Now, when we are looking for solutions, now that we know at least one solution exists, the way we look for solutions is the following. We can talk of many different types of solutions. The first kind of solution is what is called a local minimum.   So, the way, what is going on here is the following. Let us look at, let us plot, take an example. So, suppose my domain is like this, it is this interval here and maybe also and this interval here. So, this is my domain, the feasible region is this, this blue line here and suppose my function looks something like this. Now, what is the local minimum here? So, S is this and this and what I have plotted here is my function F. So, you can see in this picture, actually there are two local minimum. One is this point here and the other is this point here. This point is not a local minimum. Why is that local minimum? It is infeasible. So, at the very beginning, local minimum the way I have defined it is an X star in S. So, it has to at least be feasible. So, this point is an infeasible point. So, it cannot qualify to be a local minimum. This point is feasible and moreover, if I see that look, zoom in and see into a small region around it, the way the function looks is that it has its least value at that point. Likewise, this point is also a local minimum around this, if I search, the function has its least value over there. That does not mean that the function cannot have a lower value elsewhere. That is a completely separate matter. So, let me give you another example. Just a similar sort of region. Let us take S as this and this and suppose I consider a function like this. This is my function. This is my set S. So, now can someone tell me where, what is my local minimum? So, this rightmost point that you have is, this is the local minimum. Let me draw the function more completely. So, function keeps decreasing for that. So, why is this rightmost point a local minimum? So, if you look at this, if you look at the function on the entire region, entire ambient space, which is on R, then of course the function decreases for that. But when we are talking of local minimum, we are comparing only with points that are in S, not points that are outside S. There may be points outside S that may be better than points inside S. That is not of relevance to us. So, if you look at this point, this point is such that, now if I take a small neighbourhood around this, a small ball around this and intersect that ball with S, what I am left with is only this part, only this part. And in this part, it is the least, least part. This point gives you, the right end point gives you the least possible value. Any other local minimum? What is the other local minimum? So, if I take the right end point of the left segment, again around this I can draw a ball like this. The ball intersects only this part and in this part, this is the least. It is not at all relevant to the optimization problem that the function has further decreased here and so on. All of that is not relevant because after all we are comparing only with points in S. Is this clear? The notion, the notion of solution that I mentioned earlier in the first class is what can be better class, this is more, a better name for it is what is called a global minimum.  It is true. So, what the question here is that, so you are referring I think to the right end point of the first segment of the left segment. Yes, so if I take a radius R that is very large, then what is going to happen is say for example, if I take a radius large enough to include all of this suppose, a very large segment, a large radius, then that also you will include also this point. And so consequently, this will not be the minimum in such a large ball and this is usually the case. If you make this region larger, you will start discovering points, you will have a, you will be comparing with a larger set of points. So, consequently or it is possible that you will find a even better point than the one you started. But a local minimum, the definition is there should be some neighborhood, however small, some neighborhood of positive radius in which it is the best. So, for me to show that this is a local minimum, all I have to do is demonstrate for you one neighborhood. It did not work for all neighborhood. So, a global minimum is defined in this way. So, now come back to our two examples, can you point out what the global, can you point out in these two cases what is the global minimum? So, let us start with this one, where is the global minimum here? So, it is unfortunately my drawing is not that good. So, let us assume this one is lower than this one. What is the global minimum? Yeah, it is this point here. So, this one here, this is the global minimum of the function. Is the global minimum attained in the set? Yes, global minimum is attained in the set. In fact, this is you can see the interval, these are two closed intervals, their union that is a compact that is a closed and bounded set and the way I have drawn the function, the function is continuous. So, the global minimum is attained in this. Now, global does not mean what is the minimum of the function without the feasible region means the minimum of the function which over both feasible and infeasible point that is not what global means. For that there is a different name that is what is called an unconstrained minimum. So, I will just unconstrained minimum is simply some x star in Rn that is this is a completely separate concept. So, the unconstrained minimum need not even be a feasible point. The unconstrained minimum may not even be finite because you are now looking for the function, how the function for the function even outside the feasible point. It may even be that the function is not defined on the full region. So, all sorts of things can happen once you search outside the constraint but assuming it is finite and finite this is what it is referred to as. This is the definition. So, let us come back to the thing that I was mentioning. So, you have a global I was talking of global minimum. So, what is the global minimum in the first case you pointed out it is this particular thing here. What is the global minimum in the second the right end point the right end point of the second segment here that is your global that is your global minimum. What is the unconstrained minimum in each of these cases in the first case in the this particular point here this point here this is the unconstrained minimum and what is the unconstrained minimum here it is not attained the the the the unconstrained infimum the value of the function is 0 if it keeps going this way it will be 0 it is but it may not be it is not necessarily attained.  Now, even when Weister's theorem is not satisfied you may have that the local a local minimum can be attained and that that is very much possible. So, even though you may not a global minimum is not attained you may be able to find local minimum that are now let me cover strict local minimum.  So, if you compare with every point X that lies both in the ball and in S except for the point case where X is equal to X star itself then you will find that f of X star has a value strictly less than f of X in that case you say that X star is a strict local minimum. So, again let us go through this example in both of these in example in both these cases that we have drawn let us look at the two local minima that we had are this let us check are they strict. So, if this one is it strict this local minimum this local minimum is strict it is the way I have drawn it it is strict you can find it is you can find the ball small enough. This one also there is a curve here if you look closely enough this one is also strict what about this one this particular one this is also strict likewise this is also strict. So, these are all strict local minimum. So, what does a non strict local minimum look like? So, what must happen is that something like this. So, all these points they have the same function value take a you take this point you take this point you take this point around them you can you choose a neighborhood there will always be another point there is always another point that has the same that has the same value. This is one way in which this is one way in which you can you have a minimum that is local but not strict. So, there is a very closely related notion I will write that now which is called an isolated minimum isolated or precisely local minimum isolated local minimum x star in s x star in s is said to be an isolated local minimum if there exists an r greater than 0 such that x star is the only local minimum in B of x star, r intersection. So, an isolated local minimum is one where in which you can find a small radius around that point such that in that radius there is no other local minimum. So, now can someone tell me how is this related to being a strict minimum a strict local minimum. So, clearly a local mean an isolated local minimum to begin with has to be a local minimum does it have to be strict or is strict look the same as I implies isolated or isolated implies strict. So, the answer is isolated actually implies strict and the reason to see this is the following. So, when is the minimum isolated it is isolated when in its neighborhood there is no other local minimum. Now, suppose if it was not a strict local minimum if you have a local isolated local minimum that is not a strict local minimum then in that case what would happen? So, let us do this carefully. So, x star so suppose the answer is I am good to argue that isolated every isolated local minimum is a strict local minimum this is what we are arguing. So, why is this the case? So, let x star be an isolated local minimum and suppose x star is not a strict local minimum suppose x star is not if x star is not strict then what does that mean go back to the definition if it is not strict that means that there must be then it is just a routine local minimum and what does that mean that means that so it was a it is a local minimum means that there exists an r greater than 0 such that f of x star is less than equal to f of x for all x in this neighborhood. Now, if it and it is if it is strict then there exists an r greater than 0 such that f of x star is strictly less than f of x for all x except for x star and in this neighborhood right. So, if it is not strict then it must be that in this in this inequality here equality must be attained for some point and this must be true for every radius r no matter how small you make the radius you should continue to get a point which is all in that in that ball and in that lies in that ball and in such that there is equality here right. So, what does this mean for all this means that for all r greater than 0 there exists an x in in this which is not equal to x star such that f of x star is equal to it. So, now let us let us take some some radius r also in that radius r let us see what is going on here is your point x star in this and here is my so here is my so suppose so I am just zoomed into point x star and this is the so this ball does not look like a ball. So, this is my point x star this is my radius r around it and so suppose here is my set s and so for every radius r I can find a point x such that f of x star is equal to f of x a point x in this ball right. So, here is suppose a point x that point x now this point x has the value of f at this point x is equal to the value of f at x star now what can I do f of x star is certainly as lower less than value less than equal to all of these everything in this radius. So, what does this mean this means that so everyone is following me here see remember x star is a local minimum. So, there is certainly a small enough radius in which it is the it is the look it is the it is it is it is its function value is less than the function value of all other point. Now in every radius around x x star also there is another point whose function value is whose function value matches with that of f at x star. So, which means that if I take if I take a small enough radius then in that radius x star is both a local minimum and there is another point which matches whose value is the same as that of same as that of x star. So, what does this mean now around this other point now I can draw another small ball. So, what what can I that that that small ball is going to be that small ball is going to be inside this this particular ball right. So, all these points their value is going to be is already less than equal is greater than equal to f of x star but f of x star is the same as f of x. So, f of x is going to be less than equal to the value of all of these small all of these small which would make x a local minimum right. So, if x star is not isolated this these new points that you keep finding they themselves become local minimum for small enough radius. So, what this means is this would imply that x for small enough r.  What this means is that x star is not isolated. So, x star cannot be isolated. So, if it is isolated if it is isolated and not strict we get to a contradiction that it is not isolated to begin with. So, it has to therefore be it has to therefore be strict okay. So, every isolated minimum local minimum is also a strict local minimum. The converse is not true. So, every isolated local minimum is a strict local minimum that is what we just argued. So, every strict local minimum need not isolated. Here is an example of a function like this that demonstrates this. So, I encourage you to go and plot this when you go back to your go back home you can plot this at in MATLAB or something. So, to consider this function f of x equal x to the 4 cosine of 1 by x plus 2 x to the 4 and let us take this in say minus 1 to 1 except 0 at 0 you define f of 0 as 0. So, what you will find when you plot this is that this function has many, many undulation as you go around 0 as you go closer and closer to 0. But of course, the least possible value is at 0 but you have many, many, many, many undulations as you go closer to 0. So, what will happen is that 0 is a strict local minimum but in its neighborhood are many, many other local minimum. So, in every neighborhood there is another local minimum. So, it goes like this at 0 but then something like this. So, there are many oscillations all happening at higher and higher frequency as you go here. So, this is at 0 and then in every neighborhood I have zoomed into this but if you go for no matter how much you zoom in you will keep finding another local minimum. So, it will be this local minimum, this local minimum, this local minimum etcetera.


I pledge allegiance to the flag of the United States of America and to the Republic for which it stands, one nation and justice for all. Will the members please come to order and will the members of the audience please remain seated during the briefing. United States Congressman Bob Stump and Supervisor Holly Atkinson. Good morning. I am the duty officer for this morning's patrol and the following procedures will be in effect during the patrol. Item 1. FCCs will be given in the miracle sequence, starting with Division 1 and continuing until all units have responded. Item 2. One unit only on a 1040. Item 3. When making a vacation watch check, be sure that all doors and windows of the houses are locked. If you find the window or door unlocked, use the standard operational procedures for this problem. If you find evidence of forced entry, do not enter the house. Call me and I will request that a deputy be sent to your location. Secure the outside of the house, permit no entry other than authorized personnel. Item 4. Give me the details and we will decide what is the best method to solve the problem and act accordingly. I have received Pontiac Bonneville, four-door sedan, California license plate, license number at this time is unknown. White vinyl roof, 5 foot 8 inches, 150 pounds, 18 to 20 years of age, dark hair wears in the handcuffing of a subject. Thus qualified to receive this specialized training. In this instance, Sergeant Rose will be my subject, but if you will visualize this table as a hood of a patrol unit, I will conduct the suspect to the patrol unit, ordering him to place his hands on the hood of the car, spreading his arms out, and spreading eagle. Any time the arresting officer has a suspect, he places himself in a defensive position. In one of the positions is this. I am placing my foot inside of his foot near his ankle area. If this suspect should in any way resist an inspection or a search, I am in a position to trip him very easily. You would naturally fall to the ground being off balance. And there are several methods of which then would be employed in handcuffing. At this point, I have no assurance that this suspect does not have concealed weapons or concealed items. Therefore, I will search this suspect by a search known as a PAT search. I will check his neck area, his shoulder area, under his arm, down his arm, this chest area, paying particular attention to the belt and midsection, where it is not uncommon to find concealed weapons. I will then fall down his legs and again in the ankle area is very vulnerable. You may think that I am in a very vulnerable position at this point, but actually, if you visualize, I can very easily pull his leg out from under him, therefore, throwing him off balance and again he will be on the floor. At this point, I have assured myself that on this side of his body, there are no concealed weapons. I will immediately transfer my position, the same defense position, and I will again search this side of his body, the neck area, the arm area, under his arm, his arm, and again the vulnerable spots, under his belt and so forth. Also on his leg area. At this point, I have assured myself that this suspect does not have concealed weapons or concealed items. Therefore, I am now in position to handcuff the suspect. By doing this, I would take one arm, placing it towards back, holding his wrist in an outward position, placing the handcuff on, and I would do the same with the opposite. Again, noticing that the hand is... Thus, this suspect is now in custody and in order of procedure with that, placing it in a patrol car and ready for transport. That concludes this portion of the briefing. Sheriff Jerry Hill will make an introduction. Sheriff, good morning, ladies and gentlemen, fellow volunteer law enforcement people with the Sheriff's Office. It is my pleasure this morning to have with us a very special guest who has come here to review our volunteer programs in law enforcement. At this point in time, it is indeed an honor for me to introduce to you the President of the United States of America, Ronald Reagan. Mr. President, thank you very much.  Someone told me about the Sun City Posse's theme song and I'd like to read a few lines of it because it really does capture the attitude here. So, turn on those network cameras because maybe a lot of these people already know it. It's for you I'm saying this. When we're called, we want you to know that the Sun City Posse is rare and to go. We may be gray, but we still got the stuff to do the job when the going is rough. I know that the residents here are very grateful that you are out there on the streets keeping the crime rate low. And I've just had an demonstration from the Sheriff on that also and some figures that show that probably this is the lowest crime rate spot in the United States. I think that the people are grateful that you've made Sun City a safer and more reassuring place to live. And of course all this is a volunteer effort which makes it even more admirable. America's citizens are more involved today in the safety of their communities than they've been since the days when it was a necessity for us to look after each other. And you are following in that tradition. You are willing to avail yourself or give of yourselves to help others. And that truly is the volunteer spirit which is another way of saying that's the American spirit. We all know how frightening crime is to the old and the young. Yet older Americans also require protection from other aspects of modern life. Remember the terrifying bully called inflation that ate away at pensions and savings and that was a form of robbery also. Inflation was running in double digits in 1980. And right now it's running at just about for the last six months less than one half of 1%. And it showed its first actual decline below zero level. And a quarter declined it just recently in nearly 25 years. And just a few short years ago, who would have thought? And certainly no one was saying that we could ever return to the low inflation of the 1950s and the 60s. Well this morning, just before we're coming here, I got some figures that are going to be made public and released today probably already have in the east. And that is the figures on the other part of this recession that is the one that bothers all of us the most unemployment. Now I have to confess to you, there are things about the unemployment statistics that still baffle me. Because they say there's no change in the unemployment percentage rate. But there are 250,000 more people working in April than we're working the month before. And since December there have been 650,000 added to the list of those employed. The recent amendments to the Social Security Act are another way that we're protecting older Americans. This legislation guarantees social security will provide a secure and a stable base so that the retired can live in dignity. It assures them that America will keep the promises made in troubled times a half a century ago. And it also protects those who are still working. Their basic human needs must be met with compassion as well as efficiency. This administration is dedicated to the kinds of programs and policies that will allow the vast majority of senior citizens, older Americans, to continue to live independent lives. This is not just a matter of economic common sense, it's a matter of basic human dignity. As the proclamation I'm about to sign states, the future of older Americans should be as sweet as the memories of our youth. I do believe the future of our elderly holds as much promise as the achievement of our past. I had to make a couple of changes in the notes here. The young lady who typed up my notes for me thought she was being tactful and had me referring to them as the elderly, well as them instead of us. And I had to change a few theirs to ours. But this month we're recognizing that potential by celebrating older Americans' month. That's what the proclamation is. And now I'm going to make it official by signing the proclamation. See these federal pens will only sign one word. Mr. President, thank you for honoring the Sheriff's Posse of Sun City so completely by coming out and signing the proclamation in our behalf here. At this time I understand that when you were in Sun City last, which was about 1976, you weren't eligible to become one of our members. With perseverance I made it. Well, I think you have made it in another way also. It's our pleasure as the members of the Sheriff's Posse of Sun City to have you as our honorary member. And to complete that partially, we have this hat. In addition, we have one of our intermediate yellow shirts with the emblems on. Now, if you are going out on patrol, there are certain things that you must know and must abide by. This book of rules and regulations contains it all. There's just one more thing. I'm sorry I couldn't get your ID card, but I must get clearance from the White House and from the FBI before I can get it. Well, now that I'm an honorary member of the patrol, I imagine that makes me duty officer for the day. So you're dismissed. Let's be careful out there. Under the salt of our being, some of the minority owners on the front block in front of this is an American who will not give the rights to the security of our home, the rights to the security of the ownership of our farm, the rights to the benefit of our own business. I salute President Jamiah and the leadership of Lebanon. And may I add a word or two on behalf of Secretary George Shultz and our ambassador Phil Huffby, whose tireless efforts and dedication to reason have done so much to make this possible. They walked into the old walls with some members of the F-Troop of the Texas Army. And when I saw those fellas were dressed and what they were packing, I didn't know whether to stretch out my hand and take a run forward through the rose garden. And as I said, we have a great respect for our farm. We shall prove to the citizens the right of the people to keep and bear on shall not be infringed. During the time when the state piracy was almost unusual, a certain time the San Juan prison had been cut off. And he said, that's the one that scares most of us. So he said, there'd be a lot of smiles in this place if you would adopt government. And as I said, in the U.S. prime, with a nationwide series of reported crime, about 4% in 1982 have arrived in more than one month. Long hours of sentences in perpetrator began to pay evidence. They almost did. We stand here then. I have been told there's something wrong in the United States. Attorney General Smith, I've got a record with him. I've shared with him that he's a very resourceful justice. Senator Smith ordered an action. And Congressman Hobe. I look forward to signing a bill. Curses. Carers first. 1980s general orders. And as of today, we'll study the game we're having. To provide food. And portions will go over to her safety and education sources. There are a number of people. Marsmanship. Higher arm safety. And some of the benefits of that is a conservative characteristic of what we do. Bringing our economy back to us. That's a crucial part of keeping our free land. 250,000 months of free land in 1980. The loan will be set. Security. And then they don't tend to have the extra activity. Inflation pushing them to higher and higher taxes. To make it possible for the payers. Strictly with this protection. Our tax drivers. You're in a sentence. A trillion dollar debt because of our taxes. We've got that debt because the government spends too much. We need spending restraint. Not tax increases. To set us as we cover it. And we work so hard to achieve. Mars began when we had this security line. To be prepared to war. It's one of the best means to preserve the peace. But the Soviets won't be martyring a good thing. If they understand we're determined to defend freedom. And I'm determined that they will understand it. There are a lot of foreign trade, petroleum, natural sealings in that region. And again we forget that the country like us south of ours is approximately 10 miles. Closer to the insurers on the finish of this war should be safe. But people like us south of it are not worth it. If they come in there. They have a merciless state. They can decide your destiny. And have a thing for their own risks. Only then will there be a society not dynamic and prosperous for the rest of the world. But outside of the war is under attack. The religious and despicable government faces a choice. The only thing we can do is help the world. Change the world. Excite us in some way or the most. Or will we turn our heads to our friend. But excited about our planet Earth. Rationalizing our hatch and de-hatch. But extra something. Only we can do it. We're going to have responsibility. More depression. And bring this up on the good hand of the United States.


Welcome back to the technology metal show. I'm Peter Clausi. As always, we're here with Jack Lifton, a critical metals supply chain expert. It kind of feels like forged in fire. It's Friday, October 30th. No Halloween tomorrow. And we are thrilled to have as our guest today, Mr. Waldo Perez, PhD from Neolithicum. Waldo, nice to meet you in what's passing for in person these days. Yes, thank you very much. Nice to meet you guys, Jack. I'm in St. Catharines, outside Niagara Falls, Ontario, Jackson, Michigan, outside Detroit. And I think you're down in Argentina, right? I am in Mendoza, Argentina, yes. Okay, so let's get right to it. I've been looking forward to this for a while. Neolithicum has a very advanced lithium project in Argentina. And just before we went to air, you were telling us about the plateau, 4,000 meters elevation, 60% of the world's salt brines for lithium are there. So tell us more about that, where your project is located. Well, when it comes to lithium, there are two places and two sources. The two places are South America, the Puna Plateau, which is Chile, Bolivia, Argentina, for brine resources. 60% of the lithium of the planet is located in an area that covers this plateau. It's about 4,000 meters elevation. It's about 4,000 kilometers in length. It's about 3,000 kilometers in width. And these are the solaris, right? These salt lakes are the solaris. Yeah, inside there you have solaris. And to be very clear, our objective here is to find a liquid, which is a hypersaline brine, that is trapped in rocks. And those rocks are mostly sodium chloride, but there is also sand and another type of porous rocks that trap this hypersaline liquid in close basing in the Puna Plateau. So this is actually what the exploration looks like. You explore for a liquid, not a solid, a liquid, okay? And you exploit a liquid that you actually extract using simply pumping technology. That is the same technology that you use in a farm, in a water well, or actually if you want to go a little bit of yon in an oil and gas. Jack, have you been on site to a solar? No. Me neither. So, but I, at one point in the early part of this century, I represented SQM in Detroit. Oh, interesting. Well, I will send you a few pictures, guys. And of course, please visit our website, Good website, Waldo, whoever designed it did good work for you. And actually, you will see plenty of pictures. It's a very dry area. There is literally no life, like quite literally.  I hadn't even thought of that. So it's not like some animal has evolved and adapted to be able to live in the solar. Yeah, some did, and they are bacteria basically. So the only living animal there is a bacteria. And by the way, scientists like to study those bacteria, because they think that they can mimic life out of the planet, like literally, like in Mars or in another. So they study those bacteria. And I guess it doesn't interfere with the mining of the lithium in any way. And they're pretty small. And just as a fun fact, they don't breathe oxygen. They actually live out of the exchange of salt with water. So they don't need oxygen to breathe. You know, I'm going to have to look that up later now. It's a fascinating topic. All right. So you said there's two places where they're found. One is in the water. Exactly. And the other is a rock. It's actually a mineral called spodumen. And that mineral is actually more common in the planet. Although the best spodumen in the world is found in Australia. So at the end of the day, there are two sources of lithium rocks, which is actually spodumen being mined in Australia, and brine, which is a liquid, which is being mined in Chile and Argentina. Okay. Now, from that, there is also something to consider that is not obvious to the general public. Spodumen can produce hydroxide. There are two final products for lithium. One is lithium hydroxide, and the other is lithium carbonate. So both are used in batteries. Lithium hydroxide are used with certain type of batteries, and carbonate is used in another type of battery. But one of them has a very short shelf life, right? It takes about 30 days, and then you have to use it or it deteriorates. Well, hydroxide is more subject to deterioration. So that's why you would see that most of the hydroxide is produced near the battery plants, just to make a definition. In Australia, people mined spodumen. They shipped the raw spodumen into China, and in China, the spodumen is processed and going into a battery. Now, of course, for the battery. This is Jack's area of expertise. Sorry, Waldo. Jack, I see you frowning a bit. I need to say something because I don't want our viewers to misunderstand. Here's an old man's story. My very first project as a chemical engineer will say was to find uses for lithium. I worked in a company, had a contract with a company called US Lithium, I think it was, and it was in North Carolina, and they were mining spodumen. In those days, we never heard of brine. So the viewing public has to understand that it's only in the last generation that brine has become... Waldo, is it the dominant source now of lithium, or is spodumen still ahead? Good question, Jack. This is what happened. North Carolina was the number one producer of lithium, and you probably know why it was used by the military to separate the lithium-6 isotope to build hydrogen bomb. And the problem was, and that's why probably you were hired to look for uses for lithium, is that only like 6% of the lithium isotope using the hydrogen bomb out of the total lithium is actually the right isotope.  I think the first standing bubbles, as you know, Waldo, it was around 1980 that I think Panasonic introduced the lithium ion battery. I think it was 1983, I think, Jack. Well, I can tell you this. My group made a... We made a battery based on lithium chemistry in 1962. And Lithium Corporation of America, I think it was called, not U.S. Lithium Corporation of America, they decided that was not a good path to follow. There was no point to it. I've always been the cuss of technology. So was North Carolina also the source of the lithium for the medical industry? Yeah, yeah. North Carolina was the main producer back then because it wasn't like... Again, it was an element that the Russians were looking for because of the Cold War to build the hydrogen bomb. The U.S. had that. But what happened is that the Cold War went over and then there was no major uses for lithium. But what happened then was the telescope that they can use in glass. And Pyrex found out that if you put it in glass and ceramics, you can actually microwave them or put it in the oven. And that was the major issue. The major use of lithium until the year 2006, 2007 was actually the ceramics industry. Get out of here. Yeah, yeah. So it's only in the last, shall I say, 10 years that the battery first made it to this, to the telephones. And after getting into the smart phones and so on, it becomes so ubiquitous and also the technology became so powerful that we didn't realize but we started to depend on lithium batteries. Like when you are using a drone, when you are using all those appliances, tools that they are always running out of lithium batteries, all of them, because among other things, lithium batteries don't have a memory. Do you remember the first cell phones that they would tell you that you have to plug it in, but then you needed to take the energy out?  And that's why, of course, that technology, nickel metalizer was totally useless. So let's talk battery configuration for a second. I was involved in the development of that battery. So in China, we have a company, BYD, who touts a formulation heavy on lithium with like 0.5% cobalt, but not a high energy density. Do they have any chance of expanding that? No, BYD, as you know, is one of the largest car makers in the world.  They develop in December 2015 a new LFP battery, which is basically a battery without cobalt, without nickel. That is about 50% of the cost of the other batteries, which are made of hydroxide, and has about 80% of the range and energy density. So it is a great, shall I say, technological achievement. And nowadays, the Tesla battery, CITL, by the way, it's our partner in our project. I want to come back to CITL. Yeah, of course. They actually also created a similar battery. So let me put it like that. This battery is the battery for the cheap cars. If you need to make a $25,000 car, Tesla built in China is an LFP battery. LFP battery means it's a carbonate battery. That means it was made with rhyme, basically. Now, instead, the other batteries, like the high-density battery that takes cobalt and nickel, they are done with hydroxide. And you could do it with some carbonate converting to hydroxide or from the supplement using the hydroxide directly. So any of the two. Jack? No, I was going to say, look, we're all getting a good education on this, but we're not talking about Neolithic and Waldo's Company, which I... Look it back to that because... No, because, you know, I like broader settings. There's thousands of companies out there, but how you fit in the universe matters. And Neolithic fits in the universe in one way through its relationship with cattle, which is a very large battery manufacturer in China. Now, as I understand it, they've actually made an equity investment into Neolithic and as a shareholder. That's a pretty strong endorsement. This is a very strong endorsement and we are one of the few companies that has a relationship with a very large battery manufacturer. This is actually validation money and they are going to sit in our board. So it is very important. Now, our project was selected by CATL for some very specific reasons. It's the highest grade project in the world. If you go to independent analysts, Roskill is the lowest CAPEX, lowest OPEX, the lowest operational cost and the lowest need for capital to build the mine in the entire world. So it's really a very important project. It fits in the universe as the number one undeveloped project for leaping. Typical content in leaping parts per million of your brine. In the first ten years, our grade will be over a thousand milligrams per liter. That is in the first ten years. We get brine up to 1400 milligrams per liter, but the average production for the first ten years is going to be over a thousand milligrams per liter. And after 35 years of production, we will still be around 790 milligrams per liter, which is higher than current producing mines. So the grade of these projects is higher grade than some producing mines, like corals and so on. For the technically-minded, the amended pre-feasibility study on the Quadrubratus project came out May 7, 2019 and is available at the website and lays out all of this technical data. Aftertax NPV 8% and a 50% IRR. Yeah, the IRR is amazing. It's actually difficult to find a mining project with an internal rate of return of 50%, with a payback of less than two years. And you may wonder, well, how come? How come the numbers are so good? And the answer is the following. A very low operational cost give us very large margins and a very low need for CAPEX to put this project in production, okay, allow us to repay our debt and be out there making money very soon. So this is the secret. In nature, these two aspects, low operational cost and low capital need are usually opposite. Usually, you need a big CAPEX to act on low operational cost and so on. So it's very rare. But this project is quite unique. This project is not like the other salars. By the way, since 2008... Hang on. You can't make a statement like that and run away from it. Why is this project unique? Well, there are obviously geological reasons behind that that we can go in. But again, the chemistry of this project is unique because of the grade. It's extremely high grade. And it has very low impurities. When I talk about impurities, I'm not talking about impurities of the final product, which at the end of the day, your final product is a manufactured product. I'm talking about the impurities in the ore. In the same way that, for example, if you are, just to say, in the gold business, arsenic is not good because it's toxic and you need to get rid of. So the higher the arsenic, the more problems you have in metallurgy. For iron, silica is bad. Except in Nevada where they love the arsenic. Well, okay. But then in zinc selenium is a bad word too. But in lithium, the bad words are magnesium and sulfate. Those two elements sequester the lithium from the brand and basically precipitates in a clay that basically is untreatable. In other words, you can't take the lithium out of it. And that for that reason, the lower the magnesium and the lower the sulfate, the easier the project is to be get in production. Well, our project happens to be the lowest sulfate and magnesium project in the world. Has lower contents of magnesium and sulfate that current producing mines. And that's why our operational cost is going to be lower than that. And that makes you unique. Go ahead, Jack. I've been hearing for years that the problem with Bolivian brines is that they're too high in magnesium. And yet these brines are all interconnected. Are they not in this region? No, no, no. They are not interconnected. No, no, no. Actually, they are exactly the opposite. They are all not connected. Think of them as glass. Think of them like you have a table one guy has a glass of coke. The other has a glass of wine. And the other has a glass of whiskey. They are not connected. And actually the chemistry of one is different. Now, what controls the chemistry of the solar? Well, think this is actually the lowest part of the plateau. The lowest elevation. So it's everything that's rolled into it. It's a catch basin. It's a catch basin.  It collects everything that is in that basin. So in your basin, for whichever geological reason you have more magnesium, you have more sulfites end up in the solar. In your basin, there is no such elements because the rocks around have very low content of that. Then you have a different content. So this is what's controlling the solar chemistry, the surrounding ground. So then I have a related unrelated question. Earlier today, Jack and I were talking about something called quantum space, which is a solid state battery research that's going into a SPAC in the United States. And their metric is one times cash flow in 2027. Any thoughts on solid state batteries? Well, they are the future. Solid state batteries is what's coming next. Now I don't know how long it will take, but this is what's coming next. And only solid state batteries like an airplane to fly. And that is going to be the next thing, the revolution. Now we're talking, look, in 2008, 2009, we were talking about the revolution of batteries for this, for phones, for laptops, because everything was a lithium battery. Now in 2020, we are talking on the revolution of lithium for cars because cars are going to be dominantly electric. And in 10 years from now, 2030, 35, I hope to be retired, but we will be talking about the lithium in airplanes and those are going to be solid state batteries for sure. Let me break up the love test by asking you a question you may not want to ask. Have you determined or has your new investor mentioned what they would like from you? The market for battery electric vehicles, no matter what we like to sugar coat it in the West, is not growing that fast. It's still a minor thing. It really is. I'm in Detroit and I can tell you that the number of battery electric vehicles sold in this country in the last year is maybe 3-4% of the number of internal combustion engines. Okay, it doesn't matter what you think about the future. We buy our groceries with money we make now. Okay, so my question is, China is way ahead of the world in this. It's my understanding that the next five-year plan, I believe it's the 14th, which will be issued in just a few days, is going to mandate 20% or more of all cars sold in China in 2025 be BEVs, which means China will then be the largest market in the world for lithium-ion batteries for vehicles. Now, what percentage of what you're going to produce do you plan to sell in China versus the rest of the world? I'm just asking because I think it's a regional market, a regional market. Okay, two points about your statement. Yes, China is going to be number one and Europe is going to be number two. 160 vehicles next year are going to be sold electric and the penetration in some countries like Norway is actually 70% today. I understand that. Remember, I've been to USA. We're always on top. We sometimes have to flip the chart, okay? No, that's true. However, the state of California, for example, in the U.S., have put very stringent lots for CO2 emissions. So I agree that today we are in 3%, 4%. I personally agree with Roskill prediction that they say that the market is going to be 30% electric. That is 30% of the vehicles of the world are going to be electric by 2030. So when they say vehicles, do they mean cars, motorcycles, trucks, 18-wheelers, or only cars? Well, I appreciate Roskill and all that, but they are just analysts. They use a pencil. You are actually in the business on the ground. What is your opinion of the penetration of lithium-ion batteries, BEVs into the marketplace in the next 10 years? What I was trying to tell you, just to finish my sentence, is Roskill is saying that the penetration of electric cars in 2030 is going to be 30%. Elon Musk is saying that it's going to be doable that just following the ThetaWatt factory he plans to build in the U.S. So I fully agree that the final number is uncertain. It's very clear that the number is growing, and I have been in this business, lithium, I mean for over 10 years, 12 years, 13 years now, and I have seen the growth of the industry. I have seen, and I discover, as I say, lithium America's Kauchari project. I was the founder of that company, and now that company is in construction. I have seen a recovery go from discovery to construction now. So the industry is clearly maturing. Very clearly it is growing, and today, and this is very important, today the market is in equilibrium. So right now supply and demand are there, prices depending technical or battery grade are around 7,000 to 10,000. But let me tell you something. In one month in China, the prices of lithium increased 17%. That is no minor point. And this is important for the small investor to know, because this is coming, and because this is coming, CATL come and does the business with us. Otherwise, what a $60 billion Chinese company want to do having a board of directors in a company like us, which has a $100 million market cap? Which brings me to my next question, Waldo. When are you in production? Yeah, we are scheduled to be in production having finance next year in the year 2022. So at the end of 2022, if we finance next year, we should be at the end of 2022, that is 2022, 2023, we should be in production, okay? Of course, we still need to complete our deal with CATL. We are just to have a clear view of what's ahead of us. In the next six months, we will complete our feasibility study. As I say, we do it in conjunction with CATL to have a certification of the final product, which is going to be battery-graded in carbonate that they can take. And with that, we basically construct construction. So we can start construction next year. And with that, it takes two years to build the mine and basically start production. Okay, Jack? Is there any thought of building batteries in Argentina? No, look, just as a business for us. Honestly, I don't know CATL. CATL have their own plans. Sorry. Just generally. I don't mean your company. I mean, is there any movement in, I'll say this, in South America to have a domestic battery-powered electric vehicle industry. Total domestic. Today, BYD is building electric buses in Argentina. That's actually the largest hub for electric buses. Right now, they are importing the batteries, but this is very important. And in Brazil also, there is a plan for a plant to start battery. Let me tell you something. South America has a very strong automotive industry. Very strong. As a matter of fact, Argentina builds almost a million cars a year and Brazil like 6 million cars a year. So it's big. Let me make a point. I spent many years as an automotive supplier visiting auto plants in Brazil, in Argentina. I'm aware of what you're... The largest Ford plant I ever saw in my life was in Sao Paulo. Oh, yeah. So you needed a bus to get from one part to another. And the question is, it seems to me it would make sense for somebody to vertically integrate. You have the... You have the scientists and engineers. You have the demand. So I assume... Look, to be an internationalist, I assume the Chinese will do this and that they're already underway. And I also... Wouldn't it be just to buy one and build one? I'm sorry. These are just to buy, then build. Rather than vertically integrate yourself, have the different industries and then have one consolidator. Thinking is that maybe CATL is thinking they could make batteries in Argentina. They'll have a supplier locked up of lithium. And there's a big market down there. Yeah. I think that eventually, to be clear, we don't have discussions like that. And very clearly, CATL is a battery business and we are not into the battery business. So it's their business. But we will be an important supplier. And something very, very important for us is to consider that CATL, a $60 billion company, has set aside a $2 billion fund to... Would they call improve the supply chain of the raw material. And within that $2 billion fund, a very small portion of that is us. And this is very important. They recognize that this supply chain, shall I say, need to be improved. And think about this. CATL has doubled battery production for five years in a row. Every year, they double production. This is an amazing achievement. This, I think you need to go back in industry. You need to get back to Henry Ford to see something like that. Doubling production every year for five years in a row. That means that they are doubling the lithium consumption too. And this is when it comes for us. Believe me, no automotive company, no battery maker want to be in mining. They are different business. Let's get it clear. When a car manufacturer needs copper, they don't buy a copper mine. They don't need to do that. They just go to the market and get the best. But they recognize, they know very well that every now and then there is some critical element. That's why these are called critical elements. That they require to be in production. And they also need to be in specs. It's not only to be in production, production and in specs for them to be able to produce what they need to produce. And that is when this sound works very well. So Crystal Ball looking forward, Waldo. What's the next big piece of news coming out of Neolithio? Well, look, the next thing that is going to come up very soon is that we close our deal with CATL. What I mean by closing is that we already signed all the paper. But the Chinese government has to provide the approval which is a standard procedure. This is going to happen imminently. It's a matter of very short time. So with that they will incorporate the board member and we will consolidate we are already working of course. We will consolidate the technical team and that technical team will actually go ahead with producing the definitive feasibility study. There's going to be also information about the size that we will produce because our project is planned to produce 20,000 tons of lithium carbonate per year. But our resource, our reserve can sustain that for 35 years. So we could also increase the size of the project and we will also be updating our resource reserve estimation because there are resources and reserves that were not included in the previous estimation that was published last year. So all that is coming together during the next six months along with the final environmental permit sorry which is construction permit. So the construction permit comes along with the financing from the from the authorities of the province. So all that is going to be happening in the next six months. And again with a very important wind tail tail wind you say. Because the lithium prices are increasing significantly and remember the last time lithium prices increases it went into a frenzy of lithium and right now we are in the front runner into this race with a very strong financial partner with a pre-feasibility finish that proved that is the best project in the world for development and then the final feasibility coming along with our financial partner. So we are going to be the next new lithium producers there is no questions about that. If you were to be producing lithium in 2022 and prices do not go up will you be profitable? Hang on, rephrase the question profits is accounting with G&A and allocations will you be cash flow positive? Yes, okay. Let's put it like that and I will be selling today at the great $10,000 at home. So I am extremely profitable today as a matter of fact I can even play the game shall I be too much to lower prices and send the others to market actually. The price that SQM is producing in neighboring Chile they sell in Europe their product somewhere around $9,500 Oh, for them they don't publish but they are quoted they are quoted to be by again analysts around $3,200 so similar to ours You will be comparable to today's lowest cost producer is what I am saying or even better. They are today's lowest cost volume producer of lithium you are saying you will be at least that good maybe better. Exactly that's exactly what I am saying and by the way we have less taxes than they have they have a very severe taxation in Chile and we have a much easier taxation in Argentina so from the pure cost we are going to be similar and I am hoping a little bit but it is irrelevant a little bit doesn't matter so it is really rounding error but from taxation it is a significant difference it is much cheaper in Argentina Alright guys, final thoughts we have been doing this for about 40 minutes I have learned a lot and it has been fun I haven't had to wear my mask I picked up a mask that reads it is going to be okay and it is going to be okay someday we will all be in the same room Of course, we have not done speaking extemporaneously for an hour and a quarter, 10 miles from here so the air in my area is quite warm Well gentlemen it has been great speaking to both of you I did learn a lot I do think from my perspective that Neolithicum is undervalued in the market and it is a story that needs to be told loudly and broadly so Waldo, congratulations this is just the latest in a long string of achievements in the mining world I look forward to you getting thumped into the mining hall of fame someday Thank you Jack I really appreciate this opportunity to get to people visit our website Neolithicum.ca there is a lot more information there we are in all the media too we want to see how you are progressing Absolutely I will be here Thank you very much