Hi, how are you doing today? This is Rich and we have a Rich TV Live with a very special guest, the CEO and president of Kalanex Minds Inc., Max Porterfield. How are you doing today, Max? I'm doing great. Thanks. Excited to be here. Excited to have you here today. And thank you for joining us and let's talk a little bit about your company. So first and foremost, I want to ask you a question about exploration. Did an exploration company soar and succeed both during a recession or a slow growth economy and a booming one? I mean, is it independent of general conditions? Can you give some examples, please? I think every business here in is going to be impacted by things that are out of their control. You saw this in particular in the base metal space when you had the U.S.-Chinese trade tensions and the trade war has kind of kicked up, had a dramatic impact on global zinc prices as well as other metals out there due to global growth concerns moving forward. With that being said, you're also seeing it again with the coronavirus, which I think the handling of that, the response that's been appropriate and measured, but I think the media is stereo around that's kind of also been detrimental and blown out of proportion given what it is relative to other things out there. With that being said though, exploration is really one of the few businesses out there where you can create tremendous amount of wealth for your shoulders and that's through a discovery. And that's kind of one of the things that we're primarily focused on, again, is to about their makes discoveries within Canada and economic discoveries going to make investors money no matter the market. Absolutely. And what do you think is the upside right now in precious metals, specifically gold and silver, to very hot commodities in a world with endless government debts, negative real rates and no solution in the foreseeable future? Well, I think it's going to be a strong market for precious metals for sure. Any negative real interest rate environment you're in, you're going to see the precious metals perform well. A year to day you've seen or more recently you've seen gold perform quite well. It's pulled back a bit, but I think it's healthier and a longer-term market for the precious metals space. It's underpinned by everything you kind of mentioned there. So I definitely see higher prices. It's going to be really good for the overall industry as a whole. People don't realize it, but over three quarters of the money's raised capital spent as well in terms of exploration actually does go to gold exploration. So a healthy gold market is also going to be a healthy junior exploration market as a whole. Very good. Now the company that you're leading, Calanex Mines, has been around for several years. In terms of market cap, we're talking about a very small company, only about 4.3 million in market cap Canadian, out of which Canadian 2.6 million is cash, meaning the enterprise value is only about 1.7 million Canadian. In other words, your portfolio of assets that are base metals centered with a key component of precious metals in them, along with the intangibles, like your expertise level and rapport with shareholders and institutions, is not being valued highly by investors. Do you think this is justified or not? I don't think it's justified at all, but obviously any of the valuations is historically cheap and we're not alone in that regard. As I mentioned earlier with the pullback that you saw in the base metal space that had a big impact on equity valuations. As a company, just about two years ago, when this all kind of started with the trade tensions and led to the drawdown and zinc prices, we were trading an evaluation of between $30 to $35 million valuation. To come down to $7 million valuation today, when the assets in the company haven't gotten any worse or had dramatic impact, and in fact have done a lot of work on the exploration front to generate some very compelling exploration targets that can create a lot of value and where I can actively out there testing right now, is quite unjustified, but it's a huge buying opportunity, which is one of the reasons I was a big buyer of the stock last year buying into this drawdown that you saw in the share price. Now can you tell us about your projects and what you plan to do with them or with the ones you're more focused on in order to de-risk them, extract the value and deploy an exit strategy for shareholders? Sure, absolutely. We're focused on three prolific Canadian mining jurisdictions, and really the portfolio is again acquiring assets that are in close proximity to existing infrastructure. The biggest hurdle that a lot of these discoveries have is the up-from-cap exit to go into production. It can be billions of dollars, quite frankly, given the location and giving the people the power, the water, the access, and all the infrastructure put in place can really be the big hurdle for an exploration company when they make a discovery. So when you really focus on making those discoveries within close proximity to infrastructure, that's going to compress your up-from-capital costs because it's inherently already there and reduce your hurdles dramatically in terms of making a discovery that's economic and has a big benefit. I like to say that we're doing purpose-based exploration in a lot of ways. Right now, again, we're focusing three camps. We're currently drilling in the Bathurst camp of New Brunswick. This is an area we had a maiden PEA or Nash Creek and Superject projects we recently acquired another smaller, higher-grade historic resource and our headway property. And all the drilling that we're doing out there is to really grow the scale of the mineralization that we already have to find through aggressive drilling campaign that we've been working on over the past year and a half or so in terms of target generation. So we're quite excited about that. And again, in terms of the purpose-based, this is an area, again, that's got a rich mining history. The Brunswick number 12 mine was really the flagship mine shut down in 2013 at one point that was the largest underground zinc mine in the world. And again, that's led to a lot of job losses in the area from mining, starting now in the Bathurst camp as well as the forestry industry obviously being impacted. You've got over 20% unemployment rate in Lorne where the Nash Creek deposit sits. And just down the road in Belle Dune, there's over 20% unemployment rate where there's the key infrastructure and they're actually shutting down a lead smelter there, which is going to really today accounts for 80% of the jobs in Belle Dune. So doing exploration in these types of areas where we have the people, you have all that infrastructure in place and you've got the geologic pedigree, it creates a lot of opportunities. We're also having a ambitious exploration campaign in Flintfond camp of Northern Manitoba. Again, Flintfond is a jurisdiction that's had 32 mines in county over the past almost 100 years. The triple seven mine, which is a flagship mine in the town of Flintfond that's been operating since 2004 is again going to be shutting down in early 2022. There is no new discovery and new mine to go into production and to take that place. So making an economic discovery in an area that's got such a prolific history and is immediate need and the community really depends on is really of importance to us as well. With that being said, we also have a gold silver zinc copper deposit, it's a VMS deposit in Newfoundland called Point Leamington and we're looking at that in different opportunities there from a metallurgical standpoint as well as from an exploration standpoint generating targets to be tested later this year and then that'll aside we're always looking for many opportunities in any of these camps to kind of put together with our already existing portfolio. So that's kind of what we're up to. That's how we see things and how we're our objective moving forward to aggressively agree value to the shareholder base. Very good. Now you mentioned that you bought shares last year. So do you own shares personally and can you kind of give us an idea of how much shares are held by friendlies or insiders within the company? Yeah, sure. So yeah, I am a rather significant shareholder. I own roughly four percent of the shares outstanding. You know, my family in total, I think in addition to myself owns just under 10 percent resource capital funds, a very large private equity fund has been a long term supporter of the company owns just under 10 percent. And then family offices own another 10 percent. And that's one of the other things in terms of outside of the really supportive shareholder base and everyone having skin in the game per se on the team is we also consolidated the share structure last year. And that's kind of a big component because all ships will rise in a rising tide. And, you know, we're going to outperform, you know, in that regard because of the share structure and going through the consolidation process after kind of taking the lumps that we had from the drawdown and base metal prices in 2018. Now, how passionate are you about Kalanex? What would it mean for you to get this right? Well, if I haven't come off as passionate, I don't know if I ever will, but I'm extremely passionate about what we're doing. Obviously very, very excited about what we're doing. Quite frankly, if I wasn't doing this, I don't know what else I would be doing. A discovery in Flint Fawn in the world to me, we've got a long history in as a corporate history in the Flint Fawn camp and coming in and learning about that history, actually being an American, I'm a Canadian now as well. But, you know, this town, I can go anywhere in the world and I can mention the Flint Fawn and someone will have heard of it in an odd way. And for a town that had a peak population of 15,000 people, it's really kind of made a mark as a small town here in Canada. And then in the Bathurst camp and in the Buckins camp, being able to drive those assets forward is obviously of most importance and it can have a huge impact to those communities as well, as well as from the tax revenue being thrown off these large projects.  How can they get in contact with you and your company and learn more about this amazing project that you're part of? Yeah, you can visit our website at callanx.ca, that's C-A-L-L-I-N-E-X.ca. Our contact details are there. You can give us a call as well as email. And then most importantly, if you want to purchase shares, they can obviously do that on the TSX venture into the ticker CNX as well as on the OTC QX, I'm sorry, OTC market in the United States under the ticker C-L-L-X-F. That is fantastic. Well, thank you so much for your time today. This is the CEO, Max Porterfield of CallanX-Mayens. Thank you for watching, everybody.


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So we had started talking about projective archbikes sets. So we'll review the notations and then we go on. So we had the projective space Pn, which was Cn plus 1 without 0, divided by the equivalence relation where we have that two vectors are called equivalent. If one is a multiple of the other by a nonzero constant, the quotient space is a projective space. And then we had seen that if we have a homogeneous polynomial, we can talk about point in Pn being 0 of that. So we say that f of the corresponding point here, the equivalence class is just done by the thing with square brackets. So if Pp equal to a0 to an, we say that f of P is equal to 0. If f of a0 to an of just this n plus 1 double of numbers is equal to 0, and this will be independent of the representative. And in the same way, now if we have a set, like in the affine case, if s is a set of homogeneous polynomials, we can talk about its zero set, the set of all points in Pn, where all these polynomials vanish. And then we had related, again, as in the affine case, these zero sets to ideals. So instead of taking a zero set of a set of homogeneous polynomials, we can take a so-called homogeneous ideal and take the zero set of that. And that, again, allows us to use a bit more algebra. So I don't recall the definition of homogeneous polynomial. One way is to say it's generated of homogeneous ideal. One way is to say that it's generated by homogeneous polynomials. So if i in kx0 to xn is a homogeneous ideal, then we can define the zero set of i to be a set of all Pn and Pn, such that f of P is equal to 0 for all homogeneous elements in i. Because until now, we have only said what it means to be 0 for homogeneous polynomial. And in the same way, we can associate a homogeneous ideal to a projective algebraic set. So I should say that sets of the form z of s for some set of homogeneous polynomials are called projective algebraic sets. So x in Pn is a projective algebraic set. And in fact, if it's any subset, but just say for in this case, then the ideal of x is defined to be the homogeneous ideal of x is defined to be the set of all the ideal generated by all the polynomials f in kx0 to xn, such that f of P is equal to 0 for all P and x. This is again also completely analogous to the defined case. But now we take the ideal generated by them because we have not set what it means to be 0 at f of P otherwise. I should say that later, we will sometimes need to look at the projective 0 set and the defined 0 set at the same time. So the 0 set of this ideal in Pn or the 0 set of this ideal in An plus 1. And then so we distinguish that. So in case of need, we call this zp of x of i. And the other one may be za of i, one for projective, one for affine. And this is the homogeneous ideal. So in case of need, we call it ih of x, the homogeneous ideal. We'll see that later. So after saying that, the story that we only know what it means to be 0 when the polynomial is homogeneous, I want to immediately contradict myself and say we can also define it if the polynomial is not homogeneous and also give the opposite answer to a query about this than I gave for the other time. But it's just one can remark, also an exercise. So if f in k at 0 to xn is not homogeneous, we can define the 0 set of f to be the set of all points P equal to P in. So P equals A0 to An in An such that f of A0 to An is equal to 0 for all representatives A0 to An of P. So in other words, for all, so it's 0. So if we fix any A0 to An here, it must be 0 for all lambda. Lambda A0 times lambda An must be 0. So we could say this is the 0 set of this polynomial. So the first thing that you can notice is, so quantum exercise. So if f equal to f, say, f0 plus 1 plus fd is the decomposition into homogeneous components, then the 0 set of f is the intersection from over all i, in this case, i from 0 to d of the 0 set of f i. So we see that, so in some sense, if f is not homogeneous, it doesn't just give us one equation, but many equations. And for instance, if f has a non-zero constant part, it means that the 0 set is always empty. Hope this is correct. But this is just a small thing. The actual exercise is another one. With this definition, so that 0 set of a polynomial is actually the set of all points where 0 for all representatives, we get, so if i in kx0 to xn is a homogeneous idea, then the 0 set of i can also be written, the 0 set of i, as we have defined it here, as defined before. This is also equal to the set of all p and pn, such that f of p is equal to 0, for all f in i. So if we take this strange definition for the 0 set, then actually, we don't have to restrict the homogeneous elements. And in the same way, if x in pn is a projective algebraic set, then it's ideal, as defined here. So the homogeneous idea is just equal to the set of all f in kx0 to xn, such that f of p is equal to 0 for all p and x. So if we change what we mean by the 0 set by saying it should be 0 for all representatives, then we can use the same definition as in the affine case. But it means something complicated to be 0 for all representatives, as you see here. So but I mean, I say this just now. We will not use this very much. We'll use it once. Otherwise, we usually restrict our attention to homogeneous polynomials and work with that, because it's just easier. OK, so now we can go ahead. So now, basically what we want to do now, I mean today, is to repeat everything that we did to the previous lectures for the affine case for the projective case. So with rather small differences, one can do the same things. And the proofs are very similar, so we can go over it rather fast. So the first thing that we had in the affine case is the Zariski topology. So we want, again, to say that the projective algebraic sets are the closed sets of a topology on pn. And that's very. So I just stated here as a proposition. So let's say that, so for instance, if x is contained in y, what? Into homogeneous components. So we have, yeah. So if I f right as a sum of its homogeneous component. So this is the part of degree 0. This is the part of degree 1, part of degree d. Then the 0 set of f defined in this way is the intersection of the 0 sets of the homogeneous. The degree is the number I put up here. So say if x and y in the n are projective algebraic sets, then we have the first thing that, say, the idea of x contains the idea of y. And the proof is in the same way, the same as before, because we just have less conditions here. I mean, if you look at the definition, this is completely obvious, so this is clear. Second, if, say, y, say x in pn is projective algebraic set, then if I take the 0 set of the deal of x, this is equal to x. And remember, we made some proof of that in the affine case. And you just repeat the proof. It was a formal argument, which we will use in the same way. In the same way, if I in kx0 to xn is a homogeneous ideal, if I then take the ideal of the 0 set of I, this will contain I. This is, again, obvious from the definition, because the ideal of the 0 set of I is all the polynomials which vanish, where all the polynomials in I vanish or all the homogeneous polynomials in I vanish. And obviously, this contains I. And do I really need this? OK. So and it's again clear that, so for instance, if s in kx0 to xn is a set of homogeneous polynomials, then the 0 set of s is equal to the 0 set of the ideal generated by s. And this is just the same proof as before. It's kind of clear that the ideal generated by s contains s. Therefore, the 0 set is possibly only smaller. But then you can see that if you write any element here as a combination of any element here as any combinations of elements here, you see that also the other inclusion is true. And then we come to the thing which gives us the risk topology. So these are the two things. So if I have a family, family or a set, say s alpha of sets of homogeneous polynomials, we find that if we take the 0 set of the union over all alpha of the 0 sets of s alpha, this is intersection over all alphas of the 0 set of s alpha. If you think of it, it's again completely obvious because we just, there is obviously, except that there's a misprint like this. It just means you put all these conditions at the same time. And this just means you take the section of the 0 sets where you have movies. And then the last one is that if s and t in k and 0 are sets of homogeneous polynomials, then the 0 set of if I write s times t, which is just a set of all products of one element in s and 1 in t, notice these will be also all homogeneous if all elements in s and all elements in t are homogeneous, is equal to the 0 set of s union 0 set of t. And this is, again, the same proof as before. If you just remember how we proved this, you can just see that an element in the product will be 0 at the given point if one of them is 0 there. And that's all that goes into the proof. So in particular, if you take the last two arbitrary intersections and finite unions of projective algebraic sets, are projective algebraic sets. Now, this is the content of 5 and 6. And we have already seen that the empty set and the whole of Pn are projective algebraic sets. So that means we have that the actions of the closed sets of a topology are fulfilled.  And this we recall the Zariski topology on Pn. And then every subset of Pn is given the induced topology. This is, again, the Zariski topology on that subset. So let me just write this down. Yes? Yeah, also that. No, so this, I didn't prove that the other time, but it's also true. It's also equal to, it's an exercise to prove that this is the same SS0 set of the sum. So all three are equal. But in the moment, I only need that, so I also only wrote that. But you're right. You can also take the sum. So this, if you want, you can do as an exercise. This is your set of the sum or the sum or the idea, whatever, we'll write sum. It's anyway the idea generated by the, you could say the idea generated by the union, which if you want, is the sum. I don't even know how I would want to write that. So maybe say, and if you want, you can call this. So you take the idea generated by the union of the alpha. This will give us that. And if you want, yeah, I think that's more correct. OK, so you want to talk about the Zariski. I wanted to just write down the definition of the Zariski topology so that we have it once in the blackboard, although it's obvious. So the Zariski topology on Pn is the topology whose close subsets are the projective algebraic sets. And as before, if x in Pn is any subset, we give it the induced topology. So the topology shows that such that a close subset of x will be intersection of x with a projective algebraic set. And in particular, we use this when x itself is a projective algebraic set. It automatically has topology. And this is also called, and this is a risky topology on x. So we have introduced this thing. And so we will most of the time talk about so-called quasi projective algebraic sets. These are open subsets of projective algebraic sets. So definition quasi projective is an open subset projective algebraic set. So these are sometimes the most general kind of algebraic set. So the most general things we want to study. OK. So the next thing that we had was the decomposition. So in the affine case, it was a decomposition into irreducible components. So if you have an affine algebraic set, it's in a unique way, a union of irreducible affine algebraic sets with a property that none is contained in another. And these are called the irreducible components. And so we want to see that the same solution here. And if you remember, this was done before by somehow using the fact that AN is a Neutering topological space. So that is, if you have a descending chain of algebraic sets, then it terminates. And this follows from the fact that kx1 to xn is Neutering as a ring. Because if you have an ascending chain of ideals, it becomes stationary. And so we want to see that, obviously, the same works here. And then we immediately get this decomposition into irreducible components. So remark, proposition. So we know that kx0 to xn is Neutering. This is, after all, the Hilbert-Basey's theorem. Whether we call the variables x0 to xn or x1 to xn is somehow of no relevance. So thus it follows that the same proof, as in the affine case, shows that Pn is a Neutering topological space. We have all the same repeated, but it's anyway a Neutering topological space. Maybe I can, namely, what was it? I mean, I will all the same, the same. So it first, x1, x2 is a chain of closed subsets of Pn. Then I can look at the corresponding chain of ideals. So x2 is a chain of ideals in kx0 to xn. And as this is a Neutering, it becomes stationary. It becomes stationary. So beyond a certain n or the i of xi are all the same. And as we know that xi is equal to the 0 set of i of xi, we know that if the ideals become stationary, then also the sets become stationary. Maybe this is like this. Also the original chain becomes stationary. So if at some point the ideals become always the same, then the 0 set becomes also the same. OK. So from this, it follows that Pn is a Neutering topological space. And we had stated the other time that if you have a Neutering topological space, then any subspace with the induced topology is also Neutering. So therefore, any subspace of Pn is a Neutering topological space. In particular, every quasi-projective variety is Neutering. So we have that. And then we had proven the existence and uniqueness of the decomposition of inter-reducible components in general for Neutering topological spaces. So it also holds here. So we have already proven that every Neutering topological space has decomposition into irreducible components. And so we have it. So in particular, we have, so it follows that quasi-projective varieties have a unique decomposition into irreducible components. So I mean the statement would be that if you have a quasi-projective variety, we can write it as a finite union of irreducible quasi-projective varieties. And if we require that none of these quasi-reducible quasi-projective varieties is contained in another one, then this decomposition is unique, is precisely as in defined case. So you just take the formulation that we had in defined case, and you replace a fine with quasi-projective, and that's it. Actually, the statement was in general for Neutering topological spaces, so it follows anyway. OK. Oh. Yeah, well, I haven't yet, yeah, so algebraic sets. So it's actually, it's a debatable issue whether varieties are irreducible or not. That depends on the author. I mean, in some books, you find variety as a different word for algebraic set. And in some books, you find varieties always irreducible. So with me, a variety is always irreducible, except if I make a mistake. But if you look into a book, it sometimes is different. It depends basically on the country where the author comes from. So if you find a book in French, variety will usually not be irreducible. But if it's in English, it usually will be. So now, actually, this was precisely the point where I was now. So the definition goes now anticipated. But a quasi-projective variety is an irreducible quasi-projective algebraic set. Sometimes I just say variety instead of quasi-projective variety. There is a more general notion in algebraic geometry of abstract algebraic variety, which is really more general. But we are not going to deal with it in this course. So therefore, I don't have to distinguish from that. What else? So if we had identified, usually, identification from the beginning of the problem of projective algebraic sets, that an is viewed as a subset of pn, namely, an is supposed to be identified with this u0 in pn, a set of all points like that, where the first component is 1 or non-zero, which is the same, just by identifying a point a1 to an with 1, a1 to an. If we use this identification, we find that an is an open subset without the 0 set of the polynomial x0 is an open subset of pn. So an is a quasi-projective variety. And in fact, we get that any affine algebraic set is a quasi-projective algebraic set, just because it would be a closed subset of this open subset of pn. OK. So this was as much as we wanted to say about the Zariski topology. So the final thing we had in the section on the fine algebraic sets was the Nulsternsatz, the theorem of zeros, which gave us some kind of relation between the ideals in kx1 to xn and the fine algebraic sets, so that you can go backwards from taking the fine algebraic set. You can take its ideal, or if you have an ideal, you can take a 0 set. And these are not quite inverse projections, but you can precisely find out what the relation is. And this was the contents of the Nulsternsatz. Now we want to make a projective version of it. So this would be a fine cone and the projective Nulsternsatz. So we want to prove a projective version of the Nulsternsatz, which gives us a relation between, say, the projective algebraic sets in Pn as compared to the homogeneous ideals in kx0 to xn. So as before, we have these two maps in the two different directions. If you have an algebraic set, we can take its idea. And if we have a homogeneous idea, we can take its 0 set. And we have already seen that in the fine case, these are not precisely inverse to each other. But we can find out what the precise relation is. And now, however, the Nulsternsatz was a very difficult theorem. We certainly don't want to prove it once more. So what instead we want to do, we want to show that the statement for projective space follows from the statement for a fine space. And this we want to do by relating what happens on Pn to what happens in An plus 1 by taking the 0 set of an ideal in An plus 1 instead of Pn or taking the ideal of something. So after all, and how do we want to do that? We want to do this by looking at the fine cone of a projective algebraic set. These are all points in An plus 1, whose class lies in the projective algebraic set. So let's do this. So we want to prove this. I mean, I haven't said what the statement is, but whatever we want to prove, we want to prove by reducing to the affine case, N plus 1, making use of affine cones. So let me formalize this again by the definition. First, I have to say what a cone is and what the affine cone of a projective algebraic set is. So a non-empty affine algebraic set, say x in An plus 1 is called a cone. Well, what is a cone? A cone is a set which has a property that for every point it contains the whole line through the point. You are in a vector space. An plus 1 is just Kn plus 1. So the whole line through the origin is contained. So for any A0 to An, lambda times A0 to An will also be contained. So it's called a cone. If for all, say, p equal to A0 to An in x and all lambda in k, we have that lambda p by which I mean, obviously, the vector lambda A0 to lambda An is also in x. So that means, so if somehow here's the origin and we have that x contains this, then it also has to contain all the lines from this thing through the origin and also going on on the other side like this. And that's after what you think a cone looks like. A cone is something which looks like a cone. Maybe on the picture it doesn't really look like anything, but I think you can imagine. So now for a projective algebraic set, we can define a fine cone. So if x in An is a projective algebraic set, well, the fine cone is just the set of all points in An plus 1 whose equivalence class lies in x. So the set is, I call it C of x. So it's a fine cone is C of x, which is the set of all, say, A0 to An in An plus 1, such that if I take its class, this lies in x. And you know that the class of x just depends by this up to a non-zero multiple. So we know this thing will contain for every point the whole line through the origin except for the origin. That's not quite good enough, so we have to make sure that we also have the origin. And this would be a cone. So this is the fine cone. And we somehow see, in some sense, whether we talk about the projective algebraic set or it's a fine cone, it somehow in some sense is the same thing. I mean, we have the same information. We can get one from the other and vice versa. So well, that comes now. It turns out to be in a fine algebraic set. And I will precisely tell you now how come. OK? So this is a lemma. So let x be a non-empty fine algebraic set, projective algebraic set. Then there are two statements. The first thing is that if we take, so x is a projective algebraic set. So that means that x, so this may be x, we can write x is equal to the zero set. So I write now projective zero set. Of course, I projective space of some ideal i, some homogeneous ideal i. Then it follows that the cone of x is equal to just a usual zero set in a n plus 1 of i. In particular, it is in a fine algebraic set. And the second statement is also how the ideals are related. So if I'm in the same, maybe I, this is a general. So if the ideal, if I take the ideal of the cone of x. So this is the cone of x is now some subset of a n plus 1. I can take its ideal. This is equal to the homogeneous ideal of x. So if I have x is a projective variety, we have its homogeneous ideal. This is the same as the ideal of x. So you can see that from the algebraic point of view, if you relate to a projective variety, it's ideal and go backwards, somehow the cone is basically the same as the projective algebraic set. The ideal is precisely corresponds to it. But we are moving ourselves from the projective to the fine situation. So this I actually do not want to prove. This is also an exercise. It's actually quite easy. So it's a reformulation of this previous statement that we had that I said that if you take the zero set that if you take an ideal, if you have a homogeneous ideal and take a zero set. So then you can either define this as the common zero set of all homogeneous polynomials in that ideal, or you can define it as a zero set of all polynomials in the ideal with a slightly different definition of what a zero set is, namely if it holds for all representatives. And it's a reformulation of this statement. But I mean, it's not completely trivial reformulation remark. But it's easy to figure it out. So now, given this, we want to state and prove the Nulsternsatz, the theorem of zeros, projective Nulsternsatz. So well, it's supposed to be a thing that corresponds to the strong Nulsternsatz. There's only one very small difference. So let i in k x0 to xn be a homogeneous ideal. First statement is a bit different than the fine case. So the projective zero set of i is empty. You know that in the fine case, the zero set of an ideal is empty if and only if the ideal is the whole of k x0 to xn. Here, this is not quite the case. So if and only if i contains all homogeneous polynomials of degree n for some n. So if the ideal, it doesn't need to be that it contains all polynomials. It just is enough that for some given degree, it contains all homogeneous polynomials of that degree. So that doesn't look very similar to the fine case. But that's the only thing which is different. So if we look at an ideal whose zero set is not the empty set, we get the same statement of the strong Nulsternsatz as before. So if the projective zero set of i is not empty, then the ideal of the projective zero set of i is equal to the radical of i. And this means, again, that we have essentially one-one correspondence between the projective algebraic sets and the radical ideals in k x0 to xn, except that we have this tiny thing that the empty set is a little bit more complicated. So let's see the proof. And then we also see where this exception comes from. So we first prove one. So we put x to be the zero set in pn of this ideal. So maybe it starts here. So when does it happen that x is equal to the empty set? You have to remember the definition of the, I mean with respect to the cone. So remember that the cone of x was the set of all points in an plus one, such that its class lies in x union with a point zero. So when x is equal, x will be equal to the empty set if and only if the cone just consists of the point zero. Because that corresponds to the fact that there's no point in projective space that lies in x. This would correspond to the non-zero points in the cone. Well, we know that cx, after all, is equal to the zero set, the fine zero set of i. So the zero set in n plus 1 union zero. So the fact that the cone is equal to the point zero means that the fine zero set either was the point zero or it was the empty set. Thus x is equal to empty set if and only if z of i is equal to empty set or z of i is equal to zero. So now I can use the usual null tensor. So by the fine null tensor, we have that if I take the radical of i, this is either i itself. And therefore, the radical of i, if we are in the case of the empty set, will be the whole of kx1 to xn, x0 to xn. Or the radical ideal is the radical of i is the set of all polynomials which vanish at zero, which is just the ideal generated by x0 to xn. So in any case, the radical of i contains this. So this is equivalent to saying that the radical of i contains x0 to xn. So thus, if we have this, so for any, say, i from zero to n, there exists a number ji such that, say, xi to the ji lies in i. And so I can take, let n to be the, say, the sum of these ji's. Then we see, as all monomials, so if I take any monomial now in the xi, which has degree at least n, then the powers of one of the xi's must be at least ji. So any monomial of degree at least n lies in i in kx0 to xn in i. And so it follows that i contains all homogeneous polynomials of degree n for some n. But also, obviously, conversely, if it contains all homogeneous polynomials of degree n for some n, then its radical will contain x0 to xn, because it, in particular, contains x0 to some power and so on. So this is the first part. So this was this one little exception, which is also the more difficult part. And now the second part is quite easy. So let x to be, again, the 0 set of i. And we now know that this is non-empty. In the case it's non-empty, we want to prove something. So we just write down. So if I take the homogeneous idea, what is it, we have seen that this is the idea of the cone of x. And this is the same as the idea of the, say, a fine 0 set of i. So I take, in a n plus 1, I take the 0 set of i. And we know what x is a projective algebra. I wrote something else? Yeah, yeah, yeah. Well, OK. I mean, in principle, you see, I should have written the p here, you're right, because we have in the same two lines they're fine and the projective case. But if we're not in that situation, I'm free to write just z in both cases. But obviously, you're right that here I should write this because the next line I look also at the fine case. So and we know now by the usual null stanzatz that the ideal of the 0 set of an ideal is a radical by the null stanzatz. So you see the projective. So this is the projective null stanzatz or rather straightforward consequence of the fine one if one knows the story about cones. We have this slight complication with the empty set because it's just the case that if we have a, which comes from this relation between the cones and the projective algebraic sets because in order to talk about cones, we have to always add the 0 and this somehow messes up our argument here a little bit and therefore also the statement. But otherwise, it's precisely the same as in the projective case. Yes? OK. So actually, I maybe should have said it, I mean, so what we have said is something slightly different, which is equivalent. I had said as a remark and exercise, so you have to disprove it if you don't want to believe it, that if the 0 set of i is non-empty, we have that, let me see. So what was the statement? And then we have that the, so if x equal to the 0 set of i is non-empty, then we have that the cone of x, so this was the projective 0 set, is equal to the affine 0 set. This was one of the two statements I made. And then by definition, if x is empty, then the cone of x, just by definition, is equal to 0. If you, you can put this together and say this. I mean, it's maybe not the most intuitive way of saying the statement, but it's equivalent. I mean, OK, OK. So I want to just close this up by a few remarks. So one thing is that we see that for the statement 1, we got this exception, which came from this idea here. That if the 0 set is the empty set, we actually get that the radical of i will contain this. And so we say that the ideal x0 to xn is called the irrelevant ideal, so it's kind of a radical ideal which has the property that the 0 set is still empty, although it's not the whole of kx1, so it somehow doesn't do anything. And so we have this corollary. We have a 1, 1 correspondence to a bijection, inverse bijections between the homogeneous radical ideals. So if i in kx0 to xn is an ideal, which is not the irrelevant ideal, different. We call it relevant.  So we take the homogeneous, relevant radical ideals in kx0 to xn, in 1, 1 correspondence by these two things. We can take this projective 0 set, and we get a projective algebraic set in pn. And if you have a projective algebraic set, we can go back and take its homogeneous ideal. And this gives us bijections between the homogeneous radical ideals in x1, x0 to xn, and the projective algebraic sets in pn. The only thing is in order to have a 3D bijection, we don't miss out one ideal. We have to throw away the irrelevant ideal, which comes from this statement here. And as a corollary, we get the same thing that we had in the fine case that a projective algebraic set is irreducible if it's a 0 set of a homogeneous prime ideal. So a projective algebraic set x in pn is irreducible if x is a 0 set of i, where i in kx0 to xn is a homogeneous prime ideal. So it's a homogeneous ideal, which is also a prime ideal. And then as a straightforward consequence, if f is a homogeneous irreducible polynomial and irreducible, then we have that its 0 set is irreducible. So the second statement follows in the same way from the first as before. It's just that if f is irreducible, then the ideal generated by f is a prime ideal. And then we apply the first part. So to prove it, we only have to prove the second. And we proved a similar thing in the fine case. So the proof is analogous, so only slightly complicated by the fact that we have to somehow talk about homogeneous polynomials. So we somehow have to, we have something about that something. If something is a product of polynomials, then if a product of polynomials lies in i, then one of them must lie in i. But in order to do this with a homogeneous case, we somehow have to make the polynomials homogeneous. And so this, you need some tiny extra argument. But it's not a big deal. So first, assume x is irreducible, so it's reducible. So then we have to show that the ideal of this is not prime. We'll just see. Yeah. So it appears, I'm pretty sure that this statement is also true, but this is not what I'm claiming. So I will maybe stick to what I claim, so that I don't have to, you can see whether you can prove this. No, no, but I think I will stick to it. I will just prove it as is. So then, no, but I think I have to, no, no, but yeah, yeah, that's what I have in my notes. I think what's written here is also true, but as I haven't worked out the proof, I will stick to what I have. So reducible if and only if is a prime idea. I mean, this is a somewhat less useful statement, but that is what I have proven. Not quite sure. I think in that case, it's not so evident, well, I think to be on the safe side, I will want, yeah, anyway, let's see. So assume x is reducible. Then it follows that we can write x equal to x1 union x2 for closed subsets x1 strictly contained in x and x2 strictly contained in x. So we have two closed subsets whose union is x, but none of them is equal to x. Well, it follows then obviously that if I take the cone of x, this is the cone of x1 union the cone of x2, no? Because the way the cone is defined, this is evident. And these are both closed subsets of the cone of x. And none of them is equal to the cone of x, because it's not true here. So these are closed subsets with a c of x1 and c of x2 strictly contained in c of x. So it follows that c of x is reducible. So it follows that the homogeneous idea of x, which is equal to the idea of the cone of x, is not a prime idea. So that was quite simple. Now we want to go the other direction. So we assume the ideal of x is not prime. So I just write i for it. So that means there exists an element f and g in i such that in kx1.xn such that f times g is in i, and f and g are not in i. So normally you would say, I mean you would want now to work with f and g, take the intersection of x with the zero set of f and the zero set of g, and then we would conclude in the same way as in the fine case. The only problem is that we want to talk about, I mean, zero sets of homogeneous polynomials. So we would need that these are homogeneous polynomials. But there's no reason why they should be, because that's not part of being a prime idea that you can do that. So we want to somehow replace f and g by homogeneous polynomials. This is by looking at homogeneous components. So let i and j be some positive, non-negative integers minimal such that the homogeneous component of f of degree i is not in i. And the homogeneous component of degree j of g is also not in i. We have that f and g are both not in i. So if all the homogeneous components were in i, then f and g also would be in i. So there must be some smallest degree for which the homogeneous component is not in i. So this certainly exists. Now, so subtracting homogeneous components of f from f and of g, so of lower degree, from f and g, we can assume that f starts in degree i and g starts in degree j. Why is that? We know that all the homogeneous components of f of lower degree than i actually lie in the ideal i. So if I subtract them, I don't change the fact that f does not lie in i. As this thing itself, if I have the sum of two elements in i, then if I take something which is not in i and I subtract from it something which is in i, then afterwards it's also not in i because i is an idiot in the same here. So we find that if we subtract the lower degree homogeneous components from f and g, what we get afterwards is still not in i. So we can replace f by what we get by subtracting it, then f starts in degree i and same g in degree j. So but now we have that f i times g j is the homogeneous component of minimal degree in f times g of f times g. If we multiply things, the degree will add. And the lowest possible degree that we can get is if we take the lowest degree part here and the lowest degree part here. If we take one of them higher degree, we get the higher degree. So the part of degree i plus j of f times g is this product. But now one has to remember that f times g is an element in i. And i is a homogeneous polynomial, a homogeneous ideal. So then by the definition of homogeneous ideal, an ideal is homogeneous, if an element lies in the ideal, then all its homogeneous components lie in the ideal. So therefore also this lies in the ideal. And now we can argue in the same way as in the defined case. So we let x1 to be the zero set of i union, say, f i. So we take the ideal i and we add to it this one thing. And x2, the zero set. So in other words, I could write it as z of i, an intersected zero set of f i. x2 is the zero set of i, intersected zero set of g j. Well, we know that as f i is not in the ideal of x, it follows that this is strictly contained in x. But on the other hand, we know that if I take their union, then this corresponds to taking the product here. We have that the product of these two elements is f i g j, which lies in i. So it's the same as the zero set of i. It follows that n is the zero set. So x1 union x2 is equal to x. So thus x is reduced. So now from this, one can actually deduce what I wrote on the blackboard as part one. Let me that if i is a homogeneous ideal, so this would be in some sense part two. So this should be, so if we have in the look at the theorem of this proposition, we have this which I call part two. This should in some sense be part three. And the thing which I first wrote on the blackboard would be part two. So if i in k x0 to xn is a homogeneous idea with a zero set of i is empty, is non-empty, then it follows that this zero set of i is irreducible. And this part two follows in the same way as in the fine case. Because in the fine case, we had seen that because we have this correspondence, prime ideals are radical. So that if we have this homogeneous prime ideal with this property, then this is actually the ideal of its zero set. And therefore part one applies. And then part two follows from, part three follows from part two directly in the same way as in the fine case. Because if you have an irreducible homogeneous polynomial, it generates a homogeneous prime ideal. And therefore part two applies. OK, so my time is already up. I was a bit, I was a bit, I was a bit, I was a bit slower today. But in some sense that's maybe just as well because this was, this finished the first part of this course, which was, you know, introduction of the final project of varieties. And the next time we will start to talk about morphisms. So I mean, the idea is that when you study something, say vector spaces, many folds and whatever. So one of the main things you use to study it is the, the maps between these things which are compatible with the structure. So linear maps between vector spaces or continuous maps between topological spaces. And so, you know, and now we have to define what are the maps between varieties which are compatible with the structure of being a variety. And these maps will call morphisms. You know, a little, not so much fantasy. And somehow very important in the definition is to say what are the maps from a variety just to K to the field. These we would call the functions, the regular functions. We'll actually find out that the way to define the morphisms is to say something about what they do to the functions and therefore we first have to look at the functions. Okay, we start this next time.


He's back co-founder of enjoy basketball host of the Kenny Beachham podcast. It's Kenny Beachham and look we got a lot of really important basketball news Kenny and we're always happier here but the most important question I can come up with is the fact that we have Paul Shearer on Monday show and he said that Space Jam is a horrible way. You're from Chicago. Where are you on this as someone that's watched Space Jam like a hundred times in my life I can't give you hand Paul's take here I'm sorry I know I know he's a movie guy and I respect his opinion on movies more than a lot of people but just the nostalgia factor is enough for me to say it's a good movie. That's what I thought yeah I mean we'll like maybe I'll rewatch it but we were younger when it came out so as a kid you're a little more inspired by watching it.  Watching it as an adult is probably the ball might have watched it as an adult. All right homework assignment rewatch it come back we'll talk about it. I can do that. I like how you said it's Michael Jordan why is he living in that two bedroom house. He's playing himself. Why is the house bigger. That was fair. Kenny obviously yesterday a lot of news around the league but especially in Milwaukee the Bucks firing Adrian Griffin Doc Rivers appears to be in line to take over what are your thoughts who do you think the Bucks should hire. It's hard to have a real good shortlist halfway through the season. Before the season started obviously they had Kenny Atkinson they had Nick Nurse who's looking amazing in Philadelphia and they opted to go with the first time head coach and a lot of that was because he had the backing of Yannis and everything of the people available I'm guessing Doc is the best. It's hard to it's hard to say man it's hard to say obviously in 2008 you know he had the good run with the Boston Celtics but since then he's failed to make it past the second round in the playoffs in most cases obviously he's also never close to talent like Yannis so maybe Doc is the right answer we just we just have to wait and see I guess. You know what they say you can tell him somebody's lying. Yeah. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. He's tall. Done! It's over. Terry Reger in the middle of the show was traded to Miami. What do you think about that deal how does that look from the heat moving forward. I love it because they've obviously struggled recently offensively like I've watched a bunch of their games and even with Jimmy Butler's back Jimmy is just such a passive guy during the regular season it's not something that I don't really understand but they just need another guy that can get a bucket and Terry Reger has a very underrated season. The only thing that I worry about a little bit this year is that he's shooting 30% on catch and shoot shots. Obviously in Miami, he won't have the ball as much as he did in Charlotte, especially when the Mellow was out.  So maybe under Miami, he can get back to that. They just needed another bucket and Terry Rogier has had such great performances in Charlotte. He's been a big shot maker for Charlotte in the few close games they've had over the last two seasons. So I love it. I mean, I hate it for Cal Lauri, obviously, but I think he'll be fine with the bag that he got a few years back. So Kenny, everyone, Zach Levine, he's a name that we've been hearing for a very long time. He's been out with an ankle injury and the bulls kind of look good without him. Does he get traded before the deadline? And if so, do they just completely blow it up, trade to more, get rid of everybody? I've been waiting for the Psalms of fate that it's happened. But with the injury and something I'm sure everybody agrees on, when you have a player of Zach Levine's caliber, we've seen it here in Chicago, he's not gonna be your one option. And a lot of cases, he's probably not gonna be your two option on a very good team. So why should we pay him $40 million annually to be the third best player on the team? And I think that's where the hiccup is. The bulls have made the least amount of trades since 2021. So I'm assuming that that means the front office is holding on to all the assets and asking for crazy returns. I'm hoping that we get the trade done, mostly for Zach's sake, because even when he came back from the first injury, you can tell that he was very passive. He didn't want to step on any toes. Kobe White was playing very well. I think a change of scenery is necessary, but I don't know how likely it is because the contract is so big. So what is the deal you would most likely to see happen before the deadline? For the bulls? For anyone. For anyone? Wow. Oh, for anyone. I kind of want to see the 76ers buy in a little bit. I know they've preached flexibility from the off-season standpoint and I completely understand that, but I feel like there are some people on the market that you can trade for right now and maintain that flexibility come off-season. I think Jorlin Bede is playing some of the best basketball I've ever seen in my own two eyes. I understand the critics, like we got to get past the second round. We got to play all these games and the playoffs, but just looking at the regular season, he's having his best year and I think that they need another guy on the team that can create their own shot outside of just him and Taris Maxi. Again, I don't know who that guy necessarily is, but them just sitting on the expiring contracts and those two additional first round picks that the Clippers gave them would probably be a mistake in my opinion. I wonder if that answer will be the answer to my question because I wanted to ask you, give me a team that will absolutely not win a title unless they make a move. Yeah. Is that it? Is it? We're sticking with the... It is silly. It is silly. So they have to do something. It's just the way it is. Look, whoever did the Dak Prescott, Joellen Bede memes the other day, that's not cool, but also kind of funny. And I feel like that's what I'm hearing is like until they can get over that hump, we can't do much with it. So you need another piece. The man just dropped 70 and everybody was like, well, in the playoffs, he don't play well. So it's just like, he needs it for his own legacy. He needs it for his own respect factor. His nobody is gonna deny the fact that he's one of the top talents in basketball, but all the other top talents in basketball either have a conference finals appearance and NBA finals appearance or a championship. He has none of those things and he's about to be 30. So even he mentioned it in his post game, like I dropped 70, but it doesn't matter because I haven't played well in the playoffs. It's like this is such a great moment for him. But we're talking about April, May and June instead of freezing 30. It's crazy he said 30, like it's old. But to be fair, Joellen, from my come remember, he hasn't been healthy most of the playoff runs. He's broken his face. He's broken his hand. He's always had injuries. So hopefully this year, this is a playoff coming and he'll be healthy and then he can show you that he's not Dak Prescott. Kenny, sticking with Joellen, obviously we know about the big game the other night, looking like the front runner for the MVP. He has missed 10 games. So do you think the NBA is going to regret this whole threshold of, you know, the 65 game minimum for these awards? I think that the first year's trial, they're gonna keep it. They're gonna keep it for year number two because I'm looking at Joel and B's success and how dominant he is. The number two option in this, if Joel and B fails to hit the 65 game threshold, it's not like we're falling off from the best player to lead to somebody that's not that. It's the guy right under him, which is Nikoli Okic who's almost equally as valuable when it comes to this MVP award. So it's, I think that no matter what, we're gonna have an MVP that we feel very confident and good about. But I think that Joel and B right now, again, just thinking about the first 41 games of the regular season, he's been heading shoulders above everybody. I mean, he's putting up legendary stuff. And I think that the NBA also added something where you could refute some of the games missed. So maybe we get that from Joel and B where he ends up with 63 games. Well, how does that even work? Two or three games, how are you gonna refute it? I refute it. What do you think the number should be? Asking everybody. I think there should be a number. If you play 64 games and you're as dominant as Joel and B, you're the MVP. Okay, but what if you play 50 games and you're as dominant as Joel and B? And don't vote for him. Like I don't think there should be a threshold of games. Well, you know that's not gonna happen. There's people that don't deserve to be an all-star. Joel plays 64 games and Joker plays 66. He gets to win it even though Joel had a better season. You're picking literally the swimmest of more than that. That's gonna happen one of these years and we're gonna be like, damn, he got screwed. Well, let's wait till we get to there. Kenny, my next question to you is because I know my answer. Wimby, Chet, rookie of the year. I think it's... Don't note, don't lead the witness. Go on. Who was your rookie of the year and why? If the season was in right now, it would be Chet. Come on. But I think that once we get to April, it's going to be Wimby. There we go. No, Kenny, Kenny, I agree with all your takes till right now, don't do this. Well, you know, you're not watching the Wimby stuff. Yeah, I'm watching them win seven games and I'm watching Chet being the number one team in the Western Conference right now. Bless be real, Chandler. It's not Wimby that's causing them to win seven games. He's playing 25 minutes per game and he's averaging 26 points in that time frame. Like it's only so much one man can do. And we're talking about a 20-year-old. He's not Bron. He's not KD. He can't single-handedly put a team on his back yet. But he is one of the most impactful defensive players in all the basketball as a 20-year-old. And his points per minute, I know we're talking advanced stats here, but like his points per minute is on par with some of the best players in ball. And Chet has the luxury to be the third option almost nice. And that's not a knock on Chet because his efficiency is really good. He's such a good defensive player.  And I think that when we come to April, we're going to look at these last 40 games. But like, man, Wimby was playing out of his mind. For the individual, the rookie. Who's the better rookie? He's unbelievable. Where'd you find this guy? He's unbelievable. He knows his stuff from looking down. But I do think the only way Wimby wins as if Chet goes down like a seasoning and then getting into a knock, I think he's running away. Rookie on the best team of all year. Forget rookie of the year. Chet is an all-star this year. And he's borderline all-MBA. You don't think he's going to win rookie of the year? He's the second best player on the best team. I told a little bit they have been winning. His numbers aren't as good as Wimby's. Thank you. The points per game in the minutes are it's a nut stat from Wimby. He's, listen, he's unbelievable. Important numbers like that. He's unbelievable. But I think when you look at an award like this, you have to look at everything. And his team is one of the worst teams. And his team is one of the best teams. Are we not going to call rookie of the year anymore? Oh, I'd be pissed if he did that. It's been about 26, 27 years. Hill, Jake, it was the last one. Oh, I'd be flippin'. I wouldn't want it. Give it to him. That would be such a cop out. I also say Chet is more available. Wimby has been set out some games. Yeah, and Chet's technically it's the second year in the league. I don't want to give you a... Do you like the Spurs or no? You like the Spurs?  The true rookie hoodie? Yeah. Chet's not a true rookie. Yeah, he's not a true rookie. Neither was Blake Griffin. He still ran away with the rookie of the year. Yeah, and he could argue that as well. Oh, would Wimby playing pro since he's eight? That doesn't count for something? Well, eight. Eight.  Fine, let's stick with the Thunder for one second because they played the Wolves. They beat them. And after the game, Edwards was not happy. Thought it was very hard to sort of play against them. SGA getting the calls he got. Afterwards, SGA had the post on Instagram with another classic SGA caption. Post game, post game, you know the drill. But we want a rivalry here. So let me ask you that. One, are you here for a rivalry between Anthony Edwards and SGA? 100%, our league needs more rivalries. Like this season, we just saw the Bucks and the Pacers start to brew. And if we can get two of the top young talents in basketball to dislike each other on court, it's like, this is Canada versus USA too? Like this is everything we can really ask for in a rivalry. I'm here for it. We need, and as one of those guys that's always going to talk and I need him to continue that so we can have more rivalries. Now, the tough question is, you've got to start a franchise today. Which one are you starting? That is tough. I've seen, I think I've just seen Shay do it more consistently over the last couple of seasons. So I'm proud, I mean, Shay's all NBA for the last. He's going to be all NBA again this year. He's top three, top four at MVP. Anthony Edwards still hasn't got there. Yeah, I think he has a possibility to get there. But I'm going to take the proven all NBA player in the moment. And maybe I'll look back on this and say it was the wrong decision. But I'll go with Shay. It's hard to argue that. I'm thinking in my head, how do I argue with him right now? But it's tough, man. SGA, he's done it. He's all NBA. And I think he's a better two-way player, but not SGA. So the question is, do you think? He's leading the league in scoring. He's done it all. Do you think SGA can, as he reaches full potential, you think there's more for him? But I think Ant has a lot more room for growth. I think that's why some GMs make their draft picks of the potential of who Ant-Man could be, and besides the potential of who SGA could be. I think SGA too is in a great situation where he's 25 years old, and he's the vet. He's the leader of this young AAU team that's kind of taken over the NBA, you know what I mean? So he's got the keys. Ant does as well, but he's in a different system. Last year they struggled with the whole Rudy Gobera trade. Didn't work. Now it's starting to pan. Now it's starting to work out. I do think he's one of the better two-way players, but I'm with Kenny here. SGA, he's something. Can't beat it. Kenny, All-Star Starter's coming out on Thursday tomorrow. Steph Curry, currently ahead of SGA, and then in the East. You have Trey Young over Gauzik.  Tom and Mitchell. Tyrese Maxey, you have Boy Jalen Brunson. Salsa Patrol, you almost started in the All-Star Game one year. Andrew Wiggins started one year. Should Steph and Trey be All-Star Starters? Nah. And that doesn't mean that they're bad or nothing. Like Luca and Shay are literal MVP candidates. Steph Curry's not that this season. Like I want to see those guys. I think on the guards on the Eastern Conference, I feel pretty good about Terry's Halliburton being one. He's number one in voting. And then that second guard spot, it could be Jalen Brunson. It could be Donovan Mitchell. But it's probably not going to be Trey. He doesn't have the same respect amongst his peers as we saw in previous All-Star Voting situation. So I don't think it's going to be Trey. That's crazy to me that that could happen. But you're right, we do get some weird pops and this doesn't make any sense. Well, talking about All-Star Weekend, is there anything that you would like to see change for All-Star Weekend? Something new, something added? I just want to have the good dunkers participate. You know, I was there in Cleveland and it was... I said to the GV guys. But you know what? I'll take Mack McClam because he made it happen last year. But we haven't had, other than Mack McClam last year, like a really, really good dunk contest since Aaron Gordon versus Zach Levine. And we're just waiting. I think most players just don't want to be labeled a dunker because we saw that for both of those players for years. And then Zach Levine had to make two All-Star appearances before people start to realize that he was really good at basketball. So I just want players to be in it, man. The moment that we get people dedicated to Jaws, the Zion's dedicated, that's when things come back. But I just don't think it's possible. I don't think we can get them there. So that would be your pick. That's who you'd like to see.  I would like to see a one-on-one competition. That's much better than a skills challenge or a king-of-the-court situation. Yeah, I'd love to see Tatum play Devon Booker one-on-one with two dribbles. You know what I mean? Or Tatum against Jaylen Brown. Exactly. You remember that one. That is more exciting than watch Wimby go coast-to-coast and throw a ball through a hole. For the fans. Why do you hate Wimby? I was watching chat with them. Gug, I'm sick of it. As former players, do y'all think that the one-on-one thing would work? Would you be able to convince real players to do it? Yeah, I don't know. It's tough to even get them to play serious in the game, so I don't know. I said it's not for us. I think it's more for the fans. I think it's more interesting and exciting for the fans to see us play one-on-one for the players. One-on-one is not that big of a deal, nor do they take it as serious. It's a free way to get exposed, too. Like, if you don't play, would you get hurt? There's a lot of negative things that could happen. That's another reason why I don't see you guys taking it seriously. They don't want to get exposed. They don't want us... Pipe dream. I know, I love this time of year, though, because we're always trying to figure out how do we make the All-Star weekend better? I won't forget that. Well, first of all, don't put it in Indiana. I almost made it through a show, Kenny. We almost did it without insulting an entire city. Chandler's going to Indy this week. Yeah, he's going for us. I don't get knocked out enough. I gotta clean my garage. You might get jumped out there. Okay, so over the weekend, we had the Bruce Brown sound bite about talking about playing for Tibbs and the Knicks. He doesn't play for Una. And Dejonte Murray talking about playing for the Spurs. I don't want to define tampering, but maybe this could be called tampering adjacent. What are we doing with these little moments? Nothing. I want more of them. Because it shows us what a real priority is live. Bruce Brown wants to play for the Knicks. Dejonte Murray wants to play for Pop again. Like, being transparent could go a very long way. So we won't get situations where players trade to a team and he doesn't want to play there. So just be vocal, be honest, and maybe we can get you to the place you want to be at. Right, we'll have our dream job. I guess, man, but it's not like you're not employed by a certain... If this worsening goes to the Knicks, I'm gonna lose it. You can pitch yourself to another competing company. I kind of love it. Look, the Bucks brought in their next wife while the first wife is still sitting there. Like, it's the whole thing. It's dirty and it's weird and I love it. Candy, love having you on. Can't wait till we have you on again. Thank you so much. And we will take a quick break when we come back. No phone calls after 9 p.m. Wemby's my kind of guy. We'll run it back, return it.


Andreas, would appreciate your perspective on the topic I've been wondering about of late in the Bitcoin economy where hard money currency and monetary policy defined by code is dominant, how would or could societies address mass unemployment and the survival of the workings of commerce in situations such as we are currently facing with COVID-19? While I can appreciate concerns about unlimited printing of money and the priorities of how those funds are expended, the hyperinflation that was predicted after 2008 hasn't come about and I haven't seen a compelling or compassionate alternative being presented on the libertarian Austrian side of the argument. Do Bitcoiners declare this a healthy cleanse retreat to their citadels and wait for the pandemic to burn itself out at the cost of millions of lives in massive economic destruction? A long question but thank you so much. The bottom line here is that first of all I'm not an Austrian economist nor am I a strict libertarian or assign those kinds of labels to my political views but the thing is that the argument that this crisis is being somehow solved by this massive injection of money I think is fundamentally wrong and I think that's mostly the argument you'd hear from libertarians and Austrian economists which is that the reallocation of money through the canteone effect as it's called where the rich get richer and income inequality increases massively because of subsidies into the investment markets which are mostly concentrated among the wealthy the big businesses that have first in line access to the big banks that have first in line access to capital this actually has a very specific effect of enriching the rich and impoverishing the middle class and the lower class and the working class and so as a result what exactly is the saving of the economy doing? It's not a saving of the economy it's building gilded lifeboats for the super rich to bail themselves out we've seen in fact recently that many of the richest people on the planet have increased their wealth just in the last two months by some 24 billion dollars just off the stimulus and the increase in concentration of wealth that is a direct result of this pandemic and the stimulus that's happening also the idea that hyperinflation didn't come in 2008 sure it did it came in assets it became completely unaffordable for anyone to afford student loans health care or housing for an entire generation of young people while all of the wealth got directed to those who already had wealth invested in the stock market and other assets that got massively inflated by stimulus so again I think the idea that in a hard money society what you would end up with is a society without compassion where everyone would be on their own I don't think is true there's no reason why taxation can't work in a hard money society there's no reason why you can't have representative democracy work I don't pay taxes only because I will get caught if I don't I actually believe in in the fact that the weakest link for example in the pandemic is how healthy my neighbors are and I think it's important that that everybody has a basic quality of life and and health otherwise the whole of society suffers which of course makes me not a strict libertarian but that's just a political opinion so I I'm not sure it's all black and white I don't think the stimulus has actually saved anything not made things worse and I also don't think that in a hard money society we can solve social problems and we will be paralyzed because our money will be so awesome if you enjoyed this video please subscribe like and share all my work is shared for free so if you want to support it join me on patreon


It is a special pleasure to join you at this inaugural International Forum of the Development of the Lake Charred Region. Nigeria is excited and honored to be the first post of these annual forums, and I bring you the very warm greetings of Mr. President, President Mohammad Ibuwai, who by his relentless advocacy on the matter of the recovery of the Lake Charred area has made the whole question a geostrategic issue for Echoers and for the Africa Union. I must say that for very many of us who have watched the Lake Charred go from a blessing to some sort of a conundrum, the Lake Charred Region Recovery and Development Project is share music to the ears. But the story of the rise and fall of the Lake Charred bears repeating so that the work of recovery can be done with sufficient insights into the multiple issues that must be contended and resolved. At the height of its glory, and we've heard this repeated yesterday, the Lake Charred was one of Africa's largest natural deposits, covering 25,000 square kilometers. The Lake, a fresh water lake, provided water for over 30 million people in the four countries surrounding the Sahel, Nigeria, Cameroon, Charred, and Niger. But its huge economic value included fishing, agricultural productivity, health and of course security. Today, the Lake Charred has shrunk disastrous lengths to barely 2,000 square kilometers, a case of the devastating impact of climate change on natural resources. This sharp drop in size and the decrease in water levels has also led to a chain of catastrophic events, including the impairment of the capacity of that region to deliver food, health, and security to its population, resulting first in economic instability and downturn in agricultural productivity and subsequently in the festering in security all around the Sahel and in many cases in the violent context of food, water and pasture. The insecurity in the Sahel region has spawned off another crisis, a humanitarian crisis of immense proportions, and we've heard here that over 23 million residents and citizens of the four countries are displaced currently. The prolact project's approach to the recovery of the Lake Charred region is uninspired because it focuses on investment to support regional coordination and crisis monitoring. And we've also heard repeatedly that regional coordination is the key to resolving many of the issues in the region and connectivity and agricultural livelihoods. These investments are rightly expected to address the underlying fragility and the acute humanitarian and forced displacement crisis in the four countries. Collaboration, cooperation, and synergy between our countries and stakeholders across the region and the Sahel are the key actions that will determine the speed and effectiveness of the delivery of economic stability and peace and containing the humanitarian crisis, international cooperation, and all that is required in that area. It's important also to bear in mind that there is a need for international cooperation and collaboration, especially as we've seen in the domain of military action, and we've seen this work for cross-border security interventions, especially in terrorism situations in that neighborhood. All of the successes in our fight against terrorism exemplify what we can achieve working together. We therefore must continue to build on this spirit of cooperation in other areas of intervention and forge even stronger ties for sharing information and lessons from our different experiences. There have been several studies that deal with different aspects of the security challenge and a multi-faceted approach for long-term security and stability of the region will be informed by discussion and analysis of this body of knowledge that is already available. While there has been a lot of progress, there remains much to be done in addressing especially the drivers of insecurity and where we can improve, we must take every opportunity to do so. One of the things that the crisis has affected is social cohesion within and around many of the communities in the region. So as we rebuild the physical structures within these areas, we should be mindful of the need to foster peaceful coexistence and restore the social fabric of those communities and societies. For without sustainable peace, we are limited in how much we can attract the kind of investments necessary for the growth we need to fulfill all of the development needs of our populations. So as we listen, as we learn and share over the course of this forum, we hope to build stronger ties with our neighbors that will endure and grow beyond the immediate task in front of us, yielding results we hope over the short and long term, with new strategies, renewed vigor and drive to improve the lives of our brothers and sisters across the four countries. Our experience has highlighted the importance of dialogue and interactions, such as those confronting, such as what we expect to see in confronting the challenges and that faces our quite confident in the potential of collaboration for achieving all of our objectives. The results and recommendations of this forum are to be transmitted to the various governments to guide policy making and strategic decisions that need to be taken in the short and long term, related of possible development of the region. And I can assure you that the federal government of Nigeria will be an active participant in turning these recommendations into firm actions. I'm confident of the same level of willingness of the governments of Cameroon, Chad and Niger, which is of course evidenced by their presence here today. Finally, I would like to take this opportunity to assure all our partners in this effort of the government's commitment to working with you for sustainable, peaceful and a prosperous region. We also wish to assure you of our unwavering determination to address the crisis and rebuild the livelihoods of people who have been affected by the humanitarian crisis especially. Before I take my seat, I must commend the Honourable Minister of Humanitarian Affairs and Disaster Management and Social Development, Hajiya Sadia Umafaroop and her team, the Lake Child Basin Commission, the Northeast Development Commission and the Lake Child Region Recovery and Development Project for your commitment to the recovery and development of the Lake Child Basin. It is now my very special privilege and pleasure to declare open the first annual International Forum on the Development of the Lake Child Basin. Thank you very much.


The good old days off the SNES. The good old days when people liked 8-bit games dot the good old days when people liked these kind of games. I was a big Mario fan at the time since my sister showed me Super Mario World in the SNES. We played Super Mario World a lot and I mean a lot point. We completed every single level possible in that game. My SNES is broken at the moment since it is very old. Now I got it repaired. When I got it repaired I played every single game I had in the SNES like Super Mario World 2, Yoshi's Island, Super Mario All-Stars, Teamage Mutant Ninja Turtles and more. I wanted not to play some Super Mario World but I couldn't play it since it was very old, fell off to the ground multiple times, and was very dusty. Since my dad knew that I wanted to play Super Mario World he got me a new Super Mario World cartridge. Now of course it wasn't new and shiny because games like Super Mario World couldn't be new in 2017. I rushed into my room to play Super Mario World. Now of course my SNES was old so it took a few tries to get the SNES to work. The first thing I saw was the familiar message Nintendo presents. After that I noticed something very weird. The Super Mario World logo was blue and in the background was a world map of which I don't remember. I ignored it. I chose what save file I wanted and started to play. I got on the world map. There was something odd about it. It was completely different than what I remember. I started at a level called 4W1. In that level I got a Yoshi. I didn't want to skip the other three levels so I moved to level 1. It started like I remembered. It was a different background. The giant bullet bullet looked different but the rest of the level was the same. I moved to level 2. It wasn't that much different but it had some differences. The background was just tiles off the ground. Later in the level I saw Piranha Plant that for some reason had a fish as a body. It was that fish that you can one KO when it's not in the water but this time it was a Piranha Plant's body. As soon as the Piranha Plant got to the surface of the pipe it had fireballs appear from or slash his whatever mouth point. I got hit by the fireball and I lost my Yoshi. I knew that a Piranha Plant like that was in Super Mario Bros. 1 or Super Mario Bros. 3. I finished the level and went to level 3. It was a short level that had block spelling test. Lock loss test. 4. Well since it was obvious I was thinking that this was a beta for Super Mario World. Now betas like this are rare. Now I got to level 5 since I completed level 4. It was a castle. I entered the castle level and as soon as I started it was a cutscene but it wasn't the usual one. It was a cutscene where there was an Yoshi sign. After that cutscene I got into the castle dot the castle had these weird glitchy backgrounds and glitchy Piranha Plants. I figured out the game was a beta so it was normal. As soon as I got to the boss door I entered it dot the boss was Bowser himself. It was like in Super Mario Bros. 1. Of course I grabbed the axe and Bowser fell in lava. A message popped up saying, you're not supposed to do that yet. I ignored it because why not? When I got to the overworld map the castle was destroyed. Since it was a beta I could go to any level I wanted. At that point I entered the final level off the beta because I wanted to see who was the final boss in the beta. The castle was like Bowser's final castle from Super Mario World but you had to go to every single door. You know the doors and the numbers. Top 1, 2, 3, 4, 5, 6. All of them. I lost many lives but when I actually got through all of them it teleported me to a dark room. In that room it was a door. I was big Mario and I couldn't enter it. Why? Part of it was in the ground. And I had to wait until the time ran out to try to enter through that door. When I finally got to that door again I was a small Mario. I was to a room which had multiple other doors. Every door was a boss door. When I entered one it teleported me to a specific boss. The bosses which are behind the doors are the final version of the Super Mario World bosses and mini bosses. I figured out that the programmers and testers tested how these bosses work and if they work. Now there was one extra door which was weird. It was for small Mario in the ground again. I had to die again. Anyways, when I entered that door the boss was well let's just say not good. It was a glitchiness which used any textures it could find. After a lot of deaths and game overs I finally beat it. When I beat it a message popped up, congratulations you completed Super Mario World. After the message I got to the door, entered it, and it was the end screen, except it was only Mario and Princess Peach. I still own the cartridge to this day in my collection.


Okay, so now, yep, click the green one, hit conversions, and you know what, we have, yeah, the custom audience is already in there, so we're good with that. So let's just scroll down, and then let's just give our titles, give each one a name, so hit that drop down, and we'll just, we can simply put in retargeting, actually you know what, we'll put in, put in, yeah, put in the name of the list, and then just put conversions, or you know what, I'm so sorry, we'll do that on the ad set level, we'll do that on the second step, but this one, the ad, the name of the video, I should say the name of the video, yeah, so this is always the name of the video, and then in parentheses, you'll put conversions, perfect, and then the ad set, that's where we'll put, you can either put the name, you can, you could put retargeting, and then the list, retargeting, and then whatever that, whatever you want to name that list, purchase, or don't want to say bought, purchased, and I don't know what to put in the list, what's the name of the list, just put retargeting $85 list, like whatever, like you could just put title list, retargeting title list, perfect, and then the ad just same as the top, when will this create the seller's market and video, you know, you could just put that, you don't have to put conversions, you could just put video, when will this crazy seller's market and video, perfect, and that's it, and then continue, no, whatever, whatever, whatever makes it easier for you to just look at it and know what that is, you know, so hit continue, and then good, so now we'll just come back over here, and choose the drop down for special ad category, and then you're going with housing, and that's it, so housing, and then we'll scroll down, and we'll always make sure the CBO, the campaign budget optimization is off, which it is, and then we'll just hit next, okay, cool, and that's it, that's step one, so now step two, we're going to come over here, and your pixel is right there, so we'll scroll down, we'll make sure that our custom conversion is chosen, so go ahead and choose an event, that's where your custom conversion goes, so you'll click, you'll see your FSBO leads, that's your custom conversion, click on that, and then we'll scroll down, and then off, off, and then the budget, just go ahead and go with $10 a day, and just go, yeah, just go daily budget, that's fine, and then start date, go ahead and start it, yeah, let's start it, let's start it on, on, started on Tuesday, I would start it on Tuesday, started on Tuesday, and then you'll go ahead and just go 4 a.m., and then just go and, yeah, stretch it out 7 days, that should be here, yeah, perfect, all this stuff keep popping up, man, it's real distracting, yeah, I know, Facebook, crazy, so right there, custom audiences, go ahead and click in there, and you'll see that custom audience, I'll see what, oh, this is it right here, yep, there we go, that's the list, the customer list, yep, okay, good, and then what you'll do is, you'll always want to exclude FSBO leads, even if there's just one lead in there, like just always excluded, just get in the habit of excluding that list, yeah, that one, yeah, perfect, cool, okay, we're good, okay, so now we'll just click out of there and then we'll scroll down in locations, go ahead and just type in, type in Oklahoma City, people living in this location, yeah, go with people living in this location, and then just X out of the United States and then put in your city, perfect, okay, cool, okay, scroll down and then don't need age, gender, and you know what, here's what we're gonna do, we're gonna, on the, let's see, we're retargeting an audience, but at the same time, we do want to, we do want to narrow it, narrow it in with the detailed targeting, so that detailed targeting, go ahead and click edit, and we're gonna, we're gonna simply add, go ahead and click in there, home improvement, home improvement, so anyone who has shown any interest or any activity on any type of website regarding home improvement, we want that keyword in there, and then we want to click out, give it to that dropdown, so just click away, and then we're gonna narrow the audience, we're gonna narrow it, and we're gonna go, we're gonna, we're gonna click in there, and we're gonna go with renovation, so home improvement and renovation, perfect, so we'll go with those two, those two keywords, so scroll down, how big was that list, do you remember, how many, how many records on it, 1500 I believe, something like that, approximate, okay, so why don't we take out those words then, let's just take, let's take out, let's, we don't need to narrow anything then, if the list is that, because it's not the biggest list, so we don't want to narrow it in any further, so let's just leave them out, we'll leave those words out, okay cool, languages, you can, you can make that English, and then what we're gonna do is we're gonna for sure go manual placement, manual placement, so we'll get rid of automatic, just click on manual, and we're going to simply uncheck Instagram, messenger, audience, network, and then we're gonna, we're gonna leave the first one, which is the newsfeed, and we're gonna pretty much uncheck everything else, you know what, leave, leave marketplace, go ahead and leave marketplace, but uncheck, yeah, uncheck everything else, so the group feed, everything else, Facebook stories, in-stream, all that, uncheck all that, keep going, keep going, that way our $10 per day is really focused on just that newsfeed, because that's where all the attention is anyways, and the marketplace, that's for people that are kind of looking and searching for things to buy, or they're in the, they're in the buying mindset, so it's always good to keep it in the marketplace as well, so scroll down, and we're good there, so now that's it, so now we're gonna hit next, and that's step two, so that's the ad set level, so now we're on this third step, and all we're gonna do is just make sure that that's our page, scroll down to add setup, and we're gonna simply click on the drop-down, and go with use existing post, yep, and then select post, perfect, and then bidding wars, perfect, okay, cool, continue, and then we're gonna simply grab the link to your cartridge page, to your landing page, and that's where we'll put it in over here, so let's grab that link real quick, all we'll do is scroll down, and then we're gonna add button, perfect, okay, cool, and then you'll scroll down, and you'll always make sure that this box is checked, website events, sometimes it's checked, sometimes it's not, so you'll always want to make sure that's checked, because that shows your pixel, that's the pixel we're rocking with, and then the default offline one, and that's it, and then we hit publish, and then you can always, you know, take a look at it in the newsfeed, once it publishes, you can just take a quick, I love that color, that color just stands out, that yellow. Thank you. You got that look, D, I mean, I'm telling you, like, when you can just focus in on an area, like we're focusing in on 15 miles, like people in that area, they keep seeing you, like leads that are coming in, that's one thing, but as I mentioned before, the value and the overall branding that you're actually creating on the back end, which we can't even calculate, because I don't even know how to calculate that, just the exposure, right, just the exposure, that's priceless, like I really believe more people in that area know you than you know, than you can imagine, like most people do, like there's so many people that are seeing this right here, that aren't clicking on it, but they're seeing you, they keep seeing you, and there's value in that, you know, so, and that's one huge reason why I believe, well, actually, no, I don't actually, let me rephrase that. Some people think this way, some people, some people don't, some people just foolishly throw out money at this type of a marketing strategy. And what I'm referring to is a billboard, like a billboard, like I, like down here in my area of San Diego, I was driving, I was driving to go get something to eat just a couple of days ago, and I see a real estate agent's face on a billboard, right? This guy, this, this guy named, I don't even want to say his name. I don't even know him, but, but his face was on a billboard. And, and I already know there's not, there's not much ROI on that. I know that for a fact, like, and he spent a shitload. Anyone that put their face on a billboard spent some money. Like I'm talking like 20, 30 grand to put their face because it's a contract. You don't just put your face on one billboard. They give it to you for a few months and it's a good amount of money. And I'm looking at this billboard and I'm like, damn, I know he ain't capturing a ton of leads from that. Like I already know it, but the exposure that this guy is getting is priceless because now I see that guy's and it's on a busy inters, it's on a busy street. So although people, thousands and thousands of people are driving by it every day, although they're not necessarily picking up their phone and calling him, they see his face and that right there to a lot of us is worth it. You know, and that's why how I look at these videos. I'm like, OK, if a ton of leads ain't coming in just yet, the fact that thousands of people are seeing you in that yellow blouse, that yellow shirt like that, that's priceless. Like people are seeing you and they're getting familiar with your face and you don't even know that. You know what I mean? Like there's value to that. You know, so. So keep keep wearing things like that, like bright colors that stand out. Like that's a good look and and people people gravitate and they remember that. Oh, that really means a lot. You know, it's funny I'm a hit on two points. One is I just did a a coaching call and he was referring to direct mail. He was like, always use a yellow background. I don't know what it is, but something about a yellow background with black text or blue text just works. Can't explain it, psychological thing, but it works. And I really had not had that coaching moment in, you know, until after I had already recorded this video with the blouse on. And then, too, I want to say thank you because my comfort is black.  Would you start wearing like purple and pink and green? So, you know, I really I just want to say thank you because, you know, I don't always need validation, but in this case, because I'm so outside of what I would typically do to attract new business or to, you know, take up market share in my market. I could use that kind of confirmation that, hey, you know, this this this this one's popping. Yes, it looks really good. Watch, look at it in the newsfeed. Look at look at how it looks in the newsfeed. Click on edit right below the title. I'm about to edit, right? Yep. It's always on the third tab. So on the third tab, that's where you click on edit. And then you can hit that drop down in the in the right corner of it. So right above, yeah, right in the up. Yeah, that one. Click on that one and then just go to Facebook desktop newsfeed and and look at how it pops in the newsfeed. And again, this is this is why we we went manual manual placement. We unchecked everything else so all the budget can go right here in the newsfeed. So as people are scrolling through, they just see that yellow and it just it just sticks out. You know, so I love that. I love that. Click on learn more, go in and test that button. Yeah, bam, there it is. There's a shot right there. Oh, that's a money shot. You got it. So let this one Rock D and then let's chat. This one's set to go live on on Tuesday, right? Tuesday, on the 28th, 20 percent, I forget, 29. Yeah. So let that one, let that one, let that one go and then let's chat. When do you want to chat? Let's chat. Let's let's review this one on on. Let's see, it's going to go Tuesday. Let's let's let's chat. Well, let's chat. Let's chat next Thursday. Let's chat next Friday. Let's chat next Friday the second. OK, that's cool. Yeah, because we're we're we're I can't speak. We are reviewing the traffic. And remember, we have that one running consecutive, too. Well, not really consecutive, but it's going to be extended it until. Monday, I believe. So yeah, Friday, Friday is a good brief, and then I'll have another video up so we can decide what we go from there. If we want to extend something or run a new one. Sounds good. Do you think the same time Friday? Yeah, of course, for me, let's do it. Let's do it.