two, we've got degree two curves pretty much under control since the time of Gauss or something. But degree three, there are still lots of basic things we don't know about them. So this is sort of simplest non-trivial example. Elliptic curves have very little to do with ellipses, they're called elliptic curves for roundabout historical reasons. So the first thing we can do is we can make the rational points into a sort of group. So if we intersect a straight line with this curve, you see it intersects the curve in three points. And we can define a group structure on the points of the elliptic curve by saying a plus b plus c equals naught if and only if a b c lie on a line. And this turns out to make the points on the elliptic curve into an abelian group. That's not at all obvious, by the way. In particular, checking associativity of this addition is quite complicated. I should say that the zero point of the group is a sort of point at infinity. So strictly speaking, it's not quite a solution of this. So that gives us some extra structure to work with. In particular, the points with rational coordinates all form a group because you can check if a and b have rational coordinates, then so does c. And this group is called the Mordell group. So the Mordell group is just a group of rational points on an elliptic curve that I'll call e for short. And the Mordell group of an elliptic curve has been a sort of central topic of study and number theory for about a century. The reason why it's called a Mordell group is the Mordell proved that it's finitely generated. This means that it's a finite abelian group, which are pretty well understood, direct some number of copies of z, where this number here is called the rank of the Mordell v group. And we would like to understand both this finite part and the rank, and we sort of pretty much understand the finite part. So Barry Mazer showed that the finite part has order at most 12, so we've sort of got it under control. The rank is much more mysterious. So for example, one obvious question is, can the rank be arbitrary large, or is there some bound to the ranks of all rational elliptic curves? And opinion about this has varied backwards and forwards quite a lot. At the moment the consensus seems to be that the rank is probably bounded. So Park, Poonen, Voight and Wood have a paper on the archive a few years ago where they suggest there are a finite number of rank greater than 21. So that's still conjectural. You can't do much better than this, because various people in particular L-keys are rather good at finding elliptic curves of large rank, and he's found infinitely many of rank 19 when I last heard, and one of rank 28. Numbers may have gone up since I last checked this, of course. So the rank of an elliptic curve is still a somewhat mysterious object, and it's this rank of the elliptic curve that the Birch-Swintersen-Dyer conjecture tells us or conjectures something about. So we notice first of all that the rank is equal to naught if and only if the number of points is finite. So the first thing Birch-Swintersen-Dyer looked at is to try and tell when is the number of points on an elliptic curve finite. And the key idea is the following. If the number of points on E is infinite, then the number of points mod P should be larger than expected. So this is a very informal sort of statement because we don't quite know what larger than expected means. So the point is if you've got lots and lots of points on the elliptic curve, which you would have if they're an infinite number of rational points, then you can reduce all these rational points mod P and get points mod P, and that sort of means you're slightly more likely to have a point modulo P. So what we do is we let Np be the number of points on the elliptic curve mod P. In other words, we're trying to solve y squared equals x cubed plus bx plus c mod P, and that number is not quite equal to Np because we really ought to counterpoint at infinity at the time being a bit sloppy about. So if you've got a rational point, then most of the time you can reduce it mod P as long as P doesn't divide the denominator. So lots of rational points should make Np a little bit bigger than usual. You can see that Np is going to be approximately P because there are P choices for x, and then there are either 0 or 2 values of y, and there's a sort of 50% chance of there being 0 and 50% chance of there being 2 values of y because it depends on whether this is a quadratic residue or not. So we expect about P points mod P. So Np over P should be approximately equal to 1 in general. So this suggests you might want to look at the product Np over P, where this is a product over all primes. And maybe if this is equal to infinity, this might correspond to infinitely many points on E, and if it's finite, this might correspond to a finite number of points. Well, one problem is there's no reason why this should actually converge even if it's finite. I mean, these numbers might just sort of oscillate up and down a little bit. It's really not clear. But what you can do instead of looking at this product, you can look at the product for P less than equal to N of Np over P. And look at this as N tends to infinity. And try and estimate how much this is growing. And this is what Berkson, Swinnerson-Dyer did with a very early computer. And this was back in the 1960s, so computers were these huge things that filled an entire room and probably less powerful than what you can get these days as a $50 pocket calculator. But whatever, they managed to use this computer to calculate this sum. And what they found is that indeed the product of P less than equal to N Np over P seems sort of finite or bounded if the rank is equal to 0 and seems to tend to infinity if the rank is greater than 0. Well, obviously you can look into that a bit more closely and try and compare the rate of growth of the product over P less than equal to N of Np over P with the order of the 0. So they looked at this too. They tried to see how this number grew with N and compared it with the order of an elliptic curve. And what they found is that this expression here is, grows roughly like log of N to the G, where G is the, sorry, not the order of 0, the rank of the elliptic curve. So I'm going to say the rank turns out to be the order of the 0 of an L function, but that's coming up in the next sheet. So they did some numerical calculations and this seemed to grow very roughly like that. It doesn't mean, this isn't asymptotic to that, but the calculation suggested it sort of lay between some constant times this and some other constant times this. So the number of zeros modulo P does seem to be related to the rank of the Mordell group. Well, you can make this a little bit more precise as follows. So there's quite a lot known about the number of points on an elliptic curve modulo P. So if we have an elliptic curve modulo P, then the number of points is equal to P minus alpha P minus alpha P prime plus 1, where alpha P is a complex number of absolute value, the square root of P. This is the famous Riemann hypothesis. Well, it's the Riemann hypothesis for elliptic curves, which was first proved by Hasse. It's quite a lot easier than the Riemann hypothesis for the Riemann zeta function. And the elliptic curve has a zeta function associated with it. So first of all, we can write down a local zeta function of an elliptic curve. So this local zeta function zeta of P is, for various complicated reasons, defined to be X with sum of N P to the M over M times Q to the MS, where this is the number of points over the field with P to the M elements.  So that's a local zeta function. And you define the zeta function of an elliptic curve E to be the product overall primes of the local zeta function, except that's not quite true because there are a certain number of bad primes where you need to think a little bit harder about it. So this is a quality is not quite true, but I'm going to sort of ignore that. Now, you notice this product is, looks a bit like the product for the Riemann zeta function. So the ordinary Riemann zeta function looks like the product over P of 1 over 1 minus P to the minus S. And if you notice, this 1 over 1 minus P to the minus S looks just like this factor here. So you find this, the zeta function of elliptic curve is the ordinary Riemann zeta function times the ordinary Riemann zeta function of S minus 1. Now that comes from this term, of course, times, sorry, divided by a certain L series. This is the so-called L series of an elliptic curve. And this is this L series that's going to appear in the Berks-Swinterson-Dyer conjecture. So the L series of the elliptic curve is just 1 over the product of 1 minus alpha P to the minus S times 1 minus alpha bar P to the minus S. So it's a product of that over all primes. And what you notice is that N P over P, which is P minus alpha P minus alpha bar P plus 1, is equal to 1 over L P of 1. So the product over all these numbers N P over P is essentially 1 over L of 1, where this is the L function of the elliptic curve. So this is the product that Berks and Swinterson-Dyer were investigating, and this is the elliptic curve. Well, the trouble is this product does not converge. So you've got to be a bit careful. We're just sort of arguing informally. But you see that if you pretend that it does converge, you see that this would be finite if the L function doesn't vanish at 1. And if it diverges to infinity, then you would expect this number here to be 0. There's a big problem, by the way, at the time Berks and Swinterson-Dyer were working, it wasn't at all clear that this L series was defined for S equals 1. So this equality shouldn't be taken too literally. Neither side is really properly defined. Anyway, this sort of suggests that the number of points of E is finite should be equivalent to saying that the elliptic curve is, the L function of the elliptic curve is nonzero at 1. So this is the first form of the Berks, Swinterson-Dyer conjecture. That it gives a criterion for an elliptic curve to have an infinite number of points. It has an infinite number of points if and only if its L series vanishes at 1. Rather, I should say this has to be an analytic continuation of the L series, because as I said, the L series doesn't actually converge at S equals 1. So that's a bit of a problem. Well, you can extend this a bit. So you remember I said earlier that the product over P less than or equal to N of NP over P sort of grows a bit like log of N to the G times some constant or whatever. And this turns out to correspond very roughly to saying that the L series, L of S, has 0 of order G at S equals 1. It doesn't correspond to precisely that because as I said, this isn't really clearly a well-defined function, but informally you might guess that this growth rate sort of formally corresponds to having a 0 of order G. So this gives the next form of the Berks, Swinterson-Dyer conjecture, which says the rank of the Maudelvet group of elliptic curve is equal to the order of 0 of the elliptic curve at S equals 1. So this is one form of the Berks, Swinterson-Dyer conjecture. Berks and Swinterson-Dyer actually refined this a bit because you can say L E of S is equal to S minus 1 to the G, where you conjecture this G is the same as the rank G here, times some constant. And Berks and Swinterson-Dyer also pinned down what they felt this constant ought to be, and it turns out to be rather interesting and rather complicated. So it depends on things like the Tamagawa numbers of the elliptic curve and it depends also on the Tate Shafarovic group and on a few other bits and pieces. And so there was a sort of joke about the Berks, Swinterson-Dyer conjecture at the time which said it was conjecturing the equality of two things, neither of which were known to be well defined because, as I said, first of all it wasn't known that this is defined at S equals 1 and secondly it wasn't known at the time that the Tate Shafarovic group was finite. In fact there wasn't then a single example of any rational elliptic curve whose Tate Shafarovic group was known to be finite. So this formula involving the order of the Tate Shafarovic group was again a little bit dubious. So that's what the Berks, Swinterson-Dyer conjecture says, roughly speaking. What I'm going to do now is to discuss some of the progress that has been made on proving it and we've actually come quite a long way since the conjecture has originally stayed. So I guess the first substantial progress was made by Cotes and Wiles, I guess this would be in the late 70s. It said that suppose elliptic curve has complex multiplication. Well, I need to explain what that means. Then if the L-series doesn't vanish at S equals 0, then the Mordell group is finite. So this is one implication of the Berks, Swinterson-Dyer conjecture for some very special elliptic curves and they have to have complex multiplication and they have to have rank 0. So let me explain what complex multiplication is. So most elliptic curves have only the obvious endomorphism. So we can ask for endomorphisms of an elliptic curve E and they all have endomorphisms which take a point A to N times A for N in the integers. And a few of them have extra endomorphisms. So let me give some examples and an example of a curve with extra endomorphisms. We might look at the curve y squared equals x cubed minus x.  You see here the only automorphisms would be when N is plus or minus 1. And it certainly has these automorphisms because we can change y to minus y and map x to x and this will be an automorphism. But there are some other automorphisms to this because we can change y to I times y and x to minus x. So this is some extra unexpected symmetries which are things called complex multiplications. They turn out to be multiplications by complex numbers if you represent the elliptic curve as a torus. So that's what complex multiplication is. Coates and Wiles also assumed it was complex multiplication by something of class number 1 but that's the minor technical detail. So very roughly the idea of their proof is that if the Mordell group is infinite then they showed that L1, which could be written as some sort of algebraic number times some transcendental constant, the algebraic number would have to be divisible by an infinite number of primes which are sort of actually vaguely related to irregular primes but never mind. So you could say roughly speaking that if the Mordell group is infinite then L1 is divisible by an infinite number of primes. And this shouldn't be taken too seriously because this is actually a real number so saying it's divisible by prime is kind of meaningless but you can make sense of that. And so the next piece of work that I want to talk about was by Gross and Zagier and they showed that if the elliptic curve E is modular, whatever that means and I'll explain that in a moment. And the L function has an order 1, 0 at s equals 1 then this implies that the Mordell group is infinite and that the proof of this used something called Heidener points. So let me explain very roughly what a modular curve is and what a Heidener point is. So modular means roughly that the elliptic curve can be parameterised by modular functions. This means there's a map from the upper half plane to the elliptic curve given by some sort of modular function. And a modular function is one that, well the similar sort of modular function being variant under sl2z acting on the upper half plane by a b c d tau equals a tau plus b over c tau plus d. It turns out that you can't actually use these sorts of modular functions to parameterise elliptic curves but there are some slightly more complicated sorts of modular functions which will map the upper half plane to elliptic curves. And it turns out that if you can do this then you have really good control over the elliptic curve. So modular elliptic curves as they're called turn out to be particularly nice. And now what is a Heidener point? Well a Heidener point tau in the upper half plane is one that satisfies a quadratic equation a tau squared plus b tau plus c equals 0. Well actually that's not quite true. If you take one of these points and map it to the elliptic curve it turns out that it's not quite a rational point but it's a point with algebraic coordinates. But then by fiddling around with that and summing over Galois groups or something you can get a rational point out of it. So by looking at these quadratic irrationals in the upper half plane we can get points on the elliptic curve. And the idea of Gross and Zagier's proof was they showed that the height of a Heidener point on the elliptic curve e is related to the derivative of the L series at s equals 1. It's some complicated constant times this derivative. So the height of a Heidener point is some way of measuring its size that I won't go into in at least not in this lecture. And the proof is very simple in principle. You just calculate the height of a Heidener point and calculate the derivative of the L series and check they're equal. In practice however the calculation is horrendously complicated because each of these things is incredibly difficult to calculate and when you calculate both of these you get a complicated sum of many different terms and you have to check that each of these terms match up and so on. And the calculation is well over 100 pages long and is really terrifying to look at. Incidentally there's another interesting consequence of modular elliptic curves. Let me give an example of a modular elliptic curve. So suppose you take the elliptic curve y squared minus y equals x cubed minus x squared. Then it turns out to be related to the following modular form. A modular form is a slight variation of a modular function. And it's right, sum of cnq to the n is given by the following series. It's q times product 1 minus q to the n times 1 minus q to the 11n. So if you've done modular forms you might recognize that this is a modular form of level 11. And it turns out to be very closely related to this elliptic curve because if the number of solutions modulo p is written as p minus cp then the numbers cp are given by the coefficients of this modular form. And this turns out to be closely related to the fact this elliptic curve is actually modular in a way related to this modular function. In particular it turns out the L series of the elliptic curve is a melon transform of a modular form. In particular so the L series of this curve would be the melon transform of this modular form here. In particular this means the L series can be continued to all complex s. So for modular elliptic curves we know the L series does actually make sense at s equals 1. There's another interesting point about it. These modular forms satisfy a function equation and a certain function equation. And this implies that the L series also satisfies a certain function equation. It says that L star of 2 minus s is plus or minus L star of s where L star is L times some junk that I'm not very interested in at the moment. And we have a sign here and the sign is plus or minus depending on whether the order of the zero at 1 is even or odd. So although it can be quite hard to tell what the order of the zero is it's easy to tell whether the order is even or odd. So what Gross and Zagia did was they showed that if the order is 1 then Hegner points give you points on the elliptic curve of infinite order. If the zero has ordered greater than 1 then all the Hegner points turn out to be zero and are much less useful. So the next piece of progress I'm going to talk about was by Collier Vargin Collier Vargin, sorry. Again we assume that he is modular so it can be parameterized by modular functions and he showed that if the L series has a zero of order 0 or 1 then the Mordel Vey group or the Mordel group has rank 0 or 1 respectively. So this is a big chunk of the Birch-Swintersen-Dyer conjecture for ranks 0 or 1. His proof used these things called Euler systems which I don't know everybody says that Euler systems are named because of their relation to the Euler product for the zeta function but I must admit I've always had trouble seeing the connection. One of the interesting things about this was that he was able to actually show that some Tate Shafarovich groups had finite order which until then people had actually known they were finite order. So it actually became possible to do the part of the Birch-Swintersen-Dyer conjecture where you look at the coefficient C where the L series is about some constant times S minus 1 to the G. So far all these results only applied to modular elliptic curves so the next very big breakthrough was by Wiles who showed that many elliptic curves are modular and his proof was soon after extended by Broil and Conrad and Diamond and Taylor who showed not just many elliptic curves are modular but all elliptic curves are modular they sort of extended Wiles's results to cover some more technical cases and this was a really astonishing result when it came out I think most people before Wiles's work was announced thought that the easy part of the Birch-Swintersen-Dyer conjecture would be proving it for modular elliptic curves and it would then be really difficult to show that all elliptic curves are modular this is the famous Tanyama-Shimuro-Vey conjecture so Wiles sort of turned this upside down he showed that he managed to solve what everybody thought was the hard part of the Birch-Swintersen-Dyer conjecture in particular this shows that the L series is always defined at S equals 1 so in particular the Birch-Swintersen-Dyer conjecture actually makes sense before it talked about the L function at S equals 1 and it wasn't even known if this was a well-defined number so since then we've had a result by Baagavar and Shankar who showed that in some sense lots of elliptic curves have ranks 0 and 1 lots means at least a positive proportion and possibly even most of them I'm not quite sure what the current state of the art of this is so in some sense we've made considerable progress on the Birch-Swintersen-Dyer conjecture due to Colovargan and Gross-Sagian coats Wiles we've got pretty good control over the rank 0,1 case we know that probably most curves have ranked 0 or 1 and of course we know they're all modular which was thought to be the hard part of it so what's left to do in the Birch-Swintersen-Dyer conjecture? well what's left, what is still open is the case of ranks greater than 1 and what's the main problem with doing this? well I think one of the main problem is that points on an elliptic curve E with rank greater than 1 seem to be really hard to get hold of so if the rank is 0 then there's no problem because there are only a finite number of points so you're only a finite number of points away from having them all if E has rank 1 then Hagnar points give you a pretty good hold of all the rational points because the Hagnar points generate a subgroup of finite index but if the rank is greater than 1 I don't think anybody knows a sort of general way of writing down something that say generates a subgroup of finite index in the Mordell group so my feeling is that the main obstruction to finishing off the proof of the Birch-Swintersen-Dyer conjecture is finding a good way to generate almost all points on an elliptic curve of rank greater than 1


Thank you for stopping by today Kobe, we really appreciate it. You've been busy since your basketball career and starting Granity Studios and a lot going on, an Oscar award-winning filmmaker and now you're launching the Wisenerd series, a fantastic fantasy book, part of a series of books that are going to be coming out geared for teaching children some life lessons. And what was the inspiration for Granity? Well, the inspiration for Granity was how do we create stories that raise a certain awareness of how to deal with the journey within, the emotional journey. I feel like a lot of kids, we teach them certain actionable things, basketball, soccer, football, whatever the case may be, but we're missing the emotional component that comes along with that, the anxiety that comes along with that, the anger or the love and all these emotional things that take place from play to play, we're missing that teaching moment. And so the best way to do it, at least what I found with my children is not to tell them about it because after a while they're just like, I want to hear it no more. But instead you kind of put it into something that's creative, right? And so through entertainment, through fantasy, through magic, you start creating life lessons that are easier to digest. Yeah, in a way it feels like you're mentoring all of us through your works at Granity and the book itself has a number of characters in the book. Do you feel that the characters in the book you're drawing from personally teammates, mentors along the way? Yeah, it's a combination, a combination. So the coach himself, Rollaby Whizzenard, is somebody that was inspired by some of the coaches that I've had to pass, namely Phil Jackson. Right. Right, and the name Whizzenard actually was inspired from Phil. I mean, Phil was a big Zen guy.  And I'm like, dude, you know, they might drug test us at any minute. Like, I don't know what you're putting in these incense, you know what I'm saying?  And then another great mentor and a person I looked up to and studied a lot was John Wooden, who was known as the Wizard of Westwood. And so I took the Wizard of Westwood and the Zen guy and I combined those things and created Whizzenard. OK. All right. So a lot of it's inspired by those two coaches and Bill Russell as well. And then the kids themselves, yeah, there's a lot of me there. And there's also a lot of some of the teammates that I've had to pass. I pulled a lot of inspiration from my daughter's team that I coach now, 12 year old girls team. OK. And you'll see a lot of those same kind of characteristics within the characters. It was something you mentioned about how that try to instill these lessons in your children and they're getting tired of hearing those lessons. Right. But to be able to put them in the form of a story where you can emotionally invest in the characters in their journey and then learn from them through these narratives. It's a very powerful thing. And it's something that we've been discussing on the show for a while now. Yeah, we all have this hero's journey that we're on this movie that we're living. And it's amazing to be able to create a story that encapsulates your hero's journey and all the lessons you've learned along the way. Yeah. Thank you, man. No, it's it's it's, you know, it's funny when it comes to the art of creating, you have to have to kind of this left brain of this right brain approach of creativity. Right. But then, as you said, in the hero's journey, it does involve a lot of structure. Right. Right. So you also got to start. You got to be fundamentally sound when it comes to telling your story and make sure you hit the beats that are necessary, making sure you're taking the reader or the viewer through a journey of character growth.  You got to figure out what's going to happen not only in this book, but what are going to happen in subsequent books. Right.  It's fun mapping all that out, man. Is this something that that has been you've been working on for a while now that it's always been in the back of your mind?  OK. It's about 2,000 years of history. I sat down and thought about what it is that I wanted to create and how I wanted to create it and came up with the magic, the rules for the magic and how it relates to sports. Right. And and then from that, I started thinking of characters.  You can have the best plot in the world, the coolest looking world you know that anybody's ever seen. But if the characters aren't ringing true, it doesn't work. Right. If they're not relatable, it's not a great story. And I feel like one of the big lessons in this first book in the series is really the characters struggling to overcome their fears. Yeah, yeah. And your youth days in basketball, what were the biggest fears that you are struggling in overcoming? Well, you know, I learned at an early age from something actually has nothing to do with basketball, but everything to do with it. I was in a karate class and I was just starting out. I was a white belt. And for some reason, like we have these days during the week where you know, everybody kind of sits in a circle and you duke it out with another belt. You work on all the things that you're just working on. And so I was fairly talented, right? So the guy goes, OK, it's insane. All right, you're going to go up against this guy.  And I'm like, what the I'm not going to fight this dude, man. He crazy. Like, no, I'm not, you know, and now you have the head gear on. You got all this stuff on, right? You got foot gloves on the whole thing, right? And I was freaking out, completely freaking out. And he told me at the beginning of class so the whole class I'm freaking out.  But I remember that was about eight years old. The car on the way home, I remember thinking that my imagination made it worse in my own head. It was going to be the worst thing ever that I actually fought him. And it wasn't. It's like, it was OK. And I did pretty I did OK. Right. But that taught me a very early lesson is that we can get in our own heads so much. We can psych ourselves out so much. We can almost talk ourselves into a fearful situation as opposed to just being and I've never forgotten that lesson. And in Muse, you touch on having to travel so much as a kid and really finding solace in basketball. Do you feel like your imagination was also playing a big part in your development in those days? Oh, my God, yes, because it involves playing a lot by yourself, right? You know, in Italy at the time, soccer was and still is. I mean, it's the best thing since sliced bread, right? And so you go to the park. There's not a lot of kids back then that wanted to play basketball, right? So I had a lot of room for imagination. And so on the shooting, I'm imagining at the time being in the forum. Playing at the Boston Garden, you know, here in the crowd, you know, acting as if I was the play by play announcer. And so there's certain was a lot of imagination there. Yeah. And I know a big part of that as well was identifying those weaknesses in your game and imagining some of the other players you looked up to and the skill set that you're hoping to develop. Yeah, you I watched a lot and I studied a lot, you know, at the time, I didn't think it was study.  I wanted to watch Bird. I wanted to watch Magic, Alajuan, Barclay, you know, Robinson, Baylor and on and on and on and on. And I try to imitate those moves, right? You know, and my left hand was weak. I had to work on my left hand. That's what I did. And it was just fun. I just rather be doing nothing else. I think it's that where it becomes it's the obsession, right? It's like we wouldn't want to be doing anything else. And everything that we're doing in that moment is pure joy. And it takes us away from wherever we are and completely envelops us. But isn't that that's that's such a, you know, it's hard to find that thing that you love that much, isn't it? I mean, that that's kind of the key to this whole deal. Right. And for those of us that are really lucky, you can find what that thing is at a very early age. Other times it requires a lot more work. It requires a lot of trying and experiments. And when you find that thing, it's like, right? You don't have to wake up in the morning and psych yourself up. Like, oh, man, I got to do this today. All right, I got to get jazzed up.  I can't wait. And that's like, you know, that's more than 80 percent of the battle. I think I think that also if you're able to find something like that when you're younger, that as you get older, you can understand that process and know what it's going to take for you to get focused into something. At least that's that's how it's been for us and discovering a lot of new stuff for ourselves. Yeah, I mean, having struggles early on creates that strength and resilience that you're going to depend on as you become an adult. Yeah, those that's actually extremely important, too, because it's part of the story as well, is that you don't run from those moments. Yeah, you don't run from them. You embrace them, right? You got to embrace the storms. You know what I mean? Yeah, the fears that we have, the moments of suffering. They're all part of the process. They're all part of growth and it's nature, right? You got to be able to handle those things, man. Now, obviously, we know a lot about your relationship with Phil over the years, two stints working together.  You know, it's it's funny.  And I just said, just to make you smile. And he watched it and he responded in a very typical, filled way, saying they they move the ball extremely well. They understand how to deploy the defense, right? Like very, like very matter of fact, you know, like really looking at the execution of how they format triangles, how they read angles or some stuff. And he said, you should be very, very proud. The girls are doing a great job. So I keep them involved in how the girls are progressing for sure. And as a teammate, you were known for being intense. Is that intensity waned with your children now and coaching them? No, it's different. So like as a player, the intensity comes from the action. Like you're on the court, you're entrenched in that kind of that combat. Right. As a coach, it's different. As a coach, my responsibility is to teach them how to fish. That's my responsibility. Give them the fundamentals, teach them how to think. And then when they go out and play, I let them coach themselves because they have to be able to problem solve. And when I see things that are incorrect, I just hold on to them and then we can work on them in practice. Right. So it's having the patience to allow them to go out there to think independently, to make mistakes and all this other stuff. And then you can teach them patiently, you know, in practice every day. It's funny. Johnny and I learned a new term called lawnmower parents. This idea of parents foreseeing the adversity and getting ahead of it before their children can even feel the adversity. No way. No. Yeah, I was going to say, sounds a lot different than the perspective you're bringing. No way. No. I think our job as parents is guidance, right?  You allow them to make mistakes. And then you're kind of there to help guide them through that journey. Right. It's a journey that they have to take. It's inevitable. They have to go through this journey. I think it's our job to just try to try to help guide them through it. That's all. And you're famous for having an alter ego, Black Mamba and compartmentalizing what was going on in that part of your career personally so that when you stepped on the court, you were all business. And that alter ego changed the arc of your history, your career in basketball. That imagination with Black Mamba, it sounds to me, has been what's ignited this flame with Granity. Yeah, it's certainly part of it. You know, like I used to write ads a lot. Used to write ads. So I had an ad agency a long, long time ago and I wrote ads for Nike. My Nike ads, things of that nature. So writing and imagination was always a part. Storytelling was always there. And yeah. So the Black Mamba stuff all comes from that sort of imaginary world of creating something else, right? But I also learned from that, that even through imagination, things must come from truth. Right. Who am I on a basketball court? I'm this thing, right? So it has to be anchored in a form of truth. And that's what I try to do with what I'm creating now. And for the audience listening who hasn't had a chance to check out your book, we can pre-order it on Amazon, the Wizzner and Sirius. It's part of five. What are the biggest life lessons that you hope the audience takes away from these books? Well, the biggest journey that you'll see the characters take, which is really important for young men, right? Now, the rest of the novels are all for I have female protagonists because because of my daughters, you know what I mean? Like, I just can't help but write characters that are like based around my daughters. But for this series, I felt it was very important for young men because as young men, we are taught a very early age that any sign of vulnerability is a sign of weakness, right? Crying, that's weak. Don't do that. Right. And so I think it's very important for these young men to go through this journey of self-acceptance, first and foremost, right? Because there are a lot of things that are personally holding them back that they've buried either consciously or subconsciously, that's holding them back from reaching their full potential as young men and as athletes. And until you square with those, you'll never hit that full stride. So the first one is a really big, important story about self-acceptance. And then from that self-acceptance, it teaches you empathy and compassion because even though I can't see what magical journey you just went on, I know that you've gone through one because I have as well. So that helps me better understand and relate to others. And then we'll progress to being able to have the bravery to share what it is, what journey it is that you've just been on. And with the relationships with your teammates that you drew from in this book and now looking at relationships off the court, do you feel like you've changed the way that you handle some of your friendships or relationships? Obviously, you're well known for your intensity in the locker room. Yes. Yes. I've had to mature as my playing days went on because you start understanding that there are lives outside of the game. Right. There are personal things that happen in people's lives that are manifesting themselves through the game. And as a good teammate, I had to understand that and say, OK, let me listen to these guys. Let me let me get a better sense for who they are as people because that's that's really the true way to bring out the best in somebody else is to first understand that person right where they're coming from. Exactly. Was was there a point in your career that brought that lesson to the forefront where you realized that you were going to have to open up to these these other stories and to the to your teammates and what they have going on having having children. Yeah, that's because you have to think outside of yourself, you have an additional you have a responsibility and you know, when you have kids, it's like this responsibility is the most important thing in the world. Right. And how do you raise? How do you raise a young child?   You become consumed with trying to provide them with proper guidance and proper care and it changes you. It changes you as a person, man, and it makes you think more outwardly versus inwardly. And you talk a lot in in use about the sacrifices that were made throughout your career, whether it's not spending time with your family, not spending time with your friends, not going on vacations, those famous workouts that your teammates dreaded in that, you know, hard work gets us there part of the way. But to achieve greatness, especially now, we look everywhere, hustle this, hustle that work hard. What else is it that that goes beyond just the hard work, the effort? Well, it's it's trying to balance and win all facets of life. It's really hard to do, right? Like, how do you succeed at your craft? But how do you also have a stable family? Right.  That's the that's the gazillion dollar question. How do you balance those two things, man? And and I think that's the part that gets missed a lot. I mean, we all talk about the hard work. We all talk about, OK, be this, be that, be this, be that. But what I figured out is I got older. It's not about working hard in terms of putting in long hours, but it's about working smart. It's about working smart. When you work smart, it gives you more time to be able to spend with your family, right? And have that consistency because it's important to win all facets, man. And as we talk about this whole universe that you've created, what are you most excited about happening in this book series? Watching how young children respond to, you know, particularly young athletes, like I was a young athlete, it was like, you'd have to pin me down to give me to read a book. Right. You know, I was like, I want to run. I want to play. It's got nothing to do with me. I don't, you know. So I think finally creating something in the market that is centered around young athletes, finally, something that they can sit down and say, OK, not only am I learning a life lesson from this, which we all know kids don't really care about, right? They care about having fun while you're consuming content and that it's centered around something that they actually enjoyed doing and do. Right. So seeing their reactions to it is what I'm really looking forward to. And how did your kids react to the book? Did they put it down? No, they loved it. So like I wrote it with them. You know, they were part of the process come from them, the dialogue, the conversation between each other. I mean, that's like a lot of our conversations and how we talk in the same sense of humor and cadence. So a great deal of all of my series are inspired by my children. So and are there any teammates that made it into the book and in characters that you're yeah, they're bits and pieces of them, certainly. I mean, you know, I remember having a teammate who could work and working on his shot all day long. But as soon as a game starts, couldn't do it, couldn't do it. Or I had a teammate that, you know, practice starts at 1030. They show up at 1030. All right, practices at one, they leave at one. Right.  But what you come to find out is that there are actually other things that that are truly the reason why he doesn't want to apply himself and do extra work because he's more so afraid of the failure. Like if I really put myself into this thing, 110 percent, and it's still not good enough, then how do I feel about myself? Right. Right. So there's a there's a lot of things that I picked up and put into the book. And having a career, a professional career, especially that starts at such a young age and being forced into the spotlight. I know one of the things that Johnny and I talk a lot on the shows, how to foster the right relationships with positive, supportive people and how to weed out the negative relationships and negative influences. And obviously, some of your stature is going to have people from all walks of life wanting a piece of you. How do you assemble that inner circle of people that you trust, whether it's a project like this book or in other areas of life? Yeah, you know, the people, you know, you can feel it. So people have a certain energy about them when they're people in the world that are focused and like have a I wake up in the morning with a purpose. This is what I'm doing. You can feel that energy or you can feel it because it's a kindred spirit. So those are the people that I tend to work with a lot. And if you don't have that, I can sense it. I can sense it. But we're also very disciplined. If you're a person that's very distracted, hanging around the wrong crowd, not having that sense of purpose, we don't want to be around it. We don't want to be around it because that stuff will bring you down, man. Stuff will bring you down. So we're very, very disciplined, very, very focused on finding, you know, writers, editors, story artists. You name it that have a like true, true passion for what it is that they do. I think you mentioned earlier of being excited to get up every day to go to get after it. That is something that you're going to be able to see in people. I mean, how they approach their day, how how how they feel about getting getting out there, how what time are they going to sleep to be prepared to take it on? And it certainly is we've been discussing it on the show. If if you're afraid to go to bed because of what you're dreading the next day, that next day should be spent in fixing that. Right. Right. Right. Right. Versus hiding from it. Right. So let me just stay in the bed. Stay in the bed. It'll pass on its own. No, not who we want around us. No, no, no, you you claim that you viewed the Achilles injury as your Mount Everest, and that's a fascinating mindset.  Well, yeah, I mean, you have winning championship when you start the season. That's the mountain. Right. Now that mountain is made up of a million little steps, right, and little goals along the way. But yeah, I certainly do that. You establish your mountain. And then after that, you don't look to the summit. Forget about it. You can't even see it. Just focus on the next step in front of you, right?    The next thing you know, you find yourself at the top of the mountain. And what's your your Mount Everest right now? Right now is the stories building the studio. How do we do that? Piece by piece.  You say, just focus on the basics. What are the basics? The Wizz and Art series, novels done, bring it to market. What are those steps? Right. The other not. So the three novels that we're releasing this year are all finished. They're all finished. So now it's about executing. Right. It's about execution. And surrounding yourself with the team members who will execute. See, that's the beautiful thing is that we've been very, very fortunate to be able to do that. We have a great team. We have a great team.   So when I say, you know, you have no restrictions on creativity, be as creative as you want in design and, you know, right, whatever. And oh, OK. And then they come back and go, is this OK? I'm like, no, no, I don't think you're understanding me. You know, I am not a designer, right? You have to tell me, is this the best work you can do? If it is awesome, right? So you got to hold yourself accountable. But that's what we're going through now. And it's fun. Yeah, it's certainly a different challenge than the athletic pursuits earlier in your career. When when you were facing retirement, realizing that this was going to be behind you, what were you you thinking about the second act in your career? Well, you know, I was thinking all the wrong stuff. Like, all right, what's the best? What's the biggest industry I can get into? All right. Right. How can we generate the most revenue sort of thing? Wrong. And I kept running into a dead end. I don't know what I'm going to do. I wake up every morning, I don't know what I'm going to do. Finally, I said, OK, what is it that you love to do? I love to tell stories. Love it. Love it. All right. So what the heck does that mean? Right. So my wife asked me, all right, what are you going to do now? So I'm going to be a storyteller. She goes, all right. So let me get this straight. So when we fill out a form where Natalia is at school, she has to fill out a form. It says, what is your dad's occupation? She's going to write storyteller. Is that what you're telling me right now? I'm like, yeah, I guess. I mean, it worked well for Walt, I guess. I don't know. She's like, you are not Walt Disney. Yeah, not yet. You get but you get the idea. And so once I made that decision, then everything became about that. How do we just tell stories that are going to inspire another generation of athletes? I love that. I mean, we, our last month, each month we do a different theme. The last month was happiness and it's about finding passions and waking up to be excited to go out there and how that's going to happen. Did you go through a time where as you were waking up, as you were going through the day like, this is not working. I'm not happy. This is, because I'm not, I'm obviously not doing what I should be doing. Yeah, for my last season of playing basketball, yes. And that's when I knew it was time to retire. You know what I mean? Like that moment, I had that. And I was like, all right, time to hang it up, not look back. All right, so that's how that decision was made. And so, but now, no, like I was going through the whole year, writing, writing, writing, writing, writing. Yeah. You know, dear basketball producing that, right? So like the day after my last game, I was on a phone call with John Williams and Glen Keane, working on the production for Dear Basketball. So it was like, after one thing, we just moved right to the next. Right on. And on we go. And do you find yourself being a perfectionist and like, oh, I'm not sure I can release this yet. I'm not sure it's right in this creative process. Obviously it's a lot different than working on a jumper. For writing, yes. So like going every single, going over all the words, right? So like Dear Basketball, for example, when I wrote that, I truly did follow the hero's journey. I just, I just did it in five minutes, right? So if you look at the structure of the piece that I wrote, you'll see the same thing. You'll see the same thing. You see the call to adventure. You'll see all of that stuff in there. And just hitting all those beats in a five minute span. But I was an absolute perfectionist when it came to that. Like every word must be well cared for. The rhythm, the cadence, the one thing I did know is I wanted to end it with a like five, four, three, two, one. Because in my mind, I was like, John Williams is going to crush that. He is going to crush it. I don't know how, but I just know he will. You know, like that sort of thing. And, but then after that, you know, you work with people that are the same way.  So you just, just step back and let them be them. That's all. And I feel that with all of this going on, creative and raising a family, what do you do with your free time now outside of those two aviaries? Well, I coach my daughter's basketball team. No, but outside of that, like we'll do a lot of things together as a family. Like we love going to movies. We love going to shows. We love trying new restaurants and, you know, sitting at home and playing Uno. We're a big Uno family. Okay, family card games. Yeah, yeah, we love that sort of stuff or like play headbands and you know. So we just try to do fun things with each other, which becomes harder and harder because the kid's schedules busier than mine. Yeah. You know, but we try to find those, those kind of intimate moments as a family. And how does the inner family competition work? Obviously you're known for being tenaciously competitive. Man, listen, if you think like, you know, people that watch my kids play sports and say, okay, really competitive. And they say, oh yeah, well, I wonder why. I'm say, yeah, because you ever met their mama. But that's as every bit as competitive as I am when it comes to that stuff, man. I won't sit next to her when it comes to Uno. If I got to make her pick up two or pick up. Oh yeah. Oh no, it's not going to be good. That famous look you gave on the court, you're getting back now in Uno. She gets to me with the eyebrow. Oh. She's got that eyebrow.   Hey, Gigi, you want to switch seats?  Now mentorship was a huge part of your basketball career. Who do you consider mentors now in this second act? You know, when I first had the idea of starting a studio, the first person I spoke to was Oprah and how she went about building Harpa. And she was very patient with me and we sat on the phone for about an hour and a half. And she walked me through her journey of how she built it. Other great mentors are people like Shonda Rhimes, who is the empire that she's built over the years. And talking about character development and how to write story and how to build teams and how to grow teams. Because the other thing is bringing in young writers and allowing young writers to develop and all of a sudden they become show runners and all this stuff. And how do you do that? Johnny Ives from Apple, Tim Cook. And I'll pick up the phone and call them when it comes to structure of the company. How do you create a company that is moving in one direction versus a company that is fractured and siloed and all that sort of stuff. I've been very, very lucky to have some great mentors in my life. Debbie Allen's another one. Very, very lucky. And are you actively mentoring any of the young basketball players in the league? Yeah, so I'll bring a lot of young guys that come out in the summertime and spend two, three days, some cases a week. And we'll work together every single day. And during the season I'll get phone calls or I'll get text messages every now and then. Kyrie Irving, James Harden, all these guys. I want me to take a look at a piece of film or just have a question just about team dynamics and challenges that they may be facing. Cause you know, 20 years I pretty much, I've seen a lot. Yeah, I've seen a lot. So I try to talk to the guys as much as I can. Giannis is another one. So yeah, I try to spend enough much time as I can with those guys. I was curious in that studio when everyone's working and doing the thing and trying to create a creative atmosphere. Do you feel yourself bringing in some of the fills and into that room to let everyone do their thing? Yeah, you know, not yet. I haven't had an incident going yet. We already kind of have that. You get certain creative people and they're kind of doing that on their own anyway. So for me it's just constantly reinforcing that we are a creative company and everything that we invest, things that we build is all centered around making sure the story is king. Making sure the design elements. We try to do everything to keep you immersed into the story. But when you see the book, I love telling this because it just shows how maniacal we are. I mean, we spent two weeks on designing the barcode on the book. Just the barcode, just the barcode because we didn't want to create something that pulled you out of the story even if it is barcode. Right? Everything must be from this world. Every little detail. Everything. I love it. Thank you for joining us. We really appreciate it. It's been an honor. And we're excited to catch the rest of the series and see where the Wizzner series goes. Thank you, man. I appreciate it. Thank you for having me. Absolutely.


Vowels and consonants are the basic segments of speech. Together they form syllables, larger units and eventually utterances. Superimposed on the segments are a number of additional features. They do not characterize a single segment but a succession of segments. These additional features are referred to as suprasegmental, non-segmental or prosodic features. We will use the most common term suprasegmental and will discuss its phonetic groundings in this e-lecture. In particular, we will discuss aspects of loudness with its physical counterpart intensity measured in decibels. We will look at pitch and its physical counterpart frequency. The measure for frequency is Hertz. And we will look at length to which physicists refer as duration, normally measured in terms of time units such as seconds or milliseconds. Additionally, we will look at secondary articulation. That is, we will look at an articulatory phenomenon that stretches over more than one segment. And secondary articulation is the most important of such phenomena. Let us start with loudness. Now, in a spoken utterance, the syllables are never produced with the same intensity. Let's look at an example. Now, here's the name of a well-known English football club. And I will now read out this name without suprasegmental effects, that is, in a steady state mode. Manchester United. And you will certainly agree with me that this is not the normal mode of speech. In real speech, some syllables are unstressed, that is, they are weaker. Other stressed are produced with a higher degree of loudness, that is, they are stronger. Articulatorily, a stressed syllable is produced with an increase of respiratory activity, that is, more air is pushed out of the lungs. From a listener's point of view, stressed syllables can be identified by means of a combination of several suprasegmental features, such as loudness, pitch and vowel length. So, a normal or real pronunciation would be something like Manchester United. And then you would certainly agree that the syllables man and nigh receive more stress than the other syllables. So, in long words, such as these, more than one syllable may be stressed. And it seems suitable to assign degrees of stress to the syllables involved. So, this one would possibly be the main syllable or the syllable that receives the highest amount of stress. Manchester United. Let's look at pitch next. Now, as we said earlier on, the physical counterpart of pitch is frequency and it is measured in hertz. During speech, pitch is changing continuously. There are no steady state pitches. Throughout every syllable in a normal conversational utterance, the pitch is going up and down. Let us illustrate the pitch range used in some standard utterances of British English. And we will use the native speaker we recorded for the Virtual Linguistics Campos. Now, let's listen. Mary gave the money to her father. And we could perhaps assign free pitch levels to this sentence. Now, in the next sentence, we could possibly assign four levels. By the window reading a book. Plus a little onset here associated with the first syllable, I. And finally, three pitch levels again. He wanted to go to town on Monday. The pattern of pitch changes that occurs in these examples is referred to as intonation. The phonetic analysis of intonation is primarily concerned with the exact description of it. When we listen to a stretch of speech of some length, it becomes apparent that it is organized into tone groups. Now, here is this stretch of speech. The intonation of a language can be described as its melody. And you will perhaps agree that this stretch of speech is organized into three tone groups. The intonation of a language can be described as its melody. The boundaries between these tone groups are referred to as terminal junctures. Now, every tone group contains a nucleus. That is, a syllable that is more prominent than any other syllable in the same tone group. So in the first one, in the first tone group, you will agree that the nucleus is associated with the syllable lang. The intonation of a language. And in the second tone group, it is scribed, can be described. And in the third one, it is as its melody. So here we have our three nuclei. I love that plural, nuclei. The syllables preceding the nucleus are referred to as the head, indicated in blue. And the syllables that follow the nucleus are referred to as the tail, indicated in green. The pitch associated with the nucleus is referred to as the nuclear tone. So the tone we have in the first example, the intonation of a language is possibly a fall rise, can be described. Cribed is just a rising tone. And as its melody is a falling tone. So this then is a phonetic analysis of pitch or a phonetic analysis of intonation. Let's look at length next. The length of sounds of syllables and words and even utterances is variable. And the variations are used for a variety of linguistic purposes. Let's look at some of them. For example, vowel length, as we know, occurs in British English, seat versus sit. However, the difference between seat and sit is not just one of length only. It is really a matter of a combination of length and quality because the two vowels involved have different positions on the cardinal vowel chart. In German, the situation is really a difference between length, boat, that is, in the boat versus moral, is only a matter of vowel length. The short O occurs in unstressed syllables and the long O in stressed ones. Now another possibility is to associate length with syllables. Now look at this utterance, shall I leave now? Now if I use a very short syllable as my answer, shall I leave now? Yes. This might involve a lack of interest, lack of emotion and so on. And if I use the second option, shall I leave now? Yes. This of course indicates extreme emotional involvement. For example, and in utterances, we may have utterances that involve high speed where certain portions are lengthened, others are shortened. So for example, in this little stretch, you can read it as follows. The changing of the tempo of an utterance may increase or decrease its character. You will perhaps agree that a decrease is often associated with a high degree of sophistication involved. Now over and above these three main suprasegmental features, we have what we refer to as secondary articulation. Now this is defined as an articulation with a lesser degree of closure occurring at the same time as another primary articulation. Generally, the following types are distinguished. Now let's start with the first one, labialization. Now labialization is referred to as the addition of lip rounding, so this would be some sort of example of constant labialization. Since the tongue is not involved at all, labialization can be combined with any other primary or secondary articulation. Labialized segments are indicated by a W as subscript or placed after it as a superscript. Now the next secondary articulation we want to look at is palatalization. Palatalization is the addition of a high front tongue position to another articulation. Palatalized segments are indicated by a J as subscript or superscript. Palatalized consonants can be found in the Slabonic languages, for example in Russian, where contrasts between brat and brat are made. Vialization involves the raising of the back of the tongue during another articulation. Vialized segments are indicated by a tilde. We know that from the English examples, the English Vialized L as in pool or bill, well let's quickly write them down, so in English we would have something like pool where we have a Vialized L at the end, or we have a special superscript which is often used as a diacritic for the notation of Vialization. Now finally we have pharyngealization. Sorry I forgot to imitate Vialization with a high tongue in the back. This is about how it sounds. And finally we have pharyngealization. Now pharyngealization is the superimposition of a narrowing of the pharynx. So this is about pharyngealization. So it's a narrowing in the back of the mouth. Pharyngealized segments are indicated by a pharyngeal superscript here or subscript. Pharyngealized consonants can be heard in Arabic. Now secondary articulation which often stretches over several segments should not be mixed up with co-articulation. Co-articulation requires that two articulatory postures are of equal rank. Here are two examples. The first one draws a distinction between fronting and retracting. Now whenever ke proceeds a val as in ki, the constriction at the velum is fronted. So here is about the constriction and the additional diacritic is a little plus symbol showing that there is some sort of fronting of the tongue involved. If you compare that with the, so this would be ki, if you compare that with something like cor, you would have a retracted position of the tongue. That is the tongue is further back in the mouth. And of course you would have a second type of articulation namely labialization because you have lip rounding as in cor. Now in another example we have a dental effect. For example in words such as width in present day English you would have an effect of fronting of the d with, because the word final dental fricative automatically leads to this fronting effect making the alveolar plosive resulting in a dental articulation. So perhaps we would have devoicing too here or you could use a t alternatively as a phonetic symbol. Now this dental effect is indicated by this little tooth as a subscript. Let's summarize. We discussed the following suprasegmental features. Loudness and its physical counterpart intensity. Pitch and its physical counterpart frequency. Length and its physical counterpart duration and then we looked at secondary articulation effects. In order to find out how these suprasegmental features function in a particular language consult our respective e-lecture on suprasegmental phonology. For example the e-lecture present day English suprasegmental phonology.


169 apter blica । । । । । । । । । style option it will be very frequently trade यह वो लेए हो टीने है in contrast America's style option maybe exercise at anytime during the contract अगर उसी आम बात करेएे के मरें contract our three month contract अगर उस्वाप्ट्वागी then you have to wait for three months it can be exercise at any time यह अगर तीसरे दिन भी अमारी only few broad-bed indexes have American options. Individual stocks may, bonds may, they are more in ETFs.  Example, let's discuss. Call option on the stock, we have a call option, our price is 80 rupees. We have an 80 rupees call option, which means we have a right to buy. We can buy 80 rupees. And this contract period is 1 month. 1st January, 3rd January, 1st January. So, if this European option was there, then we would have only in the closing period, i.e. on the 31st or the last day of the settlement, we would have seen that if the stock is more than 80, i.e. 90, then we would have bought the 80. If the stock was less than 80, then we would not have exercised the option and could have bought it from the 77 market. But it can only be done on the end of the period. But if this was an American option, then in the whole month, if this stock is above our level and we think that we should lock it here, then we can do it. i.e. from 1st January to 31st January, in any spell, any trading date, when we think we can, get a good return, then we can do it. See, there is more advantage in this. In the last day, if it is above, in the whole month, at any time you can get a gain, then you can lock it. So Americans are more flexible. Settlement price is the official closing price for the expiration, establishing which option are in money, subject to auto exercise. i.e. when we said that if this is in our favourable on the expiration, then we said that we gave it the option of auto exercise, that if it is positive, then you immediately lock it. i.e. if it is the option of buying, if it is the option of the market, then you can do the option of auto exercise because we are getting Rs.1 from it. So whatever the case may be, if it is going to be a gain, then just do it. Any option that is in the money, by 1 cent even, or more at expiration, is automatically exercised. Because we have quite defaulted that the expiration is i, if it is European and we are getting a gain, then it will automatically be exercised so that you don't have to stop it. With the American style option, there are seldom surprises. The surprise is that you don't know what's going to happen. So in America, because there are daily rates and daily you can see what's happening, you don't get this kind of immediate surprise. If stock is trading at 40.12, before closing bell and you can anticipate 40 puts will expire worthless because if it is trading at 40, then the right to sell option will be wasted and the call option will be beneficial. So in any day you can determine in case of American option. But surprises comes more in the case of European option. When you own an option you control the right to exercise. Occasionally it may be beneficial to exercise an option before it expires to collect a dividend but in some cases there is a cut-off date that if you have a share then you can collect a dividend. People often have a long option they want to exercise it early so that they can actually share so that they can get a dividend. Option holder doesn't get a dividend he will get a retries appreciation but the dividend will be given in the name of the share. So some people exercise quickly so that they can get a dividend. So in the case of American option there is more possibility in European option there is no possibility. Cash settlement that is normal the advantages to all parties when options are settled in cash normally cash settlement is also beneficial because shares in exchange are not being handled just price difference is being changed half. So you don't even know which new share is coming and you can get the compensating effect along with that. Option owner will receive cash value and option sellers pay the value to the option whose option value is being made the part is going to un-award out of it buyer gets a return or his premium goes away so as a premium there is no loss. The cash value is equal to the intrinsic value means the market value or the option is settled at that rate. Settlement price is often a surprise with European as we discussed there is no surprise in America why is there because we talked about one month sometimes we do option of 3-3 months so we locked the price in January 3 months is a long period after 3 months it goes very high so when it goes very high and you have call option you can gain out of it or when the price goes down so surprise element in European is more because you have to pay the writer in American because there is a daily settlement and you can see the rates so you can manage and structure your portfolio accordingly. So the owner of low priced option worth a few nickels or less have earned hundreds of dollars someone took a very far option like this stock is 100 rupees you took call option that you will buy this in 50 rupees I will buy it in 100 rupees and the chance of coming in 50 rupees is very low and you will get very cheap but what happened is that the stock market changed out and things work out that way out of it if your movement can be in your favour if current price is 100 rupees and you have done call option then you can get money out of it because it is so low no one will be willing to do that so the main concept is that very remote options can be triggered out in case of European more because gap period is more with American option you see the stock approaching strike price and spend a nickel or two to cover it if you think the price is changing then you can adjust your first position with other option or you can gain out or exit there is more surprise element in European because as such you don't get warning you have to trigger once informally you can do it separately but surprise element is more in the case of European


I get up at 6 a.m. I'm sorry I I get up at 6 a.m. Very very cooking Get the children ready Start by 8 30 a.m. To the office back from the office by 6 30 Then freshening up the children myself prayer cook food homework sleep In this hectic schedule Where can I fit yoga in my life? No Get up at 6 o'clock And whatever time you go to bed you have a busy day Where's the time for yoga?  I have no time for myself I'm giving myself totally to everybody. What is it that you're giving your agitations? Irritations your anxiety is passing it on to children, isn't it? If you're really really concerned about your children If you are truly concerned about your children Creating a joyful and loving atmosphere for their growth is most important Not providing them shiny boots Not providing them better clothes not providing them video games not providing them something else is important You creating an atmosphere of joy and love around them on a daily basis moment to moment Is more important than all the nonsense that you're providing. Isn't it so? Isn't it so? Yes or no? So what is your focus about life? If you're able to manage your work and your children everything do it If you're unable to do what you can do everybody can only do that much, isn't it? You want to do everything in the world you will definitely go insane How much you can do each individual has to decide Somebody may be able to get up at six o'clock and do all these things joyfully Somebody else is not able to do accordingly.  Isn't it? Now you have not gotten into all this not because that's what you want to do You are trying to be like somebody else. That's your whole problem You want to have what other people have you don't know whether you really need it or not With all this work what you have earned Your children your husband your wife or whatever you're no more enjoying it And why do you need all this? All these things you created because you thought this is the source of your joy, isn't it? But right now that has become the source of your anxiety and misery Then you better look at the fundamentals of your life once again, isn't it? Isn't it so? You got educated you found a job you married you produce children all this why? Because you thought this is going to be the source of your happiness and well-being, isn't it so? But now that is taking your life If it is so you must look at it One thing is maybe if you're incapable of handling it, maybe you have to scale it down if you're Capable of enhancing your capabilities you must do that Now if you invest Let us say even 30 minutes a day into your yoga You will see you will gain immensely even in terms of time one first thing that will happen is Your sleep quota will come down Now if you're sleeping for eight hours a day that means one-third of your life.  You're just sleeping it off If your body and your mind is more energized and active your sleep quota will naturally come down So if you gain three four hours a day just in terms of wakefulness That's a huge thing. Isn't it apart from that if your body and mind was more organized You would see what I have found with people is with simple process of yoga within six to eight weeks Lot of them their level of performance becomes such What they were doing in eight hours. They're very easily able to do it in three to four hours Simply because if you observe yourself through the day Suppose we take a video of your whole day without you being aware of it You will notice how much unnecessary movement and unnecessary words and unnecessary activities are happening in your life You must do it one day Please hire a video cameraman and ask him to shoot you without you knowing about it You will see how many unnecessary things you're doing in a day If your mind became more organized these unnecessary words these unnecessary actions these unnecessary things will disappear Once they go away you have lot of time you have 24 hours to live You know Now we don't have to make this into 26 hours 24 hours are enough We can do a lot in 24 hours If we are organized and focused human beings we can do plenty in 24 hours time If you're disorganized and unfocused You think there is no time most of you are not busy.  Isn't it so Isn't it so Just too much preoccupation in the mind So whoever the lady Please invest this half an hour a day Get up at 5 30. Okay And you will see suddenly the quality of your life will be very different Don't go on with this argument. I have no time Make time and see it'll make a huge difference