Alright so what we are going to do in this lecture at the next is you know try to look at the Zariski topology but not in terms of closed sets but in terms of open sets. See if you recall that any topology and a topological space is specified by either giving a collection of subsets which is called close I mean called closed sets which satisfy the axioms for closed sets for a topology or equivalently it is given by a collection of subsets called open sets which satisfy the axioms for open sets required of a topology and you know the axioms for closed sets and the axioms of open for open sets are just got they are equivalent to one another by using the the properties of complement taking the complement of a set in a larger set so De Morgan's laws for example so usually when we do classical analysis or topology for example if you study Euclidean space n dimensional real space then the topology is given only by using open sets and the open sets are given by thought to be given by unions of you know open discs or open balls ok which turn out to be open intervals if you are in one dimension ok. Of course if it is two dimension then these are open discs and so on but so the approach is by specifying open sets but in the Zariski topology our approach has been by specifying closed sets ok called the algebraic sets and these closed sets were given by the set of the sets of common zeros of a bunch of polynomials in the right number of variables ok the number of variables should be equal to the number of copies of the field that you are taking ok. Now what I want to do is to now shift the focus and get into study of open sets ok in the Zariski topology so so what we have is so the so open sets in the Zariski topology so this is what we want to get an idea about ok. So you know k of course is an algebraically closed field and if you want as usually you can think of k to be the set of complex numbers field of complex numbers which is algebraically closed and then you are looking at an k this is just kn with the Zariski topology and of course the Zariski topology comes by looking at the polynomial ring in n variables and looking at common zero loci of a bunch of polynomials and calling that common zero locus that particular subset of an as a closed subset and then taking all possible subsets like that we closed sets and that is how you get Zariski topology ok. Now of course we have defined what a variety is a closed sub variety of affine space ok is supposed to be by definition a closed subset which is irreducible right you have done that. So now let I start with an open set here and see how it looks like so let u inside an be an open set ok. So by of course assume that u is non-empty ok and also that u is not the full space which are both open of course ok because the null set is closed the full space which is its complement is open and since the full space is closed the null set which is its complement is open so these two are both open sets they are the trivial open sets ok but you are looking at non-strivial open set proper non-empty proper open subset ok. And of course what you must understand is you must remember that any such open set u is very special in the sense that topologically it is dense ok and it is also irreducible as a topological space. So that is because we have I have told you that the irreducibility of a topological space forces that every non-empty open subset of that topological space continues to be irreducible and also is dense ok and since an itself is reducible ok because it corresponds to the 0 ideal ok which is prime and the 0 ideal in the polynomial ring is prime because the polynomial ring is an integral to line ok. So an corresponds to the whole affine space corresponds to the prime ideal name is 0 ideal therefore it is irreducible we proved that a closed subset in an is irreducible if and only if the ideal that it corresponds to ok name be the ideal of functions that vanish on the closed subset is actually a prime ideal ok that is the translation of irreducibility which is a geometric property into the ring theoretic property of primeness in the polynomial ring ok. So an is irreducible and therefore any non-empty open set is both irreducible and dense ok. So recall that u is irreducible and dense so this is something very special ok does not happen for example in the usual topology ok. For example if you take the topology of the real line given by open sets given by open intervals and or if you take the topology of the plane or 2 copies of r the real plane and give the topology to be given by open sets which are unions of open discs then you can see that a non-empty open set need not be it need not be irreducible it need not be dense ok but this is very special for the Zariski topology. Now the compliment of u which is An-u is a closed set that is by definition and what is a closed set for the Zariski topology it is of the firm Z of i where i is an ideal in the polynomial and mind you this ideal cannot be the unit ideal ok because if this is the unit ideal then the zero set of that will be the null set and then the compliment of u will be the null set and that will mean that u is the full space which is not the case and mind you this ideal cannot be the zero ideal also because if it is a zero ideal then the zero set of the zero ideal is the full space and that means that the compliment of u in the full space is the full space and that will force the set u, open set u to be the null set. So our assumptions tell you that I is a proper ideal which is not 0 okay. I should say I is a proper ideal not equal to 0 okay. Now you see now let us go back and look at it carefully I mean let us go back and recall the fact that this ideal has to be finitely generated. You see we have Hilbert's basis theorem which says that if R is a commutative ring with 1 which is noetherian then any polynomial ring infinitely many variables over R is also noetherian okay which means that and the noetherian property one of the definitions of the noetherian property is that every ideal is finitely generated. Therefore a field K is always noetherian because it contains only 2 ideals namely the full field as unit ideal and the 0 ideal therefore a field is always noetherian and therefore a polynomial ring infinitely many variables over a field is also an noetherian ring okay that is this is because of Hilbert's basis theorem or M E Noether's theorem and therefore this ideal I is finitely generated okay. So let I be generated by f1 etc up to fm okay so let I have finitely many generators f1 through fm okay then what is then what is Z of i then Z of i is going to be just Z of f1 through fm and that is that is which is actually equal to you know intersection i equal to 1 to M Z of f5 okay. So the Z of i is a set of points in the affine space which are common zeros for each of the polynomials f i okay i running through 1 to M and the common zero locus is just gotten by taking the zero locus of each of the sets in intersecting okay. Now what does this tell you about U so what will U be U will be the complement of Z i so it will be the complement of this and by D Morgan's laws this is the union i equal to 1 to M of a and k minus Z of f5 okay. So you get this you get this expression which expresses any non-empty non-trivial open sets set as a union of open sets of this type but the open sets of this type are special in fact they are the building blocks for the Zariski topology for the open sets mind you Z of f5 is a hypersurface okay it is essentially hypersurface because it is defined by a single equation okay it is defined by a single equation of course for example we assume that if you assume that say f i is actually irreducible okay then Z of f i is a hypersurface okay it is defined by a single equation and what this is this is the complement of a hypersurface okay this is the complement of the hypersurface what is this locus this is the locus where the particular function f i does not vanish it is the complement of the locus where f i vanishes Z of f i is a locus of points where f i vanishes and this is the complement of that locus okay and so it is a complement if for example the f i is irreducible then this is actually a complement of a hypersurface the hypersurface defined by f i and these sets are very special they are called they are they will turn out to be the basic open sets okay so a set of the form an-Z of G is called a basic open set open set and is denoted by D of G so this is the notation D of G, D of G is a locus where G does not vanish it is a complement of Z of G which is a locus where G vanishes okay and this is this is such a such sets DG are called basic open sets. Now the what we have just seen above is tells you that any open set any non-trivial open set is a finite union of basic open sets okay so any open set is finite union of such basic open sets okay. Now you see there is a there is if you have gone through a first course in topology there is a statement I mean there is a notion called what is meant by a basic open a collection of basic open sets. A collection of subsets of topological space is called a collection of basic open sets if this is a collection of open sets such that any other open set can be written as union of open sets in this collection so the condition for collection of subsets to be basic open sets is that they should be a collection of open sets and any open set should be written as union of such basic open sets and you can see that in that sense also any open set is writable as a union in fact it is a finite union we get more any open set is in fact not just a union of basic open sets but it is a finite union of basic open sets okay and the other beautiful thing is if you take the you know if you take the intersection of basic open sets okay that will also continue to be if you take finitely many basic open sets and take their intersection that will continue to be a basic open set okay. So note also that d of g1 intersection d of gm or if you want let me not use the same m I can be something else gr is actually d of g1 product gr okay this is quite clear because you see the d of taking the intersection of all the d of gis is trying to look at those points where none of the gis vanish and none of the gis vanish at a point if and only if the product does not vanish at that point okay. So you see these basic open sets have the property that you take finitely many of them and intersect them the resulting subset is again a basic open subset of the same time okay they are closed under finite intersections and their finite unions give you all possible open sets okay. So this justifies the terminology basic open set from the topological point of view okay. So what all this tells you is that the open sets for the Zariski topology are built up by simply taking finite unions of basic open sets where basic open sets are of this form the basic open set is just given by the locus of non vanishing of a single polynomial okay fine. Now that is not the that is just the beginning of the story in fact the whole philosophy in the most sophisticated form of algebraic geometry is that not only do these basic open sets define the most sophisticated possible object called a scheme in algebraic geometry okay but the fact is even the functions are built by looking at the functions on such small pieces. So you see by now I think you should have noticed that our focus has started shifting to looking into rings of functions okay see the last lectures what we did was we assigned to every affine variety it is coordinate ring the affine coordinate ring of functions which is simply the polynomial ring which is a ring of functions on the affine space in which the closed sub variety sits divided by the prime ideal given by the ideal of vanishing of that closed of that irreducible closed subset okay. So this is what we called as the affine coordinate ring of a affine variety okay and I told you that some in I gave you an indication in the last couple of lectures that the proper I mean the association of a variety to its affine coordinate ring is a equivalence of categories it can also be thought of as a bijection okay. So the set of isomorphism classes of varieties is bijective to the set of isomorphism classes of affine coordinate rings okay and the affine coordinate rings are of course given by abstractly they are defined as finitely generated K-algebra which are integral domains okay. So the moral of the story is I told you that you know the whole affine variety is completely controlled by its ring of functions which is in line with the statement of Felix Klein that this geometry of the space is controlled by the functions on the space. So the whole point about algebraic geometry in going from the geometric side to the commutative algebra side is to completely is to associate to the space its ring of functions okay. So the fact is that not only does not only do these basic open sets form the building blocks of any open sets but also that the very functions on your space they also come by gluing together or putting together okay just like you put these sets together to get an open set the fact is to get a function on that open set you will have to put together functions on the sets like this which you put together to get that open set okay. So the fact is this these are not just basic open sets in the topological sense they are basic open sets even in the function theoretic sense even the functions on these will dictate the functions on the union okay so the whole so what I am trying to tell you is that I am just trying to tell you that it is very important to look at if you want to study functions on open sets okay then you should study functions on basic open sets okay that is what I am trying to tell you. And why do you look at functions on open sets because you will have to look at functions if you want to go to the commutative algebra side in all this time we were looking at functions on irreducible closed subsets which are sub varieties and the functions where the ring of functions where they are corresponding affine coordinate rings which are finitely generated k-algebra which were integral domains okay. Now if you try to do that to open sets the first step you have to start with is try to understand what are the functions on a set like this a basic open set like this okay. So to that so to get into that let me so let me make a definition definition so okay so the definition the ring of functions on DG is namely denoted A of DG is defined to be the polynomial ring which is the ring of functions on the ambient affine space on which in which you are considering D of G localized at G. So look at this definition okay the definition says that the coordinate ring the affine coordinate ring the coordinate ring of functions is this polynomial ring localized at G okay and if you remember if you go back and go back to commutative algebra what this means is this is as I said this is this consists of equivalence classes of the form F by G where F is a polynomial in those many variables and maybe I will have a power of G and M is well greater than what equal to 0 and of course this equivalence class is the D I put a square bracket the square bracket denotes equivalence class and you know F by G power M equivalence class is equal to let me say H by G power L if and only if there exists T such that G power T into G power L F minus G power M H is equal to 0 that is G power L F should be equal to G power M H okay and of course so in all these things I must remind you that you when you localize at a single element in commutative algebra it means that you are taking the multiplicative subset to be at the set containing the powers of this element along with the element 1 okay. So and then it is also important to make sure that the element is not null potent okay the multiplicative subset should not contain 0 and if the multiplicative subset is going to contain powers of G and 1 and 1 is being thought of as 0th power of G if you want okay then no power of G should vanish and the fact is no power of G will vanish because the ring here is an integral domain it has no 0 devices in particular it is reduced it has no null potent so the condition that G is not null potent is not necessary it is automatic okay. So and well so leave alone this probably not so nice looking bunch of equations basically what it says is the set of functions on this locus where G does not vanish is just given by taking the usual polynomial functions and multiplying them with powers of G inverted okay. So this F by G power M can be thought of as F into 1 by G power M which is F into G power M inverted okay and that is a very sensible definition because you see on this locus G does not vanish okay therefore reciprocal of G makes sense so 1 by G on this locus if you evaluate 1 by G it is going to give you a non-zero scale up so 1 by G is certainly a valid function where G does not vanish I mean this is very this is a very standard thing that we come across always if you whenever a function is non-zero then the reciprocal of the function is also a valid function with the same properties of the original function. For example if a function is continuous then if wherever it is non-zero the reciprocal of that function makes sense and that is also continuous similarly if a function is holomorphic where the function is non-zero the reciprocal of that function also becomes holomorphic if a function is differentiable and if you look at the points where it is non-zero okay of course you always assume the points where it is non-zero is an open set which will be true because bear the function the points where the function vanishes will always be a closed set because the functions will be continuous basically and if you have a function with a certain property then at the locus open locus where the function does not vanish the reciprocal of the function will also have the same property so you should expect that 1 by g should be good enough only thing is it is not a polynomial but it is a reciprocal of a polynomial and then you see therefore the functions on this basic open set are given by actually rational functions rational function is a quotient of two polynomials. The point is that the denominator polynomial is always some power of g of course it may be a honest polynomial m can be 0 okay or it could have powers of g in the denominator okay now this is the definition now what we need to do is I need to convince you that I need to convince you about two things I need to convince you about that this definition is correct in by looking at it in another way and that involves trying to tell you that this d of g which is an open subset of an okay is actually also an affine variety there is another avatar of this d of g which makes it an affine variety it in fact becomes a close sub variety of an plus 1 okay and this fact is you would have already encountered in commutative algebra when you looked at properties of localization so you know so the fact is a of d of g is itself an affine variety this is geometric fact okay I will explain why that is correct okay and this is a geometric fact the corresponding fact in commutative algebra is that so let me write that the corresponding fact in terms of commutative algebra is k of x1 etc xn localized at g is actually equal to or maybe so let me write it here let me rub that out k x1 to xn localized at g localization is actually equal to k x1 through xn then add one more extra variable y modulo gy-1 this is the so the fact that the the fact that these basic of these basic open sets are actually affine varieties okay affine varieties means they must be close subsets of affine space irreducible close subsets of affine space what you must understand is they are in the affine space in which you have started considering them they are not close they are open mind you d of g is being considered in an and in an d of g is an open set it is a it is a non-trivial open set okay so it cannot it cannot be a close set because you know it is irreducible so if it is close then it has to be the whole space okay so because it is if it is close it is also dense so it has to be equal to if it is close it has to be equal to its closure and its closure has to be the whole space so it will have to be equal to the whole space so if you consider d of g in an it is certainly pukka open set it is not a close set but the fact is that in a higher dimensional affine space namely a n plus 1 it sits as a close subset okay so and this is this this geometric fact in the corresponding commutative algebraic factor related as we will see and the fact is that in that bigger affine space this is the affine coordinate ring of that subset which is the this which is given by the coordinate ring of the full space divided by the ideal the prime ideal that corresponds to that subset that close subset so let me explain this so what you do is so let us try to understand this so here is geometric segment here is the corresponding segment in algebraic terms and of course when I write here maybe I should say isomorphic okay this is an isomorphism as k algebras if you want okay so I have written equal to but actually it is strictly speaking I should say they are isomorphic to each other okay and of course that isomorphism comes because of universal properties the isomorphism in one direction the isomorphism consists of two homomorphisms which turn out to be inverses of each other the homomorphism from this side comes because of the universal property of localization the homomorphism from this side comes because of the universal property of the polynomial ring okay so that is how that isomorphism comes. So let me do the following thing so what you do is so here is so here is let me draw a diagram it is not a very nice diagram but anyway let me draw it so here is my an and in an in the space an which will have several coordinates I mean several dimensions that I am drawing something like a three dimensional thing and then g the locus of g will correspond to hyper surface so this is z of g okay so I am just drawing a diagram that will help you to think but it is not accurately correct and it is a complement of z of g which is d of g it is everything outside the hyper surface okay. Now what you do is you take and you see here my here the ring of functions is a of an k which is k of x1 through xn and g is of course is a non constant polynomial if you want you can take g to be reducible but it does not matter then what you do is you look at an plus 1 so here is so in an plus 1 there is one extra coordinate alright and well I am not going to really draw a picture but I am going to do the following thing I am going to look at the 0 set of gy minus 1 inside an plus 1 okay so what does that mean I am that means I am taking the affine coordinate ring of an plus 1 to be just k x1 through xn so I am taking the same n variables plus I am going to add another variable y so this is now n plus 1 variables okay and the way I have written it since I have put an extra variable this an is actually sitting as an n dimensional plane inside this n plus 1 dimensional space which is so this an is actually sitting inside this an plus 1 okay and it is the locus given by y equal to 0 when I put y equal to 0 then I get the I cut down by one dimension okay and the corresponding sub variety that I get here is actually this an that is what it means to take these variables to be x1 through xn okay and if you look at the polynomial gy minus 1 gy minus 1 is an irreducible polynomial okay this is something that you can check the polynomial gy minus 1 is irreducible alright and therefore the ideal that it generates is a prime ideal alright the ideal that it generates is a prime ideal and therefore the 0 set of that ideal is an irreducible close sub variety alright so this is this certainly is an affine variety this certainly is an affine variety in this affine space of dimension one more okay and what is the what is the affine coordinate ring of this affine variety what is the ring of functions on this affine variety it is by definition equal to the polynomial ring of the ambient variety go divided by the ideal of this variety the ideal of this closed subset which is the prime ideal gy minus 1 okay see gy minus 1 is an irreducible polynomial and an irreducible polynomial in a unique factorization domain an irreducible element in a unique factorization domain always generates a prime ideal so this ideal is a prime ideal okay and now the more beautiful thing is that there is in fact you can define a map from here to here which is a bijective map okay the map is given as follows you give me a set of points lambda 1 through lambda n in you give me a set of points here in this open set so what it means is that a set of points in an is in this open set if and only if g does not vanish at this point that means if you plug in lambda 1 through lambda n for x1 through xn in g you should get a non-zero scalar okay and you know what you are going to send it to it is very simple you are simply going to send it to lambda 1 through lambda n and the last coordinate will be 1 by g of lambda 1 through lambda n send it to this point now this point is a point with n plus 1 coordinates the first n coordinates are just as these n coordinates okay and the last coordinate is such that this point satisfies the equation gy-1 equal to 0 because the last coordinate y is 1 by g where g is applied to the first n coordinates okay so you can check that this is a bijective map okay already you know if you take 2 n tuples like this and they go to the same one there okay then they have to be the same here and every point there corresponds to a point here you can get the point here by simply forgetting the last coordinate you restrict to the first n coordinates so what I am saying is that the map from a n plus 1 to a n is the projection projection on to the first n coordinates okay and if you project this you will get dg okay you will get dg that is what is happening now you can do little bit of calculation and show that this map is actually a homeomorphism okay you can try that out you can show that this map is a homeomorphism the fact is that this map is not just a homeomorphism it is actually an isomorphism of varieties okay but that is the fact that we will have to check later on because I still not define for you what is meant by a morphism of varieties okay because an isomorphism of varieties is an invertible morphism of varieties is a morphism of varieties which has an inverse which is also a morphism of varieties okay but just grant that for the moment the fact is that this is an isomorphism of varieties and the philosophy is once you have an isomorphism of varieties that should give rise to an isomorphism of the corresponding affine coordinate rings okay. So if you believe that it will tell you that the affine coordinate ring of this must be isomorphic to the affine coordinate ring of this but what is the affine coordinate ring of this the affine coordinate ring of this is this okay but what is this isomorphic to this isomorphic to the localization of the polynomial ring in n variables at g this isomorphism comes from commutative algebra ok. So if you believe that it is fair to take the ring of functions on this to be this which is what our definition was ok ok. So what you must understand is that if you believe that these two are isomorphic is varieties ok evidence for which is that you can check as an exercise that these bijective map is actually an isomorphism in the topological sense namely a homeomorphism mind you this dg is a subset of an an iso zariski topology this is an open set so it has an induced topology ok and z of gy-1 is a close subset here that also has an induced topology zariski topology and I am saying this bijective map is not just a bijective map it is a homeomorphism it is continuous in both directions ok and that tells you that these two spaces are homeomorphic but it does not stop there they are actually isomorphic as varieties and if they are isomorphic as varieties they are the philosophy is that they are coordinate rings the rings of functions have to be isomorphic therefore you can the ring of functions on this has to be isomorphic to the ring of functions on this which by definition is this by our earlier definition but that is isomorphic to this because of commutative algebra and therefore it is correct in that sense to take the ring of functions on dg to be this ok. So this is a kind of heuristic argument which involves certain things that need that will be checked later ok so this is some justification as to why you should define it like this of course the other justification is where g does not vanish 1 by g and powers of 1 by g will also make sense as functions and therefore most general functions you can write should be of this form ok. And I should also tell you that this geometric picture is actually a translation of this commutative algebraic isomorphism ok this is the coordinate ring of this, this is the coordinate ring of that and the fact that these 2 rings are isomorphic isomorphic as k algebras is actually reflection of the fact that these 2 fellows are isomorphic as varieties ok. So it is commutative algebra this is the commutative algebra statement these 2 being isomorphic as varieties is the algebraic geometric statement and they are just you know each is equivalent to the other provided you make the right definitions alright. So that is to convince you why this definition is correct ok, so I will continue trying to tell you about the points that lie here ok with respect to the null so and so ok. So that that will also give you an idea that this is that will also give you another justification as to why this is the this should be defined as a ring of functions on dg ok, so I will do that in the next lecture.


what's up everybody welcome back to the channel I'm evil rabbit and and I'm who ate my hamster and we're actually trying this co-stream deal here on pubg we're gonna see how this works we're co-streaming on the Xbox one pub player unknown battlegrounds pubg hopefully I won't die as much this time because I keep dying in solo I did make it the top 10 though I made it to ninth place on my own in solo so I was kind of impressed I can never pick it back I can never make it past 50 so I I made it 10th on one game with zero kills because I did it in a corner that works all right I'm gonna set up a camera I'm waiting for are you loading it or what are you doing yeah I'm loading in right now oh because if you look at my screen I'm loading yeah it says it says match starts in two seconds like did you actually oh great I don't know my my connection apparently does not want to work tonight so while I'm waiting for hamster to get back into the game today is day 19 of my 25 days of Christmas giveaway here on the channel so if you want a chance to win the autographed poster of that Falcon Tire's s14 driving driven driving whatever driven by Matt Fields number 777 comment down on the video comment anything you want but keep it a little respectful thank you and that will enter you in for the random drawing for the autographed poster of Matt Fields this is gonna work I think it is do you hear walking night yet up there's there's walking yes yeah yes hamster I see you yeah don't punch me come here punk get over here I can't even hit you stop moving so I can oh there we go oh oh oh take it to the face hey who's that guy he's got a hat I want a hat oh wait racism all right so we're gonna find out where we're jumping out of this plane not yet pop off corner of the map is where we're coming in let's uh let's wait a little bit look at the back of the plane you can see how many people are left in the plane yeah I know but you can look at the back yes oh wow you can actually see how many people are left in the plane I'll never notice that before nobody's jumped out yeah oh there they go see disappearing well no look they disappear from inside the plane all right we're gonna go when I tell you to jump out we're gonna head towards like the farm you see it yeah all right ready three two one let's go sorry don't suicide I'm way below you aren't I oh yeah yeah I was trying to make sure I was at the farm before I even did anything so we gotta try and get some guns try and get some stuff and be somewhat protected kill some people in the path yeah well we need guns and I hate how long it takes to load in oh my god load in like the map is not loaded in yet oh my god xbox fails oh I got the same thing dude pubg xbox there's a real lag I'm lagging oh yeah all right we're good now okay was that on floor xbox I picked up a machete already picked up oh boy what did I find no I found a magazine pistol I mean I don't think this building is loaded in yet no I don't think it will be solely loaded sweet I found a book bag a helmet a vest some bandages oh I found a shotgun I haven't found any type of weapon this is not good but I got lucky I don't think there's I think there's anybody by us right now though so I think we're okay my gun really not you gotta it'll show if you have extra if you have ammo I know I ended up like this oh that's right I can see your screen I keep forgetting we're co-streaming and I can see what you're doing I'm running across the other houses oh I got a little bit of lag right now oh were you on these houses on this other side hamster to somebody over here come over here you gotta come here oh shit there's a guy in that building I'm coming there's a guy in that building in the building with the red in the building with the red roof I don't know if he just booked it out but I mean reload ammo in this gun real quick I got shotgun how did you have a helmet I found it but I don't find any ammo or anything he's looted this place clean I think it's a book bag you need a book bag there's a helmet over here I want a helmet like I don't have any ammo this sucks oh look we're in this we're in the zone that's good that's rare all right we're gonna head over to this little house over here let me see if I can find it's gonna run up behind the guy I tried kill him that's me I'm in front of you obviously that's you I know I said I was gonna try to run up behind him I was going to go through the house oh shit we're in a bombing zone oh shit run no we'll be okay get inside the building get inside this little hut oh look a pistol yes there's a vest in here get in oh it hasn't started bombing yet I don't care I'd never been inside the red zone yet oh I hamster hello well they try to come in here they're kind of screwed yeah there's a new helmet down here oh there's this is a I was feeling we might be we need more it we need more weapons do we gotta find some houses after this we're gonna go south as soon as the red zones clear we're gonna go to these hills alright I've run through the red zone and not died oh here we go you've never been in a red zone nope this is terrifying what happened I'm going to get my machete ready just look outside the windows I know oh wait so hot wait till it hits the house and everything like goes red yeah you know I feel so safe in this building alright we're good let's go oh red zones over yeah let's go we're gonna get some stuff I'm gonna get my pistol up because shotguns not gonna reach very far yeah well there's got parachuting no that's not a guy that's a pair that's a crate drop we are so far away from that though you're gonna go every hill huh said make up your mind where you want to run trying to find a trying to find some houses might have some stuff I need I need weapons oh look a city oh lots of houses here's some gunfire too okay but I see houses up here with doors closed so maybe maybe this would be good maybe it's so weird I look at your screen I see somebody about to shoot me and I'm like wait well oh that's you stop looking at my screen then this more pistol ammo nothing yeah 45 rounds for pistol I mean red I'll take shotgun shells if you could find another pistol oh painkillers all right so that's in good in this house to the next building you next bike but there we go find where I was nope nothing in here all right so to the city we go I'm scared to oh wait a minute I hear gunfire yeah me too there's bike yeah smoking smoking though which means we gotta be careful let me submit around here I say you want to go up in that tire see if you can find a sniper no oh level two please best you need some bandages or some in this house in this little hut keep on hearing your footsteps freaking out I see a little tower up there I want to go check that out I was destroyed those little tower up this way yeah I see it all right I mean it's not the best thing but you know what I'll take it for now I'll take a little oozy it's fun it's a new easy it's not really gonna do me any good I found it I found a red bull if you wings all right are you going to that tower find something good I'm gonna be so sad watch you find like a level four scope on a like m16 or something that's a car yes what I found what you find absolutely nothing there's a car right by my god there's a guy down where there's a guy down at the other houses running towards the street he's about to get in a Jeep or a truck whatever you want all right well there's a car by my the house that I'm in right now we can always take it we need it I'm running up here by you this week he doesn't spot me I just found a two-time scope but too bad I got nothing to put that damn two-time scope on but you're easy yeah I'm scoping the newsy I thought oh I found a fucking military helmet get wrecked okay now I really get right all right do you want to take this car let's go take the car driving is there anything in here no I already cleared it oh look we're in this oh there's a rounder car yeah so I said oops actually driver go where are we going we're gonna go I think we got to go across that bridge to the it's gonna end up it's probably gonna end up close to that uh military base oh god I'm a jump in we'll be very very careful here please oh we're getting shot at run run run run run oh we're shooting at us I don't know little shack back there I saw we stop and try and fight turn right no like it we don't have long-range rifles we're glad that's a new one get out search this place anything I mean we're gonna have to fight him sooner or later so oh that's way better than a frickin little oozy take an MP5 I think it was wild up top I hear a car anything worthwhile right so I think they may have stolen our car Amsterdam am I still standing there oh shit yeah but you might die we're kind of fuck run from the zone why why are we gonna die cuz we're outside of the zone oh bye rabbit yep I think it just glitched me out because uh nope did it seriously load me back in and about to die oh my god get out of here oh run run for your life oh I'm not gonna make that are you crazy trying to find something to drive then oh my gosh PUBG on Xbox one and it's fine oh my god I found a car go down the main road this way you can pick me up I found our car hamster yeah that's awesome I should get really intense I'm down on this main road come on I'm coming hamster pick me up over here get in hurry up get in get in get in get in get in go go go go oh my god are we gonna survive I don't know my health is getting pretty low I'm on yellow oh no there's other people trying to get out of here I don't care I'm trying to go to the zone oh my god we're out of the blue get out of here how did I love oh god just keep going hamster I don't care I'm just go I'm going full send this is full send right now who treat oh god I don't want to treat you on it in PUBG hamster get out of here how did we survive this oh god no the road right now there was so I thought that was a person here yeah this is like oh here we go it's gonna end in the military base this is not good opening oh it feels get out like a bunker like a bunker too bad it's probably out of zone like but there's a freaking first aid kit in here the hangar I'll take the gloves one black finger gloves and a jacket ooh so that's why I don't know but I'm more worried about where this zone is going next that's why drops that you're pretty close where is it right over here car car car I hear a car here it's come down the hill right there oh there's one yeah I don't have weapons to go I hate the bows because I don't know I have a two-time scope on my oh run why why are we running I got really scared because I saw the zoning coming oh no we're good we're still in the zone dude we got guys on this hill though coming I know they're coming yeah because they're out of the British coming the British are coming oh shit we're outside the zone let's go no we're not oh are we shit yeah they just brought the zone in watch out behind us though oh oh oh oh what where's it got at I don't see it where where is now probably outside the zone book it okay okay come on let's go run get on the hill oh wait no we got to go a lot further for that zone oh god that's gonna suck how many are left 26 25 oh what's in here what's in here what's in here nothing I think anything good oh shuck on choke no we got 54 seconds till it starts closing in on us so you know a little time what's this what's this in killers in killers in killers come on hamster let's go coming everybody can I do like this is like literally terrifying right now that's why I love PUBG oh my gosh I can't I don't see anybody behind us oh Jesus not bad run so far for having all these issues and then now we're back we're back in the game yeah 22 left oh god it's gonna get a hairy real fast I'm trying to find some cover I don't want to be just in the open we should be fine I think we're like the only people without rifles right now yeah probably we gotta be just I mean I got I got this I got an uzi with this next plane next plane next plane I got an uzi with a two-time scope so I mean I have some sort of distance not a lot spare them we're in the zone oh this way oh he just knocked somebody out I'm gonna take this easy kill oh who took that kill at least we're in the zone I see some guys running I wonder 15 North North 15 on the other side of the plane it's the same truck that's been running are you shooting yeah just try to shoot at it see if I can get them out all right we have to advance in okay just wait a minute 30 seconds yeah we got a minute 30 seconds till blue starts moving so we're good right now oh my gosh this is nerve-wracking I want to go over to this next plane real quick see if there's anything over there we're getting shot at oh yeah I don't know where from Steve whip dodge whip and dodge oh what'd you see oh shit where'd you get shot from I don't know we're all inside the engine I'm safe I crawled inside the engine come on come on come on come on we think he's my controller by faster faster faster faster revive oh shh hamster hurry up okay good life from where's that right go around go around the plane oh we got to get to the zone okay run the planes run the planes run the planes truck coming somewhere yeah I don't know where he is he's still the guy running around in circles we're right next to the zone too yeah the zone is closing in we gotta go well we're so close to dying right now we're kind of like in the zone ish it's just like two people in that yeah no they might be coming after us oh yeah they are god I almost shot you in the head ah did you get shot again yes shit zone get in the zone that was a good run number 10 team break number 10 okay I don't think I have enough time for another one and that we're going to call quits yeah on that note since PUBG wants to get all screwy we're gonna call that quit so you know you fall Facebook Twitter and scram all of which found description box below make sure you follow hamster as well that game was interesting I lagged out logged back in in the blue zone and then drove all the way through why because drama because PUBG Xbox one because PUBG


He's competing like near Disney, which isn't that far, but it's not that close and he lifts, he probably starts lifting like eight. So we just got a hotel down there and then we'll stay with Nads and then we'll leave. Then he's like Disney, like Westminster in a high maria. Yeah, in a high maria.  But right now I'm starving, me and Seabass just flew to LA, Nads picked us up, the best Uber driver you could ever have. One hour late, only one hour late. Dude, every Uber driver in LA though gives me car sickness, every single one. Yeah, it's bad. Nadeem doesn't. And so now we're in Anaheim somewhere, we don't really know, but we're gonna go find some barbecue because we ended up... We're staying at the Romano Hotel, come find us. What room are we? 415. 415. If you guys find me in my room, then you can have my entire bag. You can have my whole wallet too. So we're gonna go eat a barbecue because we went in Rome. And then that's it, we'll probably see you at 7 o'clock, Bart's waiting. 7 o'clock. I think Bart's just waiting, putting his opener. He's opening at 440, just kind of along the game plan, the goal is to hit around the 500 front squat. I got a triple check but... Pretty sure it's just goals 9 for 9. He's got some elite totals in his brains, but you can always adjust that. So openers, try to set you up for that elite total, or at least that's how I do it. So we'll set that up, obviously based on what he's capable of in his training. But the second and third will depend and adjust more based on the 9 for 9 than the elite total, right? Because you just don't really know until Bart's on your back. We think he'll go 440, 470, 501, but maybe he's moving a little slower, maybe he's moving a little faster, maybe he's confident he's there, maybe he's not there. So that's my goal, hopefully. All you do in game day is push your confidence and make the right call so you can be successful. I'm going to see what 400 moves I can send. I can start to play a little bit of games in my head. Again, the strategy ain't that crazy, right? You normally take about 100% of what your goal is for the day, which you think you can hit. And hopefully, based on your programming, your coaching, your training, you have a decent grasp of that. Whether you hit it in training, right? If we hit 500 pounds in training, it's about an RPE 9. We know that 500 to 520, if you taper correctly, is going to be here today. So you take from that, our opener is going to be 90-ish percent of that weight for our opener. Our second attempt is going to be anywhere from 93 to 96 or 7% of that. And then, depending on that, is where we're going to end up to 500 and 520. So, again, it's not crazy math, there's some basic math to it. When you start to duel with somebody out of meat, and your goal is to win the meat, there's a little bit of extra strategy at the end, but it's really not that complicated. You just need a dots calculator. How are you feeling, Bart? Good? Yeah, pretty good. Feels good, all the homies are here. Lifting on a weekend, always a good time, you know? How about, what happened with that last attempt on Squads? To be honest, it's probably just because I'm weak. Because first attempt went good.  I've hit consistent 450, 490s all of this whole meat prep. But you know, when your weight comes down, it does get harder and harder. So I didn't expect not to get it, especially since I did 468, I was less than 5 pounds more, but it ended up being too much. And I was in the zone, you know, I wasn't distracted. It wasn't one of those where my feet positioning was all like, everything was locked in and perfect, but that just tells me my strength wasn't there. So I can't go on it too much, but I still got two more lifts. So now I'm like focusing on, okay, put that behind me, now get on bench, and then what I got to do to make sure bench is good. So you can move the weight easy, but you're just going to try to find a way that's impossible for his butt to come up. So there's two different options. If you're flexible enough, you'll tuck your heels even deeper into you. The other option is you Y out as far as you can. So you get like a little less tension, but he doesn't really need it. Like all you need is tension. You're like, just lay down. I'll be prepared to launch. If you need to tuck your heels, you can try that.  No, not that bad.  You can still go on that bench. Yeah. Yeah, you'd be like right there. Are you flexing as far as you can on your body? Yeah. Does that make sense? But I'm going to go like that. Yeah, so then keep moving around. Okay. Yeah. Like that. But get tension on your toes. All right.  You won't snap? Hot dance. One, two, three. Thank you. Thank you. I feel great. Yeah, I feel great. I'm a little hungry. I want to watch the Kings. Sack Town. We got the playoff game in a second. But I'm excited, Bart. I think you all have a good pull. I think, actually, of all things, his pull was a little roughest in training, but he's in a good spirit, so that'll have a little energy in there. Music's turned up. Bugs. Proud. He's pulling with some really strong kids that are like right around his area. Holy cannoli. Yeah, it just happens. I can't even control it anymore. But yeah, I think it's fine. You would think by my current state that I have competed today. In fact, I did nothing today. I basically did some basic arithmetic.  I watched UFO documentaries, animal documentaries, and then movies I've already seen on repeat. I've already seen this. When we saw this little guy give birth earlier, have you ever seen an elephant give birth? No. History channel. We're trying to help you. We're heading to Austin hello early. So I'm going to try to sleep. The boys are still packing because they're young and they're unorganized.   So I don't know if this will be a new video. It might be. Or tomorrow might not be a new video. Or there might be meshed into one, three days. But we're going to head to Austin, hopefully set up, catch Bart at the airport. Hopefully just eat barbecue until I can't breathe anymore. I'm probably going to come back to 280 pounds. But it's bedtime.


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So the discus is coming off of this finger that's no good and we're going to talk about why and how to fix it in this video so check it out. Hey everybody it's Eric Johnson from Maritime Throws Nation and in today's video we are going to answer a question that a lot of you ask and that is why is my discus coming off the middle finger? What does that mean? What's the middle finger for? We always talk about this it's not meant for thrown it's meant for something that's not very polite and makes people angry. So you want to avoid it at all costs because it's going to impact your discus in a negative way as well. So one of the questions we received was why is it that I can do my stand throw so when you see me throw here and we wind back and I'm going to get that off my middle finger what happens and if I'm doing a half turn throw if I'm going to be here and I'm coming through and I'm going to throw it this way why is it that on those I can throw so this is our pillar five six and pillar three four five six and in what we were in our chain reaction system when I add pillar one two why is it that now the discus is coming off of the middle finger good question and one of the basics is when we're in the stand throw when you guys are learning to stand now whether you do it right or wrong we just going to put the discus in this position and it's easy to keep the discus back when we starting to add pillar one and two to our full throw we're changing how the arms carry so what happens is we talk about how the thumb angle changes on the discus and we start to see the hand pointing like this and when we're doing stand throws it's easy to drag the discus here what happens is when we start to add pillar one and two so when we get back to this position or we go to a full throw or we go to our South African drills or we're doing any of this type of movement this is where people run into problems on keeping the discus back so we see this is a big problem with quite a few people and what is typically happening is that carry position that you will do easier on your stand throw again pillar five six or your half turn modified wheels we call them will be your pillar three four right we're moving three four five six it's easier you're starting basically with that arm back in the full throw you would think keeping it back but you've got to open up and what happens is people start to get uncomfortable and they're carrying the discus and now the hand is sitting like this so the thumb and hand goes from here so you see this line to here so one of the things that you want to understand is that now what why that changes and why it starts to come off the middle finger is because when I get to the full throw and I start to carry the discus or I turn the discus over the orbit and the shoulder you're starting to throw yourself off balance you're going to wind up turning the hand and you're going to have the discus like this no longer stretched like this and we want to see that hand and thumb in this position so that the discus is coming off of this index finger now the faster you spin the discus the longer it stays in the air this is something you need to learn and develop and many beginning throwers don't really adequately know how to spin the discus so buying a big expensive rim weight disc some four hundred dollar disc when you don't have the skill set to maximize that is not necessarily the most advantageous thing now whether you have a low rim weight disc or a high rim weight disc if you know how to spin the discus the distance is going to be relatively close but the key is if you don't the distance is going to be significantly different because you can't adequately spin the heavy rim weight disc now why again is it coming off of the middle finger one of the things we'd recommend we posted a video called how to add 20 feet to your throw talking about the grip and release in the discus and you can go back and check that but what we're kind of reiterating is specifically why is it always coming off the middle finger and that is going to be you're going to be having to see something in your carry position so we've worked with a number of athletes again the biggest point what you want to understand is what you need to be working on is how to release the discus so doing some more walkthroughs and drills and static throws are going to be some simple things you can do so we like to do some basic drills where we're going to be here and now that's going to teach you how to move and keep the discus back and that's going to set up that better hand position which is going to change now some people say well I have a really long middle finger and some people do but even if it's that long it's still a matter of how you are angling the hand and now you're able to still have the index fingers is primarily what's on the rim of the discus and it's going to be able to snap and spin far so quick simple tip today if you guys are having a hard time and that discus is coming off your middle finger and you know that is not what it's supposed to do because that middle finger shouldn't be used for anything but grabbing things so you want to make sure that it's coming off of this finger you got to play and realize that it's really what it's coming in is this how you're carrying the discus that has a huge impact that's going to affect your orbit and your radius and the amount of power and your balance typically throughout the throw so this is a simple fix but it takes a few weeks be patient you might have a bunch of crappy throws but you have to realize that something you're doing in your throw at some point you're getting that hand position from here to here and now that's what's going to wind up having your hand your main finger come off you're shortening your radius and you're likely turning the discus up it's coming off the middle finger and you're gonna lose a lot of distance and none of us want to do that all right guys so hopefully that is a helpful tip thanks so much for watching hit that subscribe button comment below on other things you'd like to see and we will see you on the next video