Okay. Welcome to the talk. If you're coming in, please close the door behind you. Please give a warm applause to Magnus. He's going to talk about high-dimensional 4D geometry and fractals, which are used in electric sheep and for other exciting pictures. All right. Hello, everyone. So, as you might have seen in the abstract, this talk will be split into three distinct sections. The thing about the topic is that it's extremely wide. I could probably fill a lecture for the whole week, but we're not going to do that. So, I am going to assume you roughly know how to do perspective protectors in 3D. If you don't, you might as well believe me. That will be good, too. So, for the 4D part, I'm going to throw some formulas in there and how to do that. Then I'm going to talk about some iterated function systems and how they generally work. In particular, after that, I'm going to talk about fractal flames, which are a special kind of iterated function system. So, the twist we're going to do here is that for the iterated function system and for fractal flames, we're going to talk about how to do those in 4D. Now, when I say 4D and higher-dimensional, I mean R to the power of 4 and higher. So, it's not about higher-dimensional stuff as you would have it in overfields of maths. It's more condensed into something specific. All right. And there's going to be some intermission slides where I showcase some demo program. I got, like, with Cheezus URL possible. So, you can follow that along in your browser if you feel like it. And let's get started. So, when I said, when I have 3 parts, I am going to tell you what I'm skipping. So, this is a cube. We've all seen a cube. So, the stuff I'm skipping, because we don't have enough time, is how to do vector and matrix products, which is the basis for most of the linear algebra stuff you've heard of. I'm going to skip across product in 3D. I'm going to assume you roughly know what homogenous coordinates are. If you don't, it's basically at another coordinate and you have a scale. I'm going to assume you trust me on rotations. You basically, in 3D, you need a free cross-free matrix to have a rotation. There's going to, the reason for being homogenous coordinates are that we want to have some affine transformations, which is basically the same, but we can also, like, translate stuff. There's look at transformations in OpenGL. So, also skipping those, but we're going to extend them later. And there's something called the perspective transform, which is, yeah, which is basically what we saw on the slide before, which it reduces the number of dimensions. So, in the 3D case, you get a 2D picture, which you can't plot on your screen. And, well, yeah, so the perspective transform is something you do so you can later do protections. There's going to be a lot of slides like this. So, for example, since I'm going to skip over it, but I'm going to point out an indentation like vectors in our stuff are going to be bold. Vertical bars around a matrix mean that we're going to do determinant. And, when we have rotation matrices, we can just extend them to be, so you can multiply them with affine transformation matrices. So, you just add another row, and you add another column, all zeros except for the cell. So, it's going to be interchangeable. So, just a heads up. And, this is a matrix we're also skipping. I'm just throwing that here because it looks kind of intimidating. It's documented in your OpenGL manual. So, yeah, just throwing it out there. Okay, and my clicker's not working. Anyway, so now part one. You guys are going to believe me that we can do perspective protections in 3D, probably because we've been playing Call of Duty or something at some point. So, we can't do that in 4D, and this, for example, would be a test rack or a hypercube. So, in order to render this, we need to do some maths to take our 4D object, in this case a test rack, and reduce it to a 3D object, which we can then turn into a 2D object. And, if we want to do it in 5D, it's going to be the same thing. So, again, what do we need for that? It's basically the same list. Shit. And, it gets worse because we don't actually have a cross product in 4D. Damn it. Well, we don't need a cross product. We just need normals, and so I'm just going to do a difference, which is a lot shorter. Okay, so, we want to do normals. I was just showing in the slide for the cross product, and it's pretty much the same thing, but, like, in 3D, we had a cross product, and we take two vectors, and we get an orthogonal vector to that. So, this is the property we need to do our productions. Now, in 4D, we can't have two vectors and multiply them in some way to get something orthogonal because then we get a plane because we didn't fix three of the vectors. So, we have one left over. But, we can't take three vectors and do the determinant with this matrix here, and that'll do it. So, this gives us one of two vectors, just like the normal cross product. So, we just solved the normal slash cross product problem. So, yeah. And, of course, we need a number base vector because usually we just need three of them. So, I call this term because we all like quantum physics. Anyway, we can also do this in higher dimensions. It basically looks the same, except we, so, what we do is, if we have anything in N, we need one less than that, and then we can fix all the other coordinates, and then we get a vector back. That's going to be a forward look to that, which is part of the formulas we need later. I'm not going to go into the whole formulas. Most of the time, you can just read out them later. I'm just going to throw the version out that I used for this stuff. So, another thing we need is a look at transformation. So, in 3D, you have a point you're looking at, and you have your camera. So, you need to turn around and face that point. Fortunately, we don't actually need trigonometric functions because we can just build a rotation matrix by filling in the last column of a matrix with what we're looking at minus where we're from. And then we need some orientation vectors. In 4D, we need two orientation vectors. If you're looking at your OpenGL manual, you have a function that does that for you. You give it three vectors. You give it where you're looking at, where you're looking from, and which side is open. Sorry, because you could rotate the camera like this. So, in 4D, you need to fix another vector for that. So, we have two from open back, and we fill from right to left. We calculated the last column, and we do our normal or cross-product of those vectors, and then we go to the left, and we slide out one of the vectors, and then we keep doing that. And the last one, we have another normal for everything. Now, you can actually find this in some publications online, but you can't find this, which is what we do when we want to do it in 5D and stuff. It still looks the same, but it's ugly. But, basically, we still have two less in the number of dimensions, and then we slide the calculated columns in from the right and calculate towards the left. Right. So, we also want to do a prospective transformation, which is what, basically, basically, you have a camera like this instead of like this, so it goes like to the sides, so that's part of the prospective thing. Fortunately, since OpenGL is actually taking care of all the cut-offs and everything, and we really just want a 3D object, we can skip a lot of stuff, and the matrix doesn't look as nearly as ugly as a 3D case. So, we can use a symbol matrix like this. What we want to do is we only have our eye angle, which is like how wide our eye can look, and everything but the last two dimensions, I mean, the last one dimension, and this is the homogenous part, they're fixed with the eye angle. So, the last coordinate in our 4D, 5D, whatever is always kind of like a death. So, yeah. So, basically, that works. The 5D case is pretty much trivial. We just have the last two fixed, and whatever we have is corrected with the eye angle formula we had in the 3D case. So, that takes care of that. And then we need some kind of view matrix, which is basically like we take all of this stuff, put it all together, and then we're happy because we only have one matrix that we have to multiply with for our vector. And it's not that bad. It's just a couple matrix multiplications. This is actually a 4x4 matrix, and this is a 5x5, and this is a 5x5. But that's not too bad, because we can just, so we implicitly expand this 1 to 5x5 with, as I previously explained. So, not too bad. And the 5D case is pretty much the same, so we don't really have to worry about this. So, I mean, 5D and higher. So, what do we do once we did our vector matrix multiplication? So, we still need to actually convert. So, we gave it a homogenous 4D coordinate and our matrix, and we multiply those, and then we get still a 5D coordinate back. And at this point, we need to take the homogenous part out, and we also need to do a perspective division. So, this is the same function in both cases. So, we just apply that twice, and then we get a 3D vector back. And that's basically it. So, now we have a 3D vector. We do the 3D thing again. We have cameras for every dimension, and we're going. So, yeah. And now to show how that is done, or at least what it looks like. So, this is the happy cube from earlier. And we can rotate this in 3D. Nothing too fancy. It's a little program I wrote a while back. And we can do it in 4D. So, it turns inside out. Yay! It turns inside out. If we did this with a 3D thing in 4D, we would basically turn the whole thing inside out, because we do a 4D rotation on a 3D object. And we can also do this in 5D. And it gets kind of confusing after 5D. So, we stop at 4. Sainer. All right. Okay. Now, I promised some iterated function systems. We're going to have to skip over a couple of these things, so it's not too bad. So, an iterated function system, the basic idea is that you have like two, three, four functions, and you have a set of starting vectors.  And this is actually from a fractal flame paper. I don't quite agree with that, because we don't really do that at infinitum when we display it, because then we wouldn't see anything, because it wouldn't ever stop, so that, yeah. But that's what the fractal flame paper had. So, we can basically choose any kind of function we want for this. A simple one is our affine transformations, which are basically, we can take our point, we can translate it, and we can rotate it. So, normally, you do a chaos game to render these things, which is explained later, but I'm not going to do that, because we can't, it doesn't work in 4D or 3D, because you need too many points. So, what we can do is we take a sufficiently divided primitive, and then apply all of these functions recursively, and then we get pretty pictures. So, for example, if we try to do a Sierpinski gasket, we have this square, and then we can. We have three functions, and they work like this. They realign it and then make it smaller, which we can all do with affine transformations. We do that a couple of times recursively, and we get an ever nicer and ever sharper picture. So, does this work in 3D enough? Sure. We can't do that. There's no problem here. I'm going to stick with a 3D one. These are randomly generated just with a seed, so nothing too fancy here. We can rotate this. It kind of looks pretty. We can do this in 4D and turn it inside out. So, it can turn it inside out, as you see here, sort of. Well, I already function systems in 2D, but they use a special kind of function called a variation, which is defined in that Fractal Flame Paper by Scott Braves, which is referenced in the end, so you can read it, because it's cool. And the variations kind of work like this. You have your affine transformation, and you also apply a set of variation functions, which are defined in appendix. There's 49 canonical ones. They kind of look like this. So, for example, we can have a function that does nothing. We can have a function that applies signs to all of the coordinates. And also, like a normal spherical transform, all sorts of kind of funky things. There's a couple of weird constants, and they thought about some cool stuff there. So, what you do is you take a number of these variations, and then you blend them together by assigning weights for each of the variations you want, and adding it all together. So, you can have like half of a spherical one, quarter of a linear one, and another quarter of a cosine one. You can also make it more than one, but then it kind of looks weird. So, then you can also, then they also added post-transforms with this, which is you take another one of these, and do it again. And a final one. Yeah, they really like their transforms. They do it everywhere, which is kind of cool.  That's not really pretty. You can improve that by counting the number of times you hit a particular pixel, and you have a grayscale image, which is better. It's a lot better if you take the logarithm to do that, because you have lots of spots that get hit a lot of times. You have lots of randomness in there. So, you want to smooth out some of these smaller things, some small differences, but you still want to show like some of the bigger ones, so the logarithm scale kind of works for them. And if you apply a column map, the way they do that is like every function you have, because you still have more than one function. Every function gets an index on a column map, and you mix them all together, and then you get much prettier pictures, and then you add some vibrancy algorithm. It's always good. Now, as I said, this algorithm is strictly in 2D, so it looks 3D, but it's not. So, can we do that in 3D? Well, we can't do it with a Kers game, because we don't have enough memory for that. But we can do it. We can do it with a discrete version. So, yeah, I spent some fun time on this program. So, something doesn't crash. Okay. So, we need one more position. We want this to be bigger. This already kind of looks cool. It's already in 4D. So, let's stick with a 3D case for now. You still get the effect of it turning inside out and everything. So, this is kind of a random one, just the first best seed I had. You notice that it's 2D, because I just took a plane and subdivided it a lot of times. And when you run the transforms, you can sort of extend some of them, like you've seen the cosine one, and you can just add a number cosine. You've seen the spherical one. You have a formula for spheres and error dimensions. So, all this well. And we can do that. We can do it in 4D also, which means our stuff can turn inside out. But the cool part of the effect of flame diagram is actually the way the colors work, which turns out is really easy to implement in a pixel shader if you're willing to do a logarithm in a pixel shader. It sounds worse than it is. It actually works pretty well in real time. So, this is rendered in real time. It's not the prettiest set ever, but there's some room for improvement here. So, and it's kind of nice to see that it's still pretty damn smooth. So, I can do some random colors. Okay, let's take this one. So, like the yellow and the purple and blue, which is sort of visible. They're all different functions, and they get mixed together in the pixel shader, which works surprisingly well. And we can do all sorts of pretty one. And three years on is actually pretty nice, because it highlights some of the properties. Yeah, this one is pretty good. So, depending on from where we look, our pixel shader with the original algorithm has this kind of property of amplifying geometry, which is pretty cool. And we can, again, do this in any kind of dimension we want. So, we have this cool thing, and we can make it turn inside out. Whoa, sorter. Right. So, you get this nebula, and by doing a 40 inside out thing, you can make some pretty amazing pictures if you find where I kind of see in everything. So, this thing, this piece of code, is all open source. It's all available on GitHub. You can play with it. It runs in your browser. Although, unfortunately, it turns out that WebGL doesn't support, doesn't seem to support floating point textures. We just need to count ones up, but, unfortunately, the errors are clamped, so it doesn't really work. It's kind of sad. We can, but it still works in principle, and you can play with most of the other things. So, yeah. That's a program. If you're interested, there's a block series explaining most of the formulas in more detail, because pretty much just wouldn't cut it. This is my Twitter, if you're interested. Here's the original paper about the fractal flame algorithm, which is a really amazing read, and I put a lot of cool stuff in there, so I always give it a read. And, as I said, some of my tomatoes are from French. We've all seen the LSD one. And that's the end of that one, so if anyone has any questions. Okay. Thank you, Magnum, for this really interesting talk. I really, really like fractals. I'm sure everybody here does as well. Before we start with questions, if you absolutely have to leave, please be quiet. That involves no talking. If you can, please just stay until the end of questions. So, are there any questions from the internet, Signal Angel? Can you wave at me if you have any questions? Is there a question? Yes? Okay, ask away. Audio Angel, or so, could you please turn on the Signal Angel's microphone? Maybe start, let's start with a question from microphone number three, until the Signal Angel set up. Okay, hi. Thank you for your interesting talk. I was wondering in the projection transformation that you explained, you assume that the last dimension, it's one, so it's going to be depth, and then you assume that the rest are going to collapse. My question is, what happens if you don't assume that, or if there is anything that changes? Because in the projection, you're kind of assuming how the projection is done to 3D, right? If I understood correctly. That is true. I haven't actually explored what happens if we do a different kind of 3D transform in this case. I mean, that's perceptual, it could be different. It could be. I've just tried to take the perspective projection as using OpenDL and extended to 14, 15 higher. So, I haven't explored if it gets different, but it would definitely be amazing to try that out. So, I totally agree. Okay, Signal Angel, do you have a microphone? Yes, I have. Okay, please ask away. Standard user from ISC asks, are these visualization applicable to the 3D virtual reality experience, and would that give us the ability to better understand 4 and 5D fractals and projections? I'm sure that if we have something, a virtual reality headset that can do things in 3D right in front of us, that would completely improve the experience, and it would definitely help us explore the higher dimensions better. So, I haven't again tried it, but if someone would like to try that with VR Dear, I'll do it first to test it. Okay, let's go back to microphone number three, please. Yeah, just a quick question. I noticed that even for the multi-dimensional cases, you used apparently 2D primitives as the primitives, wouldn't it be possible to use the high-dimensional primitives? It would definitely be possible. So, as you said, what I did was I still used strives, and I kind of cheated by basically making them see through, as in, because if you're looking at a 3D object with 4D eye, you can see all of the sides simultaneously. So, it would definitely be possible to take higher-dimensional primitives. It's just that it's a lot easier to reason about if you have something like a 2D primitive, and you're trying to wrap your head around it. Are there any more questions from the Internet Signal Angel? Yes, there is. Okay, ask away. Twilly Sparkle from IRC asks, do you think a game in 4D Plus would be possible, and do you think it would be playable? So, there actually are games in 4D and higher. I remember at least a game called 4D Maze, and there's a couple of the adaptations of the Rubik's Cube to at least 4D, 5D, and I think I've seen 70. With Rubik's Cube, in particular, I have to admit that I can't solve a 3D one, so I would be amazed to see anyone solve a 4D one, but it's possible, and it can be done. So, actually, when I was thinking about doing this stuff, the transformations kind of look really cool, and it would be kind of cool to use it as a transformation effect, like you have your scene and you have a number scene, and then you can do a 4D swap over that, which I think would be really cool. But I'm not sure, like, I would love to see more games like this, and there are some. Okay, are there more internet questions? Not so far. Okay, one more from microphone number three. Thank you for your talk. I have one question regarding using it not just with factors like you did, but just inserting 4D or ND data sets from real data, and does it work and how it would maybe look like, and what trick you used to get the transparency effect for this data set? So, I mean, in the demo, I basically just used a transparent 2D surface, that part was easy, but I could see this used in a higher dimension to visualize data sets. So, I mean, when you're looking at a lot of stuff where you analyze stuff into different categories, you always end up with more than three, so if you would like to draw a graph, it would probably be very easy to make a planar one in higher dimensions. But I've not seen this done yet. I would love to see this done. But unfortunately, it is kind of hard to wrap your head around the 4D rotation part. So, I'm not sure if, because the graph used to make stuff easier to see. So, I'm not sure if it will make it easier to see if you're not trying to see 4D, but it will probably be cool. Okay, we have time up for about one or two more questions. Let's try microphone number two for a change, please. Thank you for the talk. I have some sort of more theoretical question. I was wondering, you told us that there are 47 types of variations and I never heard of variations. So, what actually, do they have some sort of properties? It's kind of a very small class. So, they're just basically defined at the end of that particular paper with the HTTP URL here. So, there's particular paper. So, they're specifically defined. The only common property they really have is that they're sort of aesthetically pleasing on their own and that they're all 2D. So, you can extend some of them, you can extend others. But they're specifically defined in the panics of that paper. Okay, thank you very much. Okay, one last question. Not a question, just a quick info on the 4D games question. So, there is a game that made the runs on the internet this year called, and I have no clue where the word comes from so I can't pronounce it. You can look it up. And what you can do in that game is like you have a 3D environment.  And in gameplay terms, it's really just that you shift to another dimension. I mean, a lot of games do that. But the funny thing is that that game actually implements it with the correct math. So, it looks really, really fancy. I remember seeing that. I haven't tried it. I wanted to try it. So, I mean, it makes sense that it works because when you do the 4D production, you really end up with a 3D world. So, it totally makes sense that you could use this to turn parts of the world around. So, I've seen it. It looked very cool. But I haven't tried it. But probably will. Let's thank the speaker again, please.


Yes, water is a very precious resource and we see it every day in our life. So today I want to take a few minutes to introduce you to the challenges coming up with the management of water related to mining and metals. You may not know before starting H2O Innovation and creating H2O Innovation in 2000, I was myself into the mining industry. I was managing, coordinating Exploration Campaign in Labrador and Peru and very early I got exposed to the challenges in managing water for our Exploration Campaign. In Labrador we had to manage water and bring the water through pipes and holes and we had to heat with electrical coil this water to avoid freezing of the water. On the other hand, a few years later doing Exploration in southern Peru where the water is pretty rare at 3,000 meter high, we had to hold water in trucks and we were waiting for the trucks to bring this water to conduct our Exploration Campaign. So very early indeed I got exposed to the water challenges. The water processes and the extraction processes from previous years to today I've definitely involved so there's more new technology involved in the extraction process but one thing has remained for sure is that water is related to every single step of our extraction and refinery processes. We needed into our Exploration Campaign, we needed to the flotation process, remediation, the dust minimization or management, the workers facility, the water is really needed everywhere. One of the news is that today with good technologies, with membrane filtration technologies and crystallizer we can recycle this water up to 90%. So with good practices and proactive investment we can come up with a more advanced solution. Now what is strange about or different about this industry? So unlike any other manufacturing business the mining exclusively relies on the location and we spend a lot of dollars to confirm this location. We spend a lot of dollars to confirm the proven reserves, we spend a lot of dollars to define the site but all the other industries, the manufacturing for example if you want to build a new pharmaceutical plant you will look at the facility around the plant, you will look at the population, you will look at the public transport to build your plant, you will look at how you can access power, the cost of electricity, the fiscal environment before building such plant. But in the mining, I mean you'll be building this in the middle of nowhere and the discovery then makes it even more challenging to bring additional resources. As you start the mining process or the exploration you bring people in the middle of nowhere so you'll need water for the camps. As you build the mine then you will have obviously water related to the smelter or the refinery itself and then obviously you will create the tailings, the tailing ponds will have to manage this water and again the water will have to be treated before rejected to the environment. But are we giving sufficient thoughts and time on how we're going to manage these resources? Unfortunately we have been exposed to great opportunities but clients were coming to us very late in their process saying, oh I need a water treatment plan for five hundred people that I need to move on this mine site and when do you need this? In which year? Oh we need it in six months. So it was obvious to me that you know there was a lack of planning somewhere so this morning I want to share with you a couple of things that we should pay attention to and before investing in mining whether as an investor or as a developer of a project we should pay attention to. So three important things or risks that we should look at. The first one is obviously the one related to your ability to generate revenue so because there's tremendous amount of water required to the extraction process so do you have the proper technology so how can you mitigate the risk associated to the manufacturing or extraction process? The second one is the one related to the people, your employees. As you move these employees again in remote areas and we're talking about camps of four hundred, five hundred, a thousand, two thousand, five thousand people even that you move in pretty remote area you need to provide them with water treatment systems, waste water treatment systems that will provide them safe drinking water. So the one related to health and safety risk is another important one for the workers scammed facility. Finally the last one that I will address this morning is the one related to how are you managing your tailing water ponds which represent a very important environmental risk and potentially reputational risk as well. So the first one or first case study I want to share with you this morning is a project where we got involved for the mine, Escondido mine in Chile. This as you may know is the largest copper deposit owned by Rio Tinto. In this case to get the mine running and we're hoping to get the plan going in 2016 this will make the largest arrow or desalination plant in the entire Latin America. So Rio Tinto invested to build a brand new desalination facility, a 220,000 cubic meter per day desalination plant. So this to give you an example is the equivalent of a 500,000 people that you could deserve with water. So they got this mine going, they got this plan going and the challenge and to show you how critical and important water was and the scarcity of it as well in southern Chile was that we had to bring this water up to 3,000 meter high in altitude through pipeline of 180 kilometers. So if you don't plan it properly in advance and you don't look at the resources you have around you before you get going, you may get caught with unlikely or pleasant investment to be done. So as we speak we have two of our employees flying there in Chile to assist and collaborate on the commissioning phase of this desalination plant. But again is to show you the importance of proper planning related to generation, their ability to generate revenue on this extraction process. Another one I want to share with you is the project here in Ontario, a project we did a few years ago for the client, the Beers was among the first, well their first mining diamond mine in Northern Ontario. So this illustrates very well that the Beers, despite the fact that there is abundant water resources around this area, the Beers was not afraid to go beyond and above by investing into a water treatment plant for the workers. So in this case we had to design water treatment systems using membrane filtration technology that could adapt itself as the mining process or the life of the mining project. As the Beers was expecting to get the groundwater contaminated with the mining operation they asked us to be able to design the plant so that we could adapt it to condition from groundwater to surface water over the 15 years of the life of the mine. So again we had to adapt ourselves but it shows that for the Beers it was very important to make sure they were providing safe drinking water to their workers. Because imagine the cost of flying someone by helicopter in the middle of nowhere then by plane back to Toronto to get ill for E. coli contamination or diseases. So again important risk, health and safety risk and again associated to potentially even some reputational risk. So this shows the kind of modular building that we brought on the camp containing all the water treatment facility. Now another interesting one that I want to share with you this morning is the one related to tailing ponds. You may have heard about this case study on Mount Poli. So a few years ago we received a mandate from Imperial Metal to build a water treatment plant to process their water for this large tailing pond. That's significant in size so we're talking about 24 million cubic meter of waste that we had to manage over a significant area with contaminants with arsenic, copper and selenium. So we use for that membrane process. But the interesting part is that we received the P.O. it was about $2 million P.O. In June 2014 so we start immediately to get going because it was critical that we had to deliver this plant for November on the same year. So again quite short notice to get going but the client is paying $2 million so let's get going. So immediately we get started on the engineering phase, provided the drawings, provided the submittals and here's what I want to show you. On July before we finished we had just finished the engineering phase and we had just started the procurement phase of the key and long lead items. Here's what happened and look at the impact it had on the stock. On July we saw the dam of the water pond just collapse creating a huge environmental catastrophe. So suddenly there was the lake just below the Pauley Lake increased by 1.5 meter in three or four days and 326 tons of nickel, 400 tons of arsenic, 177 tons of lead were disposed into the environment. So obviously it caused a huge impact on their reputation but it is definitely something that could have been planned in advance. Now another example I wanted to share with you which I believe is good practice is the one related to the old plant maniola previously owned by Norenda now Glencore. In this case they have been proactive right from the beginning and invested into a proper water treatment to minimize or reduce the level of water contained into their pond. So in this case we're using the water in a closed circuit, we're using membrane filtration, seawater reverse osmosis system to recycle the water and put it back into their process. So they have been very proactive in doing it, they did it in the middle of 2006 or so the investment and still run today to keep the level of the pond at low level. So as you can see I mean water is involved in every single process and is implied in every single commodity you have and strangely in 1999 I decided to think about something else than mining because I was there in Southern Peru looking for this porphyry gold system but it was very very inferred if I can say and at $290 an ounce there was no way you know we could make it happen, the economy wasn't there and we had to find other options and when I look at this to me it was obvious that despite the price of any commodities water was the commodity number one required in every single process. So I founded H2O Innovation and we can see that the investment done over the years paid off and the industry is still investing tremendously into water. So just for water systems in 2011 the mining industry spent $2.3 billion and today the industry we're expecting in 2016 will spend $3.6 billion just for water treatment system. So it is growing it is a fast growing market and we're still expecting this to grow in the coming years. So a couple of takeaways first I mean mining is very thirsty for water and I think it's obvious no matter what the commodity is we need water in every single process. I think obviously looking at the event the sad event of imperial metal we can acknowledge that prevention is better than cure. So water planning should be done in advance and there is technologies out there to help you with that.  The first one related to your ability to generate revenues. So the one related to the supply of water for your operations and the quality of supply of water you bring. The second one will be related to your workforce your people protect your people with proper and safe drinking water and wastewater and make sure that you're compliant with the legislation where you're operating. And finally the last one is the one related to tailings. How can you reduce or manage better your water tailing ponds. So strategic planning should definitely incorporate the water issues into your business. I mean it will definitely you know maximize the opportunity for you but also minimize the risks associated to your operation. So thank you very much.


Hi, I'm Zor. Welcome to Unisor Education. We continue talking about heat as it's related to molecular movements. Today's lecture is about the connection between temperature, pressure, pressure and volume of the ideal gas. Now, this lecture is part of the course called Physics 14, presented on Unisor.com. You might have found this particular lecture somewhere else, like on YouTube or some other website. I do recommend you, however, to go to this website to Unisor.com because every lecture has a very detailed notes. All the lectures are logically connected to each other and presented in the set of menus. Plus, there are exams for those people who would like to challenge themselves. Plus, there is a prerequisite course called Mass 14, which is definitely needed for this course. This is very much theory-oriented, mass-oriented kind of a course of physics. And Unisor.com is completely free, no advertisement. You don't even have to sign in unless you would like to save your exams for your teachers or parents or whatever else. Okay, so we'll talk about the temperature, the pressure and the volume of ideal gas. Now, before that, let me divert a little bit your attention back to what actually temperature is. I did address this issue in another earlier lecture. Temperature is a macro characteristic of some kind of an object. What's important is how we measure it. We measure it using the thermometers, different kinds of thermometers. But for the purposes of this particular lecture, I'm talking about thermometers which are most frequently used in your day-to-day life. Like, for instance, alcohol-based thermometer which measures the temperature in the room or outside the window. Or mercury-based thermometer which is used to measure the temperature of the body. Used to, actually. Nowadays there are some more advanced instruments. But anyway, just concentrate on the thermometer which measures temperature of the air in the room. So it goes up and down on a certain scale. So basically we are relating the temperature in the room which we have already discussed as being very much connected to kinetic energy of the molecules. Their speed, the more intense they're moving, the more intensely they bombard the surface of the thermometer. Which in turn, bombards the liquid inside the thermometer. Which in turn causes the inside molecules to start moving faster. And that's what actually the process of equalizing temperature from the air molecules which are moving at certain speed with certain kinetic energy of each of them. Through the walls of the thermometer to the liquid in the thermometer which also becomes more agitated. Or less agitated, depending on what exactly the difference of the temperature was in the beginning. But eventually the kinetic energy, average kinetic energy of the molecules of the air is equalized with average kinetic energy of the molecules inside the liquid. And as we explained in one of the earlier lectures, this more intense or less intense movement of molecules inside the liquid of the thermometer causes increasing or decreasing of the volume. And so the level of the liquid in the thermometer goes up or down. And now all we need to do is just to properly mark temperature on certain scale. So this is a very much, very brief explanation of how the temperature is measured. So most importantly is that eventually the temperature of the thermometer and the liquid inside the thermometer and the air. Or any other object, whatever we are measuring doesn't really matter. We can measure the temperature of the water in the river. So they equalize. Now what's also important is that if it's a closed system, let's say you have an isolated aquarium with water. Isolated which means there is no outside energy coming in or going out. And now you are inserting the thermometer inside that aquarium. So there is no external source of energy. Which means that whatever the kinetic energy existed before, maybe it was a little bit more in the water of the aquarium and a little bit less in the thermometer. Or vice versa. Eventually it equalizes but the total amount of kinetic energy remains the same because it's basically preserved. There is nothing outside, there is no outside source of energy or consumer of energy. Now that means that measuring the temperature of the object actually changes the temperature of the object itself. Because now the energy of the object should really be somehow equalized with energy of the thermometer. So if energy of the aquarium was greater, average kinetic energy of the molecule was greater, then it will heat up the thermometer to equalize, right? Which means certain amount of energy will be transferred from the aquarium to the thermometer. Or vice versa, depending on what is warmer. So measuring changes the temperature of the object which we are measuring. However, we have to always think about this as a non-important factor because in most of the circumstances the energy of the thermometer is really very small relative to the energy, the total energy of the all molecules of the object whatever we are measuring. In all our practical lives. I mean if it's not the case, then obviously we should use different kind of thermometers. But in our everyday life, again back to the measuring of the temperature of the room using a regular alcohol based thermometer. Obviously it's negligible loss of energy whenever we are introducing thermometer into the room. So that's okay, I mean we are changing but not very significantly and negligible actually. Okay, now what else? In one of the previous lecture we were talking about how the temperature is related to average speed. Now in most, the most important issue of that particular lecture was that if we are talking about molecules they have certain speed then the square of this speed is proportional to temperature if counted from absolute zero. Now the temperature of absolute zero is let's say the temperature in the space outside of any kind of a planetary system far from the stars. And in this case the average kinetic energy speed basically of all the molecules will be zero. So that's what absolute zero actually means and that's why whenever we are talking about proportionality we are talking about this starting with zero and this starting with zero. So whenever we have an absolute zero temperature we will have no movement of the molecules of the object. Then as the speed of the molecules is increasing then the average of the squares of the speeds of all the molecules will be proportional to the level of liquid in the theoretical thermometer whatever is measuring this particular temperature. So that's very important. So this is an absolute temperature starting from zero and this is velocity well it's square so it's basically speed averaging called the squares of the speeds throughout the whole molecules of the object. So this is very important. Now at the same time we can say that if our molecules are of the same mass then it's obviously proportional to kinetic energy, average kinetic energy of all the molecules because kinetic energy as we know is equal to m v square over two. So it's very important right now to connect this and this. So kinetic energy is proportional to the temperature. And again we are talking about absolute temperature and kinetic energy obviously also starting from zero whenever the speed of the molecules is zero. Now obviously we are talking about something which we have already established. The scientists already established the scale of this absolute temperature. It's degrees of Kelvin where absolute zero means absolute zero. There is nothing negative in the Kelvin scale there is no negative degrees as we have in Fahrenheit or Celsius. Now so zero means approximately it's minus 273 degree of Celsius. Now and one particular degree is measured as in case of Celsius as 100 of the difference between the temperature of the freezing water and temperature of the boiling water. So these are degrees of Kelvin and that's how we measure the temperature. And the kinetic energy obviously is measured in system C as Joules. So this is degrees of Kelvin and this is Joules. And proportionality obviously means that there is some kind of a coefficient between them. But let's not talk about this right now we will come to this a little bit later. Now next again I will refer you to the previous lecture where we were connecting to third of kinetic energy average kinetic energy. Let me forget about this and I will put average here. So E average means average kinetic energy of molecules where N is the number of molecules. And if you will divide it by volume then we will have the pressure. Now this is the result of the previous lecture and I do refer you to refresh your memory if you don't remember this formula. It's very important to know that the pressure on the walls of the reservoir which contains gas, right now we are talking about the gas, is equal to two thirds of average kinetic energy times number of molecules. So this is the total amount of energy because this is average per molecule and this is number of molecules. So this is the total kinetic energy. So if you will divide it by volume and coefficient is two thirds. Now it's obviously that the pressure should be proportional to the total energy. And it's also obviously that pressure should be inversely proportional to the volume. Because if the same molecules which are moving with the same speed are spread in a bigger volume, obviously the bigger the volume the less the pressure. Now what's also important is this coefficient and I'm not talking about how I derived it. I derived it in the previous lecture. So in this particular case I'm just taking this as granted. And I can express it slightly differently. I can resolve it for average energy which is equal to what? Three seconds P times volume divided by N. So this is average as basically resolved from here. Now I have already mentioned that it's proportional to absolute temperature. So our purpose of this lecture is to connect temperature, pressure and volume. Temperature, pressure and volume. What is N? Well that's not such an easy thing. N is number of molecules in the reservoir. How can we actually relate to this? Well apparently it's not easy. However here is what I can actually suggest you to do. Now from this let's just write it over there. That the P times volume divided by N is proportional to T. Coefficient doesn't really matter right now. It's too proportional. So that's what we have. Now we have to really find out what kind of proportionality we're talking about. Let me write it differently. K times where K is some kind of coefficient. T is the temperature in absolute temperature in Kelvin's degree. Now P is the pressure. Obviously we all know what it is like Newton's per square meter and this is the number of molecules in the reservoir and volume is again like cubic meters whatever it's measured. Alright so we got that. Now let's talk about the ideal gas. And usually I'm not researching very much to say something like experiment shows. But in this particular case I have to do it. Here is what's important. Molecules of different gases are obviously different. Like hydrogen is different from oxygen and oxygen is different from carbon dioxide etc. And obviously they have different masses, these molecules. Which means that since we are talking about kinetic energy as the most important characteristic related to the temperature masses are important as well as the speeds. And by the way we will determine the speed of the molecules of oxygen traveling in the air as the result of this lecture. Which is kind of interesting to know what's the speed of molecules, how they really move. We will be able to do it. So mass is important. Now what's also important is that gases are such substance when molecules are small relatively to the distance between molecules in the gas. So they are really flying colliding with each other but not very often. I mean they do have a relative freedom of movement. Well obviously when they hit the wall of reservoir that what creates the pressure obviously. But at the same time they are relatively freely moving. Now what's important is that every molecule has certain weight. And here again I'm resorting to our experiments. There are some theory and there are some experiments which leads us to certain knowledge about the molecular weight. So there is something which we call a unit of molecular weight which was some time ago decided to be one-twelves of the mass of the carbon atom. Now in these units we can measure the mass of all other molecules smaller or bigger. And in this particular case the molecule of hydrogen which consists of two atoms of hydrogen. We will talk about atomic structure of different elements later on but right now just take it as a face value that the molecule of hydrogen consists of two atoms and each one atom is approximately one unit approximately equal to one atom of hydrogen. So the mass of this would be two. It's called atomic unit of mass. Atomic mass unit. Now the oxygen which is also the molecule of oxygen which contains two atoms of oxygen. It's 16 plus 16 is 32. Now the chemical formula for carbon dioxide which is 12 plus 32 that's 44. So we do know the masses on a certain scale. Now I don't know how really many molecules are in any particular reservoir but to make experiments with the same number of molecules of different gases I can do it because if I know that for instance this is molecular atomic mass of hydrogen and this is atomic weight of oxygen if I will take a mass of hydrogen to be 16 times greater than mass of oxygen which I take so this is amount of hydrogen and I'm taking this mass of hydrogen I can weight it in some way right? I can put it in the reservoir and weight it so the mass will be proportional to the weight. Now I can take certain amount of oxygen put in the reservoir of the same weight let's say and if I will be able to match this mass of hydrogen if mass of hydrogen is 1.16 of mass of oxygen again mass of hydrogen is 1.16 of mass of oxygen then the number of molecules will be the same right? Am I right or not? If I will have the same number of molecules then the total weight of hydrogen will be 1.16 of total weight of oxygen whatever I said before that's the right thing which means I can take two reservoirs one with oxygen and one is hydrogen or hydrogen and oxygen whatever it is make sure that they have exactly the same number of molecules and make experiments so if my N1 is equal to N2 then I can say that I can make experiments with the same number of molecules now what happens is that if this is the same and volume 1 is equal to volume 2 and T1 is equal to T2 then as a consequence P1 is equal to P2 this is the result of the experiment what does it mean? it means that all gases are behaving in a similar fashion and that's why the concept of ideal gas actually came to being because people saw that different gases provided similar conditions like the same number of molecules enclosed in the same volume reservoir under the same temperature they have the same pressure on the walls so these are experiments or experiment can be done differently for instance equalize the pressure and then see the temperature so it looks like all the gases really behave exactly the same thing which means this coefficient although it's different maybe for liquids in case of we are talking about liquids but in case of gases this particular coefficient is relatively the same for all the gases I mean the difference probably will be so negligible we can't really even detect it using our instruments so that's what's very important which means that instead of having this I will write Kb where Kb is a constant called the Boltzmann Boltzmann's constant Boltzmann Boltzmann, I think that's how it's spelled so it's a Boltzmann's constant and it has specific value and specific value I have to really get somewhere 1.381 times 10 to the minus 23 joules per degree of Kelvin so this is a Boltzmann constant it is a constant for gases and that's why we have this particular equation which represents behavior of all the gases well, within certain limits I mean there are some extreme temperatures or maybe extreme pressures or something like that where it's distorted but again for the purposes of physics of 19th and 20th, beginning of the 20th century you can assume it's a constant we don't really go into extremes okay, so that's very important now, what follows from this is that average energy as we were saying is 3 seconds of P volume divided by N which is equal to 3 seconds KB times temperature now, this is known this we can measure it's just a macro characteristic so using the macro characteristic we can have the micro characteristic of the gas the average kinetic energy of the molecules and that's very, very important you see, measuring something on a macro scale having the constant basically and just measuring the temperature in degrees of Kelvin we can find out the average energy of, average kinetic energy of the of the molecules of the gas okay, fine now, what follows from this is that the P times volume divided by G is equal to KB times N now, what does it mean if you try to interpret it well, if you take a certain amount of gas which is a certain number of molecules of gas in the reservoir then this is constant if we are changing one of these parameters right, so no matter how we change these parameters pressure, temperature, volume if we are talking about the same amount of gas then this pressure times volume divided by temperature is constant because this is constant because we don't change the number of molecules so, for instance if we have some kind of a cylinder okay and it has certain volume, right for instance, it's fixed and then we are applying temperature we are changing the temperature well, if we are changing the temperature while volume remains constant then P should also change proportionally because otherwise the whole thing will not be constant so if I double the temperature my pressure should be double so if I heat it up from one degree, let's say from 100 degree Kelvin to 200 degree Kelvin which means double my temperature my pressure should also double okay whatever the gas is doesn't really matter and this has a specific name, this particular law that if the volume is constant and if the volume is constant the law is called the law of Gay-Lussac so if my if my V equals constant volume, I mean then P and T are proportional to each other then P divided by T equals constant that's my first law now, at the same time I can establish another experiment when I maintain, let's say the temperature if my temperature is constant and I'm changing the volume how can it be done? well, for instance we don't change temperature temperature is always the same temperature is constant but I have some kind of a plunger here whatever it is so initially it's in the upper position and gas molecules are everywhere but then I press it down so if I, let's say decrease my volume by factor of 2 what happens with pressure? if my volume is increasing temperature is constant then my pressure should my volume is decreasing then the pressure should increase so the pressure times volume is constant and finally if my pressure is constant if my pressure is constant then volume divided by T should be constant right? so this is Gauss-Sack law now if temperature is constant that's the Boil-Marriott law and this is the Schar's law so each of these laws were discovered separately and later on everything was combined into something which is kind of a combined law the pressure times volume divided by temperature for a particular amount of gas is constant no matter how you change you can change all three characteristics by the way but this product of P times volume divided by T should be constant alright, so these are three laws and then I promise to find the speed of the molecules of oxygen and that's how we will do it so we will do it using this and also I know that the molecule of oxygen has mass again I have to resort to some experiments whatever it was provided 5.31 times 10 to the minus 26 kg that's mass of one molecule one molecule of oxygen now knowing the mass knowing temperature well let's say room temperature is like 20 degrees Celsius which is 293 degrees Kelvin knowing Boltzmann's constant which is this one I can establish my mv square average divided by 2 that's what kinetic energy average kinetic energy is so if I will multiply this time this time this I will get average kinetic energy knowing the mass I can derive average speed and average speed then I will take the square root of that to get the speed to be 478 meters per second which is pretty fast so the molecules of oxygen in the air which we are breathing are moving with average speed 478 well maybe my calculation is not exactly correct somewhere around this number between 400 and 500 meters per second that's all we are not talking about a concrete molecule it can be faster or slower this is very much around average which is pretty fast however you have to take into consideration that as molecules are moving no matter how small they are they are still colliding with each other so the direction is changing so that's why the molecules maybe are moving very fast but it doesn't mean that the molecules are flying away from us somewhere else or there is some kind of a significant wind there is no wind unless there is a wind from outside so if you are in a room you don't feel this because no matter how fast they are it's still within certain microscopic dimensions so you don't feel it as a wind but anyway that's interesting kind of an equation which we can make using theory well not only theory we did use for instance the mass of oxygen which was determined completely outside of the scope of this lecture and the Boltzmann constant which also was calculated somehow in any case using pure theory and this is very very important this is very very important equations this is dynamics this is the ideal gas so using this theory and certain experimental facts we have derived to some very unexpected result about the speed of the molecules of oxygen in the air which we are bracing with okay I do recommend you to read the notes for this lecture they are on Unisor.com notes basically contain exactly the same information presented in a textbook-like format and well that's basically it that's it thank you very much and good luck


Hey guys, it's Andy Elliott in this video. I'm gonna talk to you about the objection I want to talk to my dad and I'm gonna get back with you. This is a very common objection in the automotive industry I'm gonna show you how to handle it. Check it out All right guys, so here we go so when somebody says I need to talk to my dad number one Okay, they don't need to talk to their dad if they needed to talk to their dad Their dad would be there with them does that make sense if it was so important for their dad to be there with them They would have had their dad with them. This is a smoke screen. I understand in all my videos You notice I keep saying that's bull crap. That's not real. That's a smoke screen Look, maybe somebody wants to talk about something with their dad But my question is is the dad making the payment is the dad paying for the down payment Is the dad gonna be co-signing on the deal? No, then it's their decision. Does that make sense?  You need to like your car. You already said you love it So let's wrap up the deal. You're just going to press through.  That's a joke man. Come on inside.  It's Andy a lot of you leave comments Tell me that you need help do me a favor. I'm gonna say the best way to get a hold of me Shoot me a text message right now<PHONE_NUMBER><PHONE_NUMBER> I'll help you with whatever you need. I got your back for life Let's get back to the video guys. This is simple. Take the word track. I just gave you write it down No matter what anybody says to you. I don't care what it is. Okay. No four or five ways to overcome every single objection I've got a hundred objections wrote down I know five different ways to overcome every single one of them You guys need to know the same thing and whatever industry you're in guys If you're not making at least a half a million a year in sales at least okay We're in the air of the worst salesman in the history time customers are dying for great customer service It's time for you to go be a pro and stop being an amateur text me<PHONE_NUMBER> guys I will help take you to the next level. I will personally coach you. Let's get you the next level. Let's get you paid. Let's go Hey guys, I just want to tell you the true one percenters. You made it till the end of the video Do me a favor share it with the friend that wants to go to another level Make sure you like the video comment below so I know who you're set your notifications and then subscribe to the channel We got daily sales training videos dropping. I'll see you soon


President Bola Tinibu says the federal and sub-national governments of Nigeria have the mutual responsibility of ensuring the country's peace and stability. Speaking during a meeting with the Nigeria Governors Forum and GF at his residence in Lagos on Tuesday, the president reiterated his condemnation of the latest killing in Plattus State. Addressing the governors, the president issued a stand directive to security agencies to halt the carnage in Plattus State and intensified a pursuit of those responsible for the recent tragic events in Boko's and Burkina Ladi local government areas. Condoning with the victims, President Tinibu emphasized the sanctity of human life and called for a paradigm shift among those with contrary beliefs. President Tinibu acknowledged the presence of Governor Simina Laifabura of Ubarra of River State at the meeting, commanding him for his efforts to peacefully resolve the political challenges in the state. My condolences to you, President Bola Tinibu. We have to stop the carnage. We have to take care of our people. Mission, life. More sacred. And as we bring it up, we will take your mindset. This is a condolences. And we have to be honest to all of you. And we have to take care of it. You have to say everything we don't know. I read your statement. And she made me work for the state flagship programs and reliance on things. We saw that we would increase the number of government and governments as such in the working areas. To some of you, it was a long time. When I read it, it was a long time. I said that I have to do my rounds and go back. If you are home. And I was invited to ask you to hold the round of applause for the people. Let's be glad to have the responsibility. If I have to stay in a big island, our district is so big it won't be bad. Thank you. Thank you. Thank you.


All I can say right now before we get into the battle is from the bottom of my heart thank you to every single fan that paid to come watch this live and on top of that thanks to everybody that paid to watch it on the pay-per-view. Make some noise for yourself. I want to see the battle so let's get straight into the battle MC on my right-hand side we've got O'Shea Mayne providing with a humongous intro but all I'm gonna say right now is please go person out there please log on to our website www.thomeblock.com and leave your opinion on this absolutely guaranteed classic battle that's about to go down you know the score. All right O'shea gonna go first yeah? O'shea. Yeah yeah I'm ready yeah. All right we're at check point two is number one let's go. Yo then as I spit Jed the C in lunacy stands for this lunacy because this shit's a great pleasure respect because you've got a lot more to lose than me so I hope this is a shit but we're no glad to see the return of this tape measure.