Let's check this out. We should be alive. There we are. Awesome, awesome, awesome. Hi, everyone. This is Chicho. Welcome to my channel and welcome to another live stream. And today we do mathematics. Coolio, how's it going first? Awesome, awesome. What's the day today? Today is May 18th, 2020. Smith, how are you doing? The man, the legend. Hope you guys are doing well. This is the last stream we've set up for the five set that we started five days ago, I guess. It's ball search. We're going to get the emote going for that, man. After I've been busy with taking care of the podcast stuff, right? So I think I got a nice rhythm going for the podcast that we're loading onto SoundCloud and whatnot. And I'm going in and putting a little intro at the beginning and a little ending at the end with a little tapping of the bowl. So we'll see how it turns out. It's fun to do. It's fun to do. I love sort of messing around with the new platform and learning the ropes and stuff. Elder God, how are you doing? You've been going crazy with the emotes. Awesome, awesome, awesome. I'm going to go do my little intro for this thing. For those of you that are live here, you know who we are, right? Listen, 999 8G Cho, hope you're doing well. Thank you very much. Thank you very much. Enjoying our time together. We've had a great, great five days of streaming going on. So that's been fantastic. Connor Higgins, how are you doing? Hello, hello. Havery, Fraz, X, how are you doing? What does it mean to take the reciprocal and how does one do it math math? Oh, I love it. You're coming up with a math question right away. Fantastic. Let me do my little intro to this thing and we'll talk about the reciprocal. Okay. Good evening, Chishol. Good evening, Brett. How are you doing? Brett Kelly, 69. So as far as who I am, I'm on Patreon. If you want to follow this work, Patreon is a great place to follow this work. If you want to support this work, Patreon is a great place to support this work. Okay. I don't put anything behind paywalls. You can just follow. And after you get into the rhythm of what it is that we're doing, if you do have the funds, Patreon is a fantastic way to support this project. We are live streaming this on Twitch. So if you want to catch these streams live, Twitch is where you want to be at. And that's twitch.tv backslash chicholive, one word. Okay. I do announce these live streams 30 minutes before we go live on Twitter, Gavs, Mines, VK, and Elo. Okay. As long as the platforms are working fine. I try to post it on Gavs, but Gavs is having little hiccups. All the platforms have hiccups every now and then, right? So hiccups permitting, censorship permitting. They go on Twitter, Gavs, Mines, VK, and Elo. Patreon, we're doing everything on there within reason, of course. And we are live streaming, not live streaming, podcasting a lot of the streams on SoundCloud. And I've already started uploading. We did a test run with three or four of them from the previous set of live streams that we did were recorded with the lapel mic. I loaded those on during the last week. And today I'm loading on the three readings of WikiLeaks that we did in the last couple of years. We did a reading of Vault 7, actually three, four, four, I don't know how many years now. Well, the first reading we did was Vault 7. The CIA hacking tools reveal. So I just uploaded that this morning on SoundCloud. Then we did the Guantanamo Bay files. And I loaded that onto SoundCloud a couple of hours ago. And we're going to load on the introduction to the OPCW Leaks from WikiLeaks, most likely later on today. Okay. And I'm slowly going to be uploading, uploading previous live streams and videos we have done onto SoundCloud. So you're going to, you can expect a lot of podcasts, a lot of audio being loaded on SoundCloud next few months, really, because we've got 900 plus videos on YouTube and at least 400 of those, if not more, more than that. 500 of those are have a lapel mic associated with them. Okay. Real quick, what were your thoughts on Guantanamo Bay? All my thoughts on Guantanamo Bay. Torture, bad. Not prosecuting war criminals, bad. Occupying another nation's land, bad. Guantanamo Bay should be closed. The land handed over to Cubans. Everyone that participated in the torture program for the United States should be thrown in jail. But that's politics. That's for another stream. Okay. And we will be uploading these videos to YouTube and Bitshoot. And if you want to support this project, YouTube membership is a fantastic way to support this project as well. Okay. Oi, Oi, Chicho. Have a great day today. Awesome, Graham. Awesome, awesome, awesome. Coolio, I have fallen asleep to the whispered Vault 7 WikiLeaks thing so many times that I probably know the whole document leaked by the heart of my subconscious. Awesome, fun. Everybody should know that. Everyone should know that. That was one of the most crucial leaks that WikiLeaks has released. And again, that's politics. We'll leave that for another day, right? Maybe I framed my question wrong. But thanks for your answer. My pleasure, Liz. What's 2 plus 2 again? It should be 4. Okay. If you're just dealing with integers, by the way. Keep politics. Thanks, Elder God. Smith got to define 2 plus and equal sign. Of course. Okay. Let's go straight into the mathematics. Okay. I'm going to take down these guys. Done. Fun, fun, fun. What are we in? Oh, seven minutes. That's plenty of time. Hello, Gandalf. Hello, Oliho.  Catholic traditions. Good evening, folks. I'm really busy today, so I will only be able to learn tonight. No worries, Catholic traditions. I hope you have a... Well, I was going to say chill Monday, but I hope your busyness goes well. I hope you get everything done well. Just so you know, it's a holiday where I am. So I got up this morning. I had one student cancel, and I just sent an email out to everyone saying, Okay, we're canceling today, canceling today, canceling today, canceling today. That way I'm just doing this. And I was working on the podcast, so that was fun. What is E equals MC squared? Energy is equal to mass times the speed of light squared. That means there's a lot of... Yeah, I know Elder God. There's a lot of... I think it's the clan that's in here. I think there's two of them that have the same name, but different, right? Basically, it means that this thing here, this little thing here, contains a lot of energy, right? A lot of energy, not only if we could harvest that, right? Energy and mass are actually the same thing. That's the point of that equation. Inverse, inverse. You contain a lot of energy.  Ding-Bopper.  Please consider Ding-Bopper.  We'll do something like that. I have been meaning to deep fry something large at some point, if I can get it. Find X, Y, Z, such that... That equals K for each K from 1 to 100. That's a riddle, man. You should... Riddles I'm not good at. I'm just here to teach high school mathematics. Okay, let's do inverse function. Inverse function. Inverse function. What is an inverse function? So to understand functions, first thing we have to do is look at a Cartesian coordinate system, right? So let's throw a Cartesian coordinate system on there, on the board, right? X, Y axes. X, Y axes, right? So in mathematics, time out, time out as I got. We don't need to chop heads off, but we can throw them in the cage for about 600 seconds. Oh, fun. You got to play it nice here. Oliho, okay. And Oliho 3, okay. Throw them in the sky cell. If you've watched Game of Thrones... Oh, the sky cells is not the one they throw them down. They shoot. They go down, open up the doorway. Nah, we can just time out a little bit. Maybe, maybe. So in mathematics, one of the things we do, right? We want to understand functions, okay? And functions are basically us trying to understand how a system works, right? And almost every type of system, you can look at it and quantify it. And that's what mathematics allows us to do. Mathematics allows us to quantify different systems. That way we can understand them. We can make predictions. We can figure out where they came from. We can start manipulating them, looking at them from different light, switching the variables, introducing new variables, taking out variables, seeing how the different variables are connected, right? And some of the most simplest functions that we can have, we can throw in a Cartesian coordinate system, X, Y axes, right? We can just say there's only two variables in play, right? The X variable and the Y variable. And usually on the X axis, this is the independent variable, right? And you have Y here as the dependent variable. Thank you. Thanks. Soon we'll have a little emotes that we can use on this thing. I learned from the last math stream, no half measures, no half measures. Yeah, I'll do God, thank you. Yeah, me too. That one pissed me off a little bit on the previous stream. And by the way, gang, I timed this stream a little bit, not best timing because we're going to have the sun coming in. Unfortunately, I forgot to remember that the sun is changing. So we have a skylight here. So the sun is going to start shining here. If the sun takes us out that we can't see the board, we might just chat, right? So I'm going to try to finish this inverse question right away. Okay. Comment as he gets a lot. Nice. So take a look at this thing. Usually this is the independent variable. This is the dependent variable. And what is Y dependent on? Y is dependent on X, right? So for example, height of a tree, how tall a tree gets from a sapling is dependent on time, right? Time is not dependent on the height of a tree. Agreed? Okay. So you could put your time variable on the X axis and you could put your height of a tree on the Y axis. And you could see, you know, if you have a seed, right? If you grow from seed, the height is zero and then the sapling grows and grows, you know, grows fairly fast initially and then tapers off and it reaches a maximum height, right? So that could be one type of function to grow. If you have an orchard, if you have a farm, if you're in the forestry sector, this is exactly the type of thing you would do if you're trying to optimize your production, if you're trying to preserve forests, if you're trying to understand how the ecology works altogether, right? Rain and stuff like that. And it's not just time that matters. It's the soil that matters. So there's another variable there. It's rain, it's sunshine. It's the different types of climates you're in and whatnot, right? So that's what a function is. It's important to appreciate that, right? So let's assume we have the following function, okay? We'll just do it graphically initially and then we're going to do it algebraically. So graphically consider this. Let's assume we have a function that looks like this. It could be anything that you might want to think about, right? Let's assume our function looks like this. That's our function. Does that even come out as black? That's supposed to be brown and that's black, right? So that's our function. Let's figure out what an inverse of this function is, right? Because if we're going to write this function, we will write this function as, and y, we can write as f of x. I'm not sure if you're familiar with f of x, right? You could write this as f of x. That means y is a function of x. Got it? It's just a terminology. Y is a function of x, okay? Now, if we want to do it inverse graphically, what we're doing is we're flipping the x and the y, okay? We're going to look at a function that is presented as... Let's do this in blue. I'm not sure how dark this is going to come out. That's okay. That's okay. Let me grab a better blue pen. I got about a whole bunch of new pens. So we're going to use darker, right? So let's assume this is our original function, which is this guy. Now what we're going to do... Hello, hello, hello, Spider-Man. Troll's a mastery for real. Some people do, right? So what we're going to do is we're going to look at this function, but flip it, right? We're going to look at a function that is x is equal to f of y, right? What we're doing is we're saying, hey, we know that y is dependent on x and this is what the graph looks like. What would happen if x was dependent on y, okay? And if we're doing that, what we're really doing is we're flipping this graph along the x, y, y equals x axis. So what we're doing is we have a mirror here. This is the line y is equal to x, y is equal to x. And what we're doing is we're flipping this function about this line, about this mirror. So we're grabbing this thing. Just imagine this function being on this line and we're going... We're flipping it, right? So what we're doing is the graph of... So what we're doing is the graph of x is equal to f of y is going to look like this.  As you touch a mirror, right? The mirror touches your finger exactly.  And that's what happens with inverse functions. Wherever you have the line crossing the y is equal to x line, mirror line, the function stays exactly where it is. And whatever is on this side flips to this side. Whatever is on this side flips to that side. So this guy comes here, that guy goes there, this guy comes here and that guy goes there. So what happens is let's try to draw this. We're going to draw this in blue, right? So we're going to draw this in blue. So just imagine, first thing you need to do... You need to use reference points to be able to graph it properly, right? Because sometimes it becomes complicated, right? So take a look at this thing. Let's assume this point here for this function. This guy was 0 and negative 8, right? So what you're going to do if you're going to flip around about the line y is equal to x, right? You had y is equal to f of x as this guy. If you're going to flip it into x is equal to y of f, what you're doing is you're switching these coordinates. So your coordinate here, this guy, is going to be 0, negative 8 and 0. So let's go about the same distance. So it's going to be here. Negative 8 and 0. Let's assume this point here was negative 7.5 and 0. So you flip it. This point here now becomes 0 and negative 7.5, right? And we can do this with all the x and y intercepts, right? So there's only one y-intercept, but there's three x-intercepts. So when we flip this thing, we're actually going to have three y-intercepts now, right? So let's find out what these three points are. Let's assume this guy would be, if that's 8, that would be 4, that would be 2. So let's assume this is 1, 1 and 0, and let's assume that's like huge. Let's assume that's 10 and 0, right? If that's the case, then our flip relationship now, because it's no longer a function, is going to be 0 and 1, 0 and 1, and it's going to be 0 and 10. Let's put it up here. 0 and 10. Now what we want to do is graph this thing. So this is the way this graph is going to look like. This guy is going to flip. So this guy is going to go here. Am I graphing this properly? This guy is going to go up here. So these two points are going to touch, and the graph has to go through here and go through there, and then it's going to hit that guy, right? So it's going to go through here. It's going to come out. It's going to hit this. Okay. Where is that guy going to go? Am I graphing this properly? Oh yeah, that guy comes here.  It's not to scale. Okay. Does that look legit? That looks pretty pathetic, right? But basically, this is what the graph looks like. I should have tried to do an inverse function of an easier graph to flip, right? So this thing comes here. It goes like this, goes like this, goes like this, goes like this, and comes out. Okay. That's what an inverse function is. We take a function like this and we flip it. Okay. It looks good, and that makes perfect sense. Okay. That's what we're doing. That's what it means visually. Okay. Graphically. Let's do it algebraically. Okay. And if you want to take a pic of this, you can just freeze the screen and take a pic of it, right? Now, we're not going to, you know, I don't know what the equation of this function is. I'm just going to give you a brand new equation, and we'll do two different ones. We'll do a linear one. We'll do, and we'll do a rational function as well. Like the every day since pandemic started. Okay. Let's erase this guy. So take a look. Now, what if we had a function that was this? And I hope we can use f of x. Okay. Because f of x is a sweet way to do this. Screen shot time. So take a look at this thing. Let's assume we had the following function. f of x, which is really just your y, right? But I'm not going to write y, because we don't want to run out of letters to use. We don't want to double up on things, right? Confuse things, right? Let's assume we had the following function. f of x is equal to 2x plus 5, right? And we want to take the inverse of this. Okay. Now, if we want to take the inverse of this, what we're going to do is we're going to flip this. Oops. I should get my spelling correct, right? Flip this. Flip this about the line y is equal to x, which means take the inverse of this. Okay. That's all it means. Inverse is just a short way of saying, flip this about the line y equals x. And we'll graph this thing as well, right? So if we're going to graph this thing, the y intercept, that's just a linear function. The y intercept is 5. 1, 2, 3, 4, 5. And the slope is 2 over 1. So 1, 2 over 1. So that's what this line looks like, right? Now, if we're going to flip this about the line y equals x, I see a great curve to me. Next one. So take... Oh, they're going awesome. So this is the line y is equal to x, right? So if we're going to flip this about the line y is equal to x, this is what we're going to get, right? We're going to get this guy. This point goes over here. And that point goes over there. And let's make this more accurate. This is what it looks like, right? We just took this line and went... And this guy goes... And the point where it touches stays where it is. But we want to find the equation for it too, right? So if we want to find the equation, flip these two things around. Now, remember, f of x is just y, right? So let's write y when we flip it. So if we flip it, we're going to go x is equal to 2y plus 5. And that y is this guy, right? But we don't write equations in terms of x. We write equations in terms of y, right? So we're going to isolate y. If we isolate y, you grab this guy, bring it over, and that becomes negative 5 is equal to 2y... Oh, sorry. x minus 5 is equal to 2y. And then divide everything by 2, right? So y is equal to 1 over 2, x minus 5 over 2. That's this equation, right? This point here is 0 and negative 5 over 2, which is negative 2.5, your y intercept. And your slope is up 1 over 2, 1, 2. My graph is not to scale, right? So we just found the equation of the inverse of this function, and we graphed it as well. Easy? Now, keep this in mind. What if the function is more complicated? Let's erase this and look at a more complicated function. Okay, if you want to take a screenshot. Let's do a more complicated function. What if we had the following? Is 2 over 5, right? I think so, it was, wasn't it? Yeah, you had to divide by 2, right? So you had x is equal to 2y plus 5. You grab this thing over and become x minus 5 is equal to 2y. Divide everything by 2. So y is equal to 1 over 2x minus 5 over 2. No, the intercept will still not be 5. Remember, the reciprocal of this thing, if that was the original function, right? 5 is the y-intercept, and then 2 over 1. And 1, right? That's the y-intercept for the original function. The original function was this. Let me rewrite it. y is equal to 2x plus 5, right? So let me erase this. Because we're flipping it right now, right? Plus 5. That was the original function, right? So if we flip this, remember the flip means we're flipping about the line y is equal to x. So if this guy was 0 and 5, it becomes 5 and 0 now. It's no longer the, it becomes 5 and 0 now. It's no longer the y-intercept. It's now the x-intercept, right? Now think about it this way. Here, let me kick it off to a function that is just points, not a line. So let's assume you have the following function. Let's assume you had a function that was just table of contents, right? x and y, right? So you had 0, 5, 3, 4, negative 2 and 0, 1 and 1. And let's go 0, 0. And we need a negative number here. Negative 3 and 5, right? So this is the function we want to take the inverse of. So taking the inverse of this function, it just means you flip these guys, right? So if you're going to flip it, you're going to take the inverse of this function. This new function that you have now is x and y, right? They're different x's and y's, remember, right? This guy goes here, 5, 4, 0, 1, 0, negative 3. And these guys go here, 0, 3, negative 2, 1, 0, 5, right? Oh yeah, this is not a function. We have to change this guy. Because I gave you the same x value and two different y's, right? So let's make this an 8, right? That means this guy will be an 8. And it doesn't have to be a function. It just could be a relation, right? So if we're going to graph these two things, right? I'm going to erase this. So let's throw both these functions on the Cartesian coordinate system, right? 0, 5, 3, 4. So 1, 2, 3, 4, 5, right? 1, 2, 3 and 4, negative 2 and 0, 1 and 1, 0 and 8. Oh, I still gave... I still gave this to you. I have to change this guy. So let's call this one 8 and 0, right? 8 and 0. So this guy becomes 0 and 8. Because it was still not a function, right? So this guy becomes 0 and 8, right? So 8 and 0. 1, 2, 3, 4, 5, 6, 7, 8 and 0. And then 5 and negative 3. 1, 2, 3, 4, 5, 1, 2, 3, right? So that's our original function. Now we're going to do the flip of it, right? So if we do the flip, it's 5 and 0. So this one that was 0 and 5, because 5 and 0. 1, 2, 3, 4, 5 and 0. 4 and 3. 1, 2, 3, 4 and 1, 1, 2, 3, right? So that point became that point. 0 and negative 2. 0 and negative 2. So that point became that point. 1 and 1. Well, if you flip this, that stays exactly where it is. What does that tell you? That point is on the line y is equal to x, right? It's on the mirror line, okay? I think my problem is that my... My mind, the function is 2x shifted by 5, which you then change to 1 over y shifted by that. I want to shortcut that instinctively. Yeah, you can't do it because that's not what it is, right? I realize what you want to do. You want to change only the... What do you call it? The slope of the function. But that's not the case. What is happening is you're switching the x and the y's. Wherever you had x in the inverse is now the y. Wherever you had y is now the x, right? That's really what's going on. It'll make it clear when we do a rational function. Take a little bit of rational function. Because rational functions, what happens with mathematics? For simple functions, sometimes we have brain farts and we make silly mistakes and we make assumptions, right? For more complicated functions, because your brain can no longer process it that fast, you have to slow down and then you see really what's going on, right? So let's assume we had the following function. Let's assume we had f of x is equal to 2x plus 5 over x minus 1, right? Now this is a rational function. We have an asymptote. We have an asymptote at x is equal to 1. Now we're not going to bother graphing this because we're just going to do it algebraically, right? Because whatever this function looks like, the inverse of it is a flip along the line y is equal to x, right? So all you have to do is graph this function and then flip it, right? Which is a little bit harder visually to do. It's better just to do it algebraically and graph the inverse function starting from the algebraic expression, right? But if we're going to do the inverse of this, what do we got to do? Wherever we see x, we put y and wherever we see y, we put x, right? And f of x is y, right? So for this function, so what we do is if we're taking the inverse flip, you can call it flip about y is equal to x, okay? So what do we do? We take f of x and call it x and we take all the x's and call them y's, right? Cool. What's the name of the game now? The name of the game is we've got to get y by itself. We've got to get the y's by themselves. There isn't two y's, there's only one y. They just happen to be in different places in the equation, right? So we've got to mess around with this thing algebraically. So first thing you're going to do is you're going to grab this guy, cross-multiply it up, right? So this becomes xy minus 1 is equal to 2y plus 5, right? Now we've got two different y's in two different places. We've got to bring them all over to one side, right? Now first thing we're going to do is we're going to multiply the x in. So this becomes xy minus x is equal to 2y plus 5. Then bring all the y's to one side. So xy minus 2y and take everything else to the other side. So we're going to grab this, bring it over, and we're going to grab that and bring it over there. Is equal to 5 plus x, right? How are we going to get these two y's to become one y, right? Because this is xy and that's minus 2y's. We can't combine them because this has an x, this doesn't. But what we can do is take out a GCF. The GCF of this is y, right? Factor, right on, right? Rasta, Rastapec, right? Factor out the y. That's what's common between them. So you take out the y. Y comes out, you've got x minus 2 left, and I'm going to rewrite this as x plus 5. Cool. To get y by itself, just divide by x minus 2. Divide the whole thing by x minus 2. So now you have y is equal to x plus 5 over x minus 2. This function is the inverse of this function, right? That's just what happened. Now, is this a different function than that? Yeah, most definitely. Take a look at this thing. The 5 state where it was, the 2 is gone, and instead of being x minus 2 in the bottom, x minus 1 in the bottom is x minus 2. It's a different function, right? And this graph is going to look different. That's what it means when you take an inverse function. Graphically, you're flipping about the line y is equal to x, which is basically a 45-degree line coming off the x-axis. It's a mirror. Algebraically, you're switching the x's and y's, replacing the x's with the y, and replacing the y with x, and then isolating the y. You can do this with quadratics as well. You've got to do a complete square. So you've got to complete the square and then flip it, and then switch it. You can do this with any function. Now keep in mind any function that you have, if you take the reciprocal, like the first one we started off with, when I drew this thing, and then we took the inverse, and it looked like this, right? The inverse isn't necessarily a function. It could be a relation, but it's not necessarily a function. So for example, one of the most common types of functions you get, take a look at this thing. I'll show you this because it takes us from a quadratic function to a rational function, right? So you're okay with this? I hope. Session seven. Do you have any questions regarding this? I feel like I'm gaining IQ by this. Nice. Look at this thing. We'll wait until session all good, man. All good. I've got my matcha here. Super delicious. Check this out. I'll show you my snack. My partner made vegan banana bread with chocolate and walnuts, and I got homemade blueberry and blackberry jam. I'm just dunking it in and having a snack, okay? Now I'm going to erase this and I'm going to show you something else. It's really good for the brain for sure, session seven. And there's a blast from the past. It's the same question, right? We just did it, but I'm going to show you something else as well. Watch this. Take a look at this. I hope you guys are getting sunshine. All my math, geometry teachers were enthusiastic about teaching and the others were, well, were hating their life. I wonder why. Take a look at this thing. Let's assume we had a quadratic function. We had y is equal to x squared plus, let's make it plus five again, right? So this is a parabola and the parabola looks like this. Y intercept is five, one, two, three, four, five, and it just opens up, right? It's a simple quadratic. Now if we want to take the reciprocal of this thing, we'll go this. That's the line y is equal to x. Let's make it darker so you see it, right? So what we're going to do, we're going to grab the same goal, right? So this guy just goes like this. So the reciprocal looks like this. One thing I've definitely missed since leaving school is doing math every day. Yeah, Connor, dude, for me, when I got back into teaching mathematics, I had to relearn all this stuff and I realized what I was missing. It just gave me an amazing perspective on everything, right? Sending a time out to the sun. So take a look at this thing. So this guy, this coordinate here is zero and five. So if we take the reciprocal, zero and five, we take the reciprocal, we flip it. The x and the y flip, right? So this guy becomes five and zero. One, two, three, four, five and zero, right? And this guy just goes phew. So this part goes here and that part goes there. So the graph looks like this, right? Now this isn't a function, it's a relation. This is a function because for every x there's only one y, but this is no longer a function, right? So what we end up doing is this. We represent this as just the top part if we're talking about functions, okay? Smith, Havre. Reciprocal is the multiplicative inverse of a number. That means that for any x, the reciprocal x to the power of negative one, it is the number such that x times x to the power of negative one is equal to one and x to the power of negative one. Yeah, and there are functions that the reciprocal is the original function. Like for example, just imagine if you had a line that went, it was just y is equal to x, right? So let's assume you were trying to take the inverse of y is equal to x. So switch the x and y. If you switch the x and y, you get x is equal to y. Well, that's the same thing as y is equal to x. So the inverse of this function is itself, okay? It looks exactly the same. That's the simplest one because that is on the mirror line, right? Are we fans of summer around here? I live in Texas, so I'm not. Yeah, I'm a fan of summer. In Canada, everybody's a fan of summer. Almost everyone anyway, right? Now take a look at this thing. Let's take the inverse of this algebraically. If we take the inverse of this algebraically, we go x is equal to y squared plus five. Grab this guy, bring it over. x minus five is equal to y squared. Square root both sides. So y is equal to square root of x minus five. This is the inverse of that, right? This is a radical function, right? And the radical functions in general, exponential functions, not exponential, quadratic functions look like this, right? Rational functions, yeah, radical functions look like this. So they usually eliminate this part because they want to make it a function. So they represent this. If you're going to define the inverse as a function, you're going to kill this part. Because in general, sometimes you kill the top part. It depends on the function you're working with. Okay. Grab not me. I'm an autumn guy. For your information, I have a friend in San Antonio, I think, SA. Autumn is beautiful too. The seasons are amazing. But for me, I like summer. I grew up in a desert, so I miss the heat, miss the sun. It's brilliant. Hey, glad you're around, Chicho. Awesome, Lark. How are you doing? I'm in Australia heading into winter. I don't vlog. That's funny. Love when you do math. Me too. I love what I do math too. And this is fun, explaining the inverse function. In my part of the world, just so you know, they start encountering this in grade 11, grade 12. Okay. 16C is not winter. No. Here, we're actually... Yeah, we're about the other guy. We're almost the same type of weather as you guys in the UK. We've got a lot of rain and a lot of rain. We've got lush green and stuff. Because it's F. Because if X is greater than 5, then you take the square root of a negative value. And we are no longer in the XY coordinate system. Yeah. But it's not necessarily the reason that's not why we kill the bottom.  Because if we have this, right? If we do a vertical line test, right? For a given X value, let's assume X is 8 here. If X is 8, then Y can be this or this. The definition of a function is, for a given input, you can only have one output. For a given X, you can only have one Y. So it no longer becomes a function. It's a relation, but it's not a function. I'm from Swiss. What's up? True. Winter is perfect here. 20C days and 10C nights. Nice. If X is less than 5. If X is less than 5, you're here and it's not a function. Right? If we put X is here. For this, if you say X is equal to solve Y for X is equal to 4, right? So you're going to go Y is equal to square root of 4 minus 5, which is the square root of negative 1. That doesn't work in the real number set, right? It's non-existent. When X is 4, it doesn't work. It is exciting, especially. Math and the irony is that I can't stand math growing up, but I've learned to appreciate it. Yeah, I love mathematics until I got some bad teachers and they took the love of math out of me, right? And then I stayed with it in university and I took it and I appreciated its power. But the passion wasn't there as much as it is now, not even close, right? Do they teach complex numbers in high school there? Oh, dude, Smith, they used to. When I went to high school, they taught us complex numbers, right? And then they took complex number out of high school education here like 20 years ago. More than 20 years ago. Yeah, more than 20 years ago. And they just gutted the high school education system here to a level where it's a pale reflection of what it should be. Really, it's sad. Okay. 45 minutes. We did a lesson on inverse functions and it took us 45 minutes. That's not bad. Can you show the trick for dealing with fractions like 3 over 4 divided by 6 over 7 or something? Yeah, sure. Cool, man. I'm a few hours north of here recently moved here from Canada. Ah, session 9. You went to UK from Canada. I learned complex numbers in high school. I think most of our kids learn them to these days. Do they teach complex numbers where you guys are grabbed? They don't do it here anymore. Sucks. Smith, me too. We learned it quite early. You can extend your functions to complex numbers to keep functions functional continuity. I don't teach so I've totally lost all that ability. I would have to review everything, relearn everything. Especially algebra and long division. Brutal for me, but luckily during my college years, that all changed. You should teach us some basic proofs. Certain proofs we can do. She moved from UK. Can you explain triple differentiation in my university exam next week? No. Actually I can do triple derivatives of just polynomial functions. Those are easy, right? But let's do dividing by fractions. Speedy Gonzales style, right? So take a look at this thing. There's two ways you can write division. Three ways, really, right? I could say two divided by five. I could say two over five, like this, slant. Or you could say two divided by five, right? These two are the most common, right? Writing math when you're doing it by hand. And you see this when you're reading textbooks and stuff like this. They can put it all on one line, right? Now what if we had a fraction divided by fraction? What if we had two over five divided by three over four, right? Now this becomes a little complicated to deal with, okay? So what we end up doing is using this symbol to represent it. So this is really equal to two over five divided by three over four. And when you write something like this, when you have something like this, all it means is change this to multiplication and flip the number afterwards, right? So this really becomes two times one over five. So for this one, when you have fraction divided by fraction, the top one you write exactly the way it is. You change the division to multiplication and you flip this guy. So this becomes four over three, right? Now one mantra, wait, I understand this. So one mantra that I always tell my students is, reduce before you multiply. And reduce before you multiply means if you have fractions, anything from the top can kill anything from the bottom, right? As long as there's no plus and minus between them. Now there's no plus and minus between these, but nothing from the top kills anything from the bottom. So all you got to do is just go top multiplies top, bottom multiplies bottom, eight over 15. That's what that divided by that is, right? Now what if you had something more complicated? But why? That's what I want to know. Why does it work that way? Because division is really multiplication, right? And multiplication is really addition, okay? So take a look at this thing here. I'll explain to you why this is. Evening, Jijo, evening, Jijo. Dramatou, how are you doing? Take a look at this thing. Why this is the case? So when you're learning mathematics and, oh yeah, you want to take, here let's do triple differentiation. Let's take a third derivative of a function. We'll take a third derivative of a polynomial function and then I'll show you what this is, right? So if you take the third derivative of a function, and I'm just going to do polynomial functions, that's all I know, right? Five x to the power of four minus two x squared plus five, right? If you take the first derivative, this number kicks down, right? And you reduce it by one. So five times four is 20 and that becomes x to the power of three minus. This number kicks down four and reduces by one. So it becomes x to the power of one. A constant becomes zero. If you take the second derivative, you do the same thing. This number kicks down, so it becomes 60x squared and that's just the one. One kicks down minus four and reduces x to the power of one to x to the power of zero. So it's just one. If you take the third derivative of it, this number kicks down. It becomes 120x and constant becomes zero. So the third derivative of this guy, the third derivative of this guy is that guy, right? That's all you're doing. Just draw it over, draw it over, draw it over, draw it over. That's all. As for why you flip, why you flip, take a look at this thing. When you first learn algebra, you learn about addition and then they usually teach you subtraction and multiplication and division. I like teaching it as addition, multiplication, subtraction and division. So first thing you do when you're learning algebra, you learn about plus, minus, multiply, divide, right? You learn about adding, subtracting, multiplying and dividing. Now keep this in mind. You don't have four different operations here. You only have one operation. All of these is really just addition, okay? That's all it is because the formula tells me to. So you don't really have all these guys. These are just shortcuts, I guess, if you want to think about it that way, right? Because subtraction, if you go 2 plus 2, you get 4, right? If you go 2 plus negative 2, you get 0. So you don't go plus a negative number. You go 2 minus 2, which is 0. That's your minus sign, right? If you have 2 plus 2, plus 2, plus 2, plus 2, you get 1, 1, 2, 3, 4, 5, you get 10.  So all you got to do is you flip, rotate the addition symbol to 45 degrees and you go 2 times 5 is 10. So it's a quick way of doing it. Division is the same thing, but all you're doing is you're taking a number, dividing out, subtracting out these things, right? So if you want to think about division as version of multiplication, but you're not multiplying by a multiple, multiple numbers of the same thing, you're dividing it out. So if you had this, right? If you're going to divide by something, let's assume you had 10 times 1 over 2, right? If you have 10 times 1 over 2, that's equal to 5, right? Now, one thing you can do is say, well, that's the same thing as saying 10, top, multiple, top, bottom, multiple, bottom, divided by 2, right? Which is 5. Now, one of the symbols that we have for division is 10 divided by 2, right? So the division really becomes, changes to multiplication and flip this. That's 2 over 1. It becomes 1 over 2, which is 5, right? I'm not sure if I went through the whole process of explaining it properly, doing the jumps, but that's basically what it is. Division is really multiplying by fractions. That's all. That's all division is. Multiply by fractions. And I'm going to put out a series. I've already put out the videos regarding counting, adding, and multiplying. And this summer I'm going to complete that set of preliminary videos we're going to put out, how to do simple mathematics, how to do addition, subtraction, multiplication, and division. I'm just going to complete that module, early childhood education, or early math education, really, right? So there is a couple of videos coming out, which I'm going to go into this in detail and just really crunch it down and cover all the angles with it. But that's all it is. If you're multiplying by a fraction, you're really dividing by the... what do you call it? The inverse of it, right? Does not equal... No, it doesn't. Okay? No, it doesn't. That's the reason why I said I didn't really explain it too well, right? Because I connected it up to multiplication, which is really what you want to do. Apologies if I didn't explain it well. I have good days and bad days, and this one I haven't really... I haven't worked on trying to explain it properly from the base down for a long time. That's why I'm going to wait until the summer so I can fill in the gaps for it, right? Because I always connect up division with multiplication, because division is really a fraction, multiplying by a fraction. Chi-cho is my math... Chi-cho is my math situations. I'm always looking for 100% or a whole. Is this a normal protocol to basic math? No, 100% or a whole. Oh my God, what do you mean? It's my math situations. I always look for 100% or a whole. Is this a normal protocol for basic math? So you're trying to get 100% on everything? Is that what you're saying? Divide it, divide it, divide it, yeah. Thanks, Smith, by the way. Please do complete the simple math videos. I'm trying to teach for you. Yeah, session 7. Initially, when I started doing the math stuff, I decided to start with the real number set, but I've had so many people over the last few years come to me to try to teach their kids in elementary school. The youngest now I've started working with is basically eight years old, right? And one of the reasons that's happening, I've been dealing with the problems of kids coming out of elementary school. Like, when kids come out of elementary school, man, they know zero mathematics in general. It's horrendous. So in grade 8, they're like, what do you mean multiplying by fractions, adding fractions? They don't know anything. The reason they don't know anything is because elementary school is not teaching them anything. So I've been dealing with that for two decades, but the last five long enough, five, six, seven years, really, I've had a lot of parents contact me and say, hey, can you teach my, because I've worked with their siblings that are in high school, can you teach their brothers and sisters that are in elementary school and start working with them? Wow, what a disaster elementary school is. Total disaster. Wait, do you have math for year 10s? Dehilo, year 10s. I'm not sure what that means, year 10s. I do teach 10th grade and I work with students that are 10 years old, yeah. That's the problem with the way math is taught. As a controlled protocol, like getting fractions to decimals. Oh, as a controlled protocol. So converting from fraction to decimals. Yeah, they don't do that well. It's horrendous, like Elder God. Man, the way basic algebra is taught is so problematic, so problematic. For someone that knows the power and we all know how smart kids are, right? And what they're capable of doing, watching kids struggle with basic concepts of mathematics is extremely frustrating. Extremely frustrating. Yeah, because X to the power of negative one is one over X. Yeah. I'm so excited to show my kid your math videos. It's going to be exhilarating to learn with him and show him your awesome Spider-Man. And really, as a parent, I can honestly say if you have to learn with your kids as you are teaching them, it's essential because the education system is not going to do it. They're going to fall behind and you have to jump on it right from the get go because if you try to help them out in grade 10 or grade 11 math and you haven't learned with them along the way, there's going to be serious problems, right? Yeah, I don't trust the school system. That's why I'm going to teach her in addition to the schools. Yeah, that's what I would highly recommend. That's what I recommend. And keep this in mind by the way, session seven. Parents have a hard time teaching their kids. Really, I've had students where both the parents, the mother and the father were high school math teachers. And I was teaching. I was tutoring the kid in math, right? And this wasn't a one-time situation. It was the only one where both the parents were high school math teachers. But I've had parents, I don't know how many parents I've had that are math teachers, but they send their kids to me to teach in mathematics because the family dynamics doesn't allow the kids aren't really receptive to learning math from a family member. And I've encountered that myself because I had family members that I tried to teach mathematics to and they weren't as receptive as my regular students were to mathematics. I should have hired someone to teach a math tell you the truth, but I couldn't find anyone. There wasn't very difficult to find good math teachers, math tutors. So... Elder God, I'm seeing my nieces soon and it's an emergency for math to teach math. How old are they, Elder God? How old are they? If you're seeing them, if they're struggling with math, let us know, okay? And we'll set up specifically math streams for elementary school kids and we'll just say simple mathematics, help them out and explain them in a certain way. I was a substitute in private school and it was bad, Hannah says. I think part of the problem is that the parents parent their kids poorly and the schools aren't evolving with the times. Yeah, the schools are definitely not evolving with the times and parents, they're overwhelmed, man. That's the problem. Our current political economic system overwhelms people. UK schools are even worse. Canadian isn't that good, man. I can only imagine what public schools are like. It's not about public school or private school. It's about the teacher. I have students from both private and public and home school and special ed and people on the spectrum and stuff. All of it, right? I can honestly tell you, I have parents that have sent their kids to school that pay like $30,000 a year for high school. Like, oh my, what in the world are they thinking? And I've had parents that send their kids to public school and the kids are on the same level. It's about the teacher. It's not about how much people are paying to go to school and it's not about how much they're not paying for the kids to go to school. It's about parents becoming proactive in their children's education and the type of environment to grow up in and social settings. There's a lot of factors at play. And also schools don't discipline students enough. They let go too much. Possibly, discipline for sure, I believe in harsh discipline. I don't. The problem with our centralized education system right now is one of the main problems is class size, right? Huge. You need personal care where you're trying to educate generations coming up. You need that. That is the most important asset of any civilization that is a cliche, but it's your kids. The most important asset, ask any parent what is your most precious thing in life? They'll say, my kids, right? A society's answer should be the same. What is the most precious thing for any society, any country, any community? It should be the kids, right? But it's not. Based on the current political economic system the most precious thing that people consider to be the most important investment they have in their lives is their home, right? It shouldn't be. The most important investment in your life is your kids. You should be investing in your kids, period. End of story. Nothing else even comes close. Nothing. Also schools don't... I'm concerned. I'm very clever. I'm considered very clever and I can do math. I know easily in my head, but I can't articulate it to people. Yeah, Elder God. For me as well, when I first started teaching I tried to find a way to explain some of the things I knew. But the reason I really didn't know how to explain it was because I didn't really know why the mathematics worked out that way. Even now there are times where I try to take a step back and try to figure out why do we do this, right? And I'm amazed as to what I find, right? And trying to... Teaching is difficult, really. I didn't realize... That's one reason I really got into it heavy is because it was extremely challenging, right? It was so challenging that I was like, wow, this thing's like getting me pumped, right? What else can you want out of life other than getting something that excites you to do, right? Session 7. I haven't considered that she might not want to learn from me. I'll keep that in mind. Yeah, session 7.  It's not the knowledge, okay? It's the dynamics of the parent and the child. Okay. Smith, if we write x to the power of negative 1 is 1 over x for multiplicative inverse, we could, but won't, don't write x to the power in the subscript for additive inverse. Ah, that's cool. I've never seen that, Smith. The problem with the initial and that was that the first 2 in the string of subtraction was a negative additive inverse. I got to look into that more, Smith. Was it negative additive inverse? Was it negative? That's what it was. It was a positive 2. Boom. Thank you for that. Yeah, I wrote it down. I want something that's not meshing well, so I jumped to the multiplication, right? Ah, thanks for that. That's cool. The little nuances, Smith, eh? The little nuances. Brilliant. Brilliant. Gram. It doesn't have anything to do with discipline. It has to do with compassion. Gram. I agree with Gram 100%. It has to do with love. Krishna... By the way, I've mentioned this before. I'll mention it again. The most important book, the most important book, any parent, any educator needs to read is Krishna Morty's education and the significance of life. It's hard to really get a grasp for what he's saying until you finish the book. Okay. When I first started reading it, his main thesis, his main statement there is, we, us, adults, parents, society, we do not love our children, right? And as soon as he starts saying this, I'm like, what is he talking about? We don't love our children. And then he goes about explaining in a short little book. It's a very quick read. You could read it in one day, right? He goes about explaining. I took a few days because I was taking notes and I was thinking about what he was saying, right? And I've read it like three times so far. He goes about explaining what he means by, we don't love our children, right? And the main thesis is, we send our children to centralized institutions that are horrendous to try to educate them about life and how to live their lives and who they are, which obviously the central education system doesn't. What kind of a society does that to their children, their most important asset, right? Hence, we don't love our children. It's powerful, important read. Session seven. I'm with you regarding investing your kids, Chicho. I retired when my daughter was about one. One. So I could refocus my attention to her, leaving her development to strangers while I sat in the office all day was doing, was doing my head in. Yeah. Session seven. I like really, I don't have any kids, but I have family members that have gone through the education system. And I've cringed. I've had to go to school. I've sat in a room with the principal and the disciplinary people with family members in the room. And they were like interrogators. There were like police officers, FBI agents trying to fish for words coming out. And there was one time where they were digging and I put my hand on the family members knee and I prevented him from speaking because they were setting a trap for him. Unbelievable, right? Like, if I wasn't a calm, cool person, I would have gone up, flipped the table and thrown them out of the window, right? For putting a child in that situation. Unbelievable, right? Absolutely disgusting, right? No, I don't. Wasis. Elder God. Wasis. Yes, we are all Chichonians. Some of us might not be his children. It's a community. We are a community. That is 100% for sure. And personally, I'm very, very grateful for it. Can someone calculate my name? 12 Musk. I have no idea. Elder God might be able to. He's very good at deciphering. Very good at deciphering, right? Fantastic at deciphering things. I'm going to have a little bit of vegan banana bread with homemade blackberry and blueberry jam. I'm going to pop. Take a look. With coconut flour. Coconut and whole wheat flour. With walnuts and chocolate chips or chocolate chunks. I got to remember. Not to set up a stream.  That's one thing I've learned in my old age or middle age, I guess. Look, if you're young, do what you need to do to experience life to the best of your abilities without taking yourself out of the game. I've seen a lot of people take themselves out of the game. Especially in their 20s. Even teens. Like my first funeral I went to. I was in grade nine. One of our friends. Done. So we go to a funeral. I've seen a lot of people take themselves out of the game in their teens and in their 20s. So don't take yourself out of the game. It's a beautiful ride. Stay in the ride. Do what you need to do to experience life. But as you grow older, realize that this is a machine that you have. You have to feed it good fuel. By feeding it good fuel, you become just physically healthier and mentally more stable and emotionally able to deal with life throws at you. Food is a huge part of that chemistry. And it is chemistry. You're taking this in, your body breaks it down, turns it into fuel, feeds your body. So eat healthier as you grow older. Very, very important. Legendary Rob Boss. Baking nuts in bread ruins nuts for me. I like my nuts crunchy and all that moisture in the bread softens it too much for my taste. It's why I don't like nut bread. One of the things Iranians do is, and I do it as well and I've shown you guys this, I soak walnuts and almonds. And what that does, it makes some moisture.  But what it does, it makes it easier to digest. So that's important. Some people can eat walnuts or almonds if they're not soaked. And I don't mind them like this. It's yummy. Math was always my favorite subject. I loved being presented with the problem and enjoyed the process of working it out. I loved the satisfaction of finally cracking something I'd struggle with. Math is fun to make. Yeah, Connor. And I tell you truth, I felt that way until I hit grade 12. When I hit grade 12, I had a crappiest, most brutal, horrendous math teacher ever. I couldn't believe this guy. The guy was just writing it out, right? And he took the fun of math out of me, right? To a level where I almost considered not going into the sciences.  And then I took a sort of a year break or something like this and then I went back into the love came back to me, right? Teachers are extremely important. And that's the kicker, right? When kids go to school, there might be a time where they have amazing, amazing, amazing experience and they have one bad teacher that just destroys them, right? You have no idea how many students have had that one teacher ruined their education prospects, right? And one of the jobs I have is to bring that love back into their lives, right? I feel like walnuts hold up. I guess walnut isn't so crunchy to begin with. Walnuts hold up for sure in the baking. And walnuts are very oily as well. So it's not that innate ability, learning, alternator, innate ability. We're wired to learn. We're wired to do mathematics. Nate, how are you doing? I'm doing well. I've only had one good math teacher. The last two I had were harsh and I couldn't understand them. Their English was unacceptably bad. New Year's Eve, 1971. New Year's Eve, 1971. Elder God, that's your birthday. New Year's Eve, 1971. December 31st. Is that what your birthday is? I'm back. Sorry. Cool, Leo. How's it going? I had to mute stream for a bit. Hope I didn't mess too much. Good math. We did a good inverse. Sort of took it from the beginning and explained that to the best of my abilities anyway. Well, let's say above 80% of my abilities, 90% maybe. I'll have to really look out at see if I skipped any main parts. I really want to homeschool but I don't want to take away the social aspect and making friends that comes with school. Thoughts you show. I personally, I can honestly tell you, if I have kids or if I had kids, I would send them to public school. Because in public school they'll encounter every type of social setting, every type of person within reason. I would never send them to private school. I would send them to a public school because those are the people that they're going to encounter in the real world. I don't want them growing up in a bubble. But I would supplement their education, either teaching them myself the subjects I knew, and if the dynamics didn't allow that, I would hire someone to teach them. Supplement their education, but I would definitely send them to a public school. Because those are the people that they're going to encounter if they plan on living in any city or anything like this. So they need to be able to know what's out there. The good and the bad. I'm not one to cradle kids. You got to show the reality of this life to children. The good and the bad. Really. Family members. I can honestly tell you, I've taken family members out into downtown at three o'clock, four o'clock in the morning to skateboard to just kick it. Two o'clock in the morning when they were in high school. Because they wanted to go experience that. So I took them there. And there were some amazing times where they came out with me and we took snacks and we'd go to a major skate park. It's like the old timers, the hardcore people, doing whatever they're doing in the corner. They're doing some professional skaters doing their stuff. We'd go kick it around downtown in the streets that are empty. And let them ride. I made myself a little skateboard that I took the wheels and made it a low rider because I wasn't into doing tricks. I would just ride around with them. And I would just go out with them and let them do their thing. Experience life. Cool. He was born at the dawn of a new year or since he's an elder god at the dawn of mankind. Well, now it's mostly online classes depending where you are. And those online classes, I have some students that are taking their online classes in school. They're brutal, man. There is no online class really. They don't care. They're not really learning. They're just filling the dots and checking the boxes. They're being sent homework bare minimum. And it's not really education. It's a make work project for them and just check in. It's not a good system. This system doesn't know how to do it. Elder God, no. Just breaking down that guy's name. Oh, you're breaking down that guy's name? Check it out. What's this? New Year's Eve 1971. What was the guy's name? Let's check this code out. 12 months. How did you do that, Elder God? How did you do that? What? I'm going to write down his name. You tell us. That's code. That's cool. Let's check this out. Where's the guy's name? X-A-E-A-A-E-A underscore 12 Musk. 12 Musk. And this is New Year's Eve 1971. How? Oh darn. There goes my backstory. It's only a first attempt. Could be wrong. Okay. Better than my attempt that I can't do that. Is this Roman? I'm not sure what A-E-A stands for. He could be goofing around, but it could be code as well. For sure, Graham. I'm going to send my kid to school for the social education, but then keep track of what she's learning and teaching myself. Yeah. As well as keeping tabs on their friends. For sure. There's some people that have some issues in the world. Exactly why I haven't pulled them for homeschool. Yeah. Wasis. Isn't his name just that silly Allen Musk name? Is it? I don't know. 12 Musk. Musk explained the name on Joe Rogan's experience. If that's what you're wondering, did he? I think that's what Allen Musk named his son. Did he? Oh well. I like Elder God's interpretation better. Yeah, that's Allen Musk's son's name. Is it? Or the alphabet representation? I would never name a kid that. Why? Let the child grow up without these preconceptions of who they should be and playing games for them, right? X, Ash, Angel is how it's pronounced. X, Ash, Angel. Okay. We'll take it down. We don't care about that. Allen Musk's child hopefully grows up well. Yeah, silly. Salut, gang. Matcha. The date was interesting, yeah. How did you get the date? 1971. 1971. Quiet today, it's good. Stereotype 41. I think social education aspect of school is overrated. I guarantee kids can pick this up naturally. And school isn't the only way to achieve this. I learned so much more outside of school, interacting with people from more diverse backgrounds. And it really depends where you grow up, right? Which school we're talking about. Like, I'm in Canada. The high schools here aren't as crazy as some of the high schools in the United States, right? Even though they're becoming worse and worse. Okay. And I would, personally, I would talk to the kid. Ask him if they want to go to school or if they don't. I think it should be left. Yeah, this is matcha. Matcha is just tea ground up from where I understand. And then you just make it. It's tea, ground up tea. So you get all the antioxidant stuff. But personally for me, regarding school, ask the child. Does the child want to go to school? If they don't want to go to school, then start giving them a set discipline.  Kids need discipline. Kids need direction. Kids need participation. Kids need, what do you call it, a collaboration, right? Everybody needs collaboration, to tell you the truth. But I wouldn't let the kids do anything they wanted to do. I would give them direction in what they wanted to do and help them out, right? So they're, you know, they could be kids that don't want to do anything. That's not acceptable. Okay. They need to learn, right? I've come across people where they say, you know, they don't, anyway, I won't go there. No, any cool gravity equations? Oh man. Coolio, I did a lot of gravity surveys as a geophysicist, but I don't remember the equations. And the instrument, the gravity instruments are very sensitive. So you lay down the gravity instrument and you set your stuff. You take the measurement and you move along and you take gravity measurements along a certain area. And I've processed a lot of gravity, aerial gravity surveys and stuff like this, but I don't remember the equations. This is 20 plus years ago. Just basic alpha number code. Is that what it is, Alpha God? Okay. I'm in Canada as well. How's your day going? Going well, Robson. How are you doing? Robson Bailey. And welcome to chat. 1% of our most worth is that much. Net worth doesn't mean he has that amount available. No, it doesn't. Paper. Kids need structure. Kids need structure. 100% agree. I do not like billionaires. I don't know. Spider-Man. Nate, I went about it differently. XAEA12 Musk could be written as XA13 to the power of 13. If A is Ploff's A constant, E is the base of the natural logarithm. M is missiles, melt-ins constant. Mu is Ramajan, solder's constant. Omega is Hafner, Sarnak, Kirkury constant. K is Spinkolski's constant. Then his name is something like 3.96 times 10 to the negative 11. Times what? Wait a second. Times the inverse of the name is negative 0.9999. Hilarious. kids need active participation in their lives, 100% ground, they need to interact. Elon Musk is just another egocentric maniac out for power money. I don't spend too much time thinking about Elon Musk or any of those people, right? I would argue he's not egocentric, but I do agree that he is turning out to be just another greedy capitalist. Coolio? Yeah, right? Power, right? And I definitely disagree with them flooding the skies with satellites, right? Why do we need NAS when you have computers? Who created the computers? What can you do with them? Computer is just a machine. If you don't understand what the machine does, you know nothing. And that's the situation many people are in, right? Because our political economic system is just a machine. They don't know how it works, so they know nothing, right? In essence, they are slaves to the system, right? Learn your mathematics, get your freedom, stereotype. I wholeheartedly agree about asking kids if they want to go to school and also completely agree with giving them some type of structure. It depends on the kid. It depends on the kid, right? And feed their curiosity. Do not force them to live the 24-hour cycle time. You know, kids need a lot of sleep. They're growing their bones and stuff like this. But if they want to, you know, go out in the middle of the night and experience the evening life, go out with them. Show them, right? That's what I did anyway, right? And I think I did good. I think I did okay. We have to know how to program those computers, yeah? Robinson Bailey, thank you. Well, family as well. What more can one ask for? Nothing more, man. Tyrion Snow, okay. But your average person doesn't need math, right? No. The average person needs math more than anybody else, apart from those who build it. Nope. No. You need to know math. Everybody needs to know. If you're not literally, it's like saying the average person doesn't know how to read. That doesn't need to know how to read and write 100 years ago, right? The average person needed to know how to read and write because the average person, they're gonna grow older and older and technology is gonna progress and all of a sudden they're gonna blink. They don't know how to read and write. How are you gonna get on a computer and do searches, right? I disagree that kids need structure. Kids need active participation with their lives. Structure is oppressive. I don't agree with that necessarily. It depends on the structure. I don't think this should be jailhouse structure, but it should be some kind of structure where you're saying, okay, we're gonna have dinner together. Let's have, let's cook together, right? Agree. That's part of the participation, but that is some kind of structure, right? Kids should be free to pursue their own interests with an active facilitator to help contextualize the things they're learning in that process. Some billionaires are okay in Spider-Man. Do you go to the store? You need math to put, not overspend. Do you pay taxes and bills? You need math. Math is important in every field of industry. And in just problem-solving, it's the most incredible problem-solving tool we have. That's the reason we came up with it, right? This is a fun question. Can you recite Pi off by heart? No one can. Pi goes on forever. Math is different than counting through writes. I disagree with that. I think being a billionaire is unethical. I disagree, Graham. It depends what you do with your billions, right? And that's not, to me, that's not a definition of wealth. Like, it's like saying, I disagree if somebody has too many friends. No, maybe there's social creatures, they need lots of friends, right? To me, the definition of wealth is not a billionaire. That might be Wall Street's definition of wealth. That might be confused people that have defined what wealth is. They don't know what wealth is to them yet, right? To me, wealth is many other things. Yes, but I was more just trying to use widely relatable complex. Cool you. I was just playing with you. Tyrion is not crazy, though. People need basic math, but things like functions transfer transformations. I spent over a decade as a professional scientist, and the only time I really used a lot of complex math was in those lecturing to the uni kids. And here's a kicker session. But your knowledge was there, right? By understanding functions and variables and how things are related and how things affect each, each, each other, each, each system, you had a better understanding of the connections in our world. I find that people, if you're not literate in the language of mathematics, I don't want to say I find people don't know it. There are people who understand how things are connected in the world, but once you know mathematics, you can really have a better understanding how things work.  You don't need to know mathematics and physics and science to appreciate this flower. And Feynman's response was, no, you do not. But if you do know it, then you can appreciate it more in depth, right? You can appreciate its beauty, its aroma, right? That it grows and it's surrounding the stuff. But you can appreciate it to a level that someone that doesn't understand doesn't have that knowledge, right? So I think the more you know, the more you can appreciate things, right? There was a point in my life, Smith, there was a point in my life. There's a point in my second year of university when we revisited all the arithmetic algebra and such that we ever learned and were taught that it was all a special case of much broader and more abstract mathematics. The vast majority of what's learned in high school is applicable to the real world, but mathematics is an abstract language to explain logic. Logic is the language of reasoning. Nice. Elder God. 314. 6. Nice. Yes. But if he asks the specific question of function transformation, sure. But he was saying math in general. Cool. Agree? Agree. Cool. Yeah. It's all I know. Now fact check if I was right. It's all I can currently remember for Pi 3.14156. It's 159. Just Google it. Dr. Goet. Dr. Goet might have the more accurate uncensored response overall was fact checking one two. Himrio. Mirio. Mirro. I gotta start calling you Mirro. Mirro. How are you doing? Chicho. I am good at math. But whenever I look at these majors, majors jobs out there, most of them deal with coding, programming, and from my past experience, I'm not that good at it. Any idea on jobs that will require math in it, but not as much coding. Teaching is the only subject I'm aware of as of now. Geophysics, it doesn't require coding. You do a lot of interpreting. Okay. So as a geophysicist, you take data, you collect a lot of data, you require a lot of data, and you run filters through it, and you run programs through it, and you look at different types of equations, and you can create models for it, right, to interpret the data. You do seismic refraction, radar reflection, and stuff like this. So geophysics has a lot of that. Hydrogeology has a lot of mathematics in it, or it can have a lot of mathematics in it. Stock market, investing, trading can have a lot of mathematics in it, or it does have a lot of mathematics in it. In banking, create multiple different types of derivatives and throw them out into the system and let people gamble away, right? Aside from that, there's got to be lots of engineering in general, would have a fair bit of mathematics if you're doing it, right? Catholic tradition, a structure can be oppressive at its worst, but it can be enabling and even empowering at its best. Yeah. It all depends on how you do it. I agree with Catholic tradition. So structure is just a tool, right? Coolio, chicho. I've been meaning to ask this in a math stream for some time, although it would fit into a philosophy stream as well. Do you think math inherently exists, or is it an invention of humans? I think we have an innate math ability. I think we have an innate ability to do mathematics, period. I wrote an article on this, by the way. It's not a scientific article or anything. I just collapsed a whole bunch of data and links and stuff like this and compiled it together and said math is an innate human ability, right? And this is the example I use, by the way. I say even animals have an innate mathematical ability, calculation ability, right? I haven't tested this out, by the way. This is something I mentioned a long time ago, right? Take a monkey, put him in a room, put one banana on this side, and put 10 bananas on this side, right? And do this for multiple monkeys. See if the monkeys go for the one banana or for the 10 bananas, right? If the majority even go for the one banana, maybe they don't have the ability to process that there's a bunch of bananas over here. If the majority even go for a bunch of banana, maybe you could say they don't have the eyesight to see the one banana, or you could interpret that as saying, hey, they know the concept of more. Less more. That's the root basis of mathematics. If you want to think about it, less more, quantify that. Less more, less more, less more, and then start giving it numbers, right? So I think math is an innate ability. The language of mathematics, the syntax we've come up with is the human creation of sort of taking our innate ability and creating the language of mathematics for us to do more complex calculations. I'm very good at statistics, but I'm terrible with the basics. I lacked appreciation that Feynman was talking about. Hopefully I can pick it up. Thank goodness I found a stream, Robinson Bailey. Fun, fun. Am I missing a lot of chat? No, not too much. Lots of engineering positions involve mathematics, but not coding, yeah? Smith, Kulio. I agree. I argue math is inherent. We discover the relationships as we climb higher. What do you think? Graham, Catholic tradition is right. I agree with Chicho. It depends on the kind of structure and why that structure is in place, but I agree with Chomsky that it is duty of the person enforcing the structure to be able to defend why the structure is in place. Otherwise, that I agree with. 100% Graham, why do we have to? That's the most common question any educator, any parent will get from kids growing up. Why, why, why, why, why, why, why? They need to know why, because their brains are processing saying, how is this connected to everything else? Why am I doing this? The system beats the crap, beats that out of us as we go through the centralized educational system. We need to get that back into our lives as we grow older, not related to math. But have you ever been to Ireland? Yes, I have Connor. Yes, I have. I have O'Connor. Are you Irish? I'm going to find your link on my website. Is that cool? You will appreciate this. I'm going to find your link on my websites. Let me find it for you. I was there soon after the Good Friday Peace Accord was passed in 1998. Check this out. This is an article, graffiti and murals from Northern Ireland taking a walk in Belfast in autumn of 1998. Here's my, I flew over England, sorry, England. You didn't accept my Euro pass. So from France, I flew over England, went to Ireland, spent like five days in Ireland, and then came back. And while we're at it, here's the math article I was talking about. Why is math important? What did I call this? Because the language of mathematics plays a vital role in evolution. So here, this is the this is the innate ability math thing I put together, by the way. Robinson Bailey stock market, although it has a lot of mathematics, can be very stressful. So be careful, be careful. Yeah, I personally wouldn't do it. I've done it for myself, personal trading and stuff like this, but I would never go into Wall Street. Horrendous. Okay, thanks for the lecture. My pleasure, Miro. Even doing a rota needs math. What's a rota? What kind of math are we talking about? Wait, I want to do the banana test and a pub. One cider. Oh, dear God, videotape it. Show it to us. One beer or one cider? Five ciders. How drunk are the people have to be not to be able to do the mathematics? You're funny. Okay, I'm going to skip some of the chat gang. Just if it's not existence of math itself makes me think we're in a simulation possibly. I think a lot of these math conversations get bogged down in semantics. When some people say math, they mean complex counting. Like Chicho's monkey example while others mean calculus. Oh, fun. Computer run on ones and zeros. So it only makes sense that a universe created or simulated by one would as well. Why is why stolen from us? Why? The ones and zeros in our case are just the size of quarks. I am Irish. Awesome. Definitely going to check it out. Awesome, Connor. And if you ever make it out there, I'd be curious to see how many of those murals are still up. There's a difference between math and value. Math, I think, is dependent on a syntax. Value is not, even though value is the basics for math. I think syntax is us evolving as part of evolution. We've taken an inability and quantified it, been able to create a language for it, to do more complex math. Wiggity-woo. Math is a way to categorize and manipulate the value. Math encompasses complex counting and calculus plus, though. What's this? Libertatheists. Math is a blanket category and the things you guys are describing as math are just absets. Subsets of it. Geometry is a branch of mathematics for sure. Rota. Staff shift pattern. Rota. Staff shift pattern. Case, man. How are you doing? Inertia is a property of matter. Inertia is a property of matter. Time is a property of matter. Gravity is a property of matter. Gravity and time could be considered to be the same thing, almost. But mathematics itself covers geometry, to calculus, to everything in between. Case, man. Metatrondria. Metatrondria is the powerhouse of the cell. Theist. Okay. How about imagining numbers? Federal reserve. That was generated via the printing machine. Actually, it's not even a printing machine anymore. It's just a press of a button on some kind of computer. Would you like a trillion dollars? There you go. You are my friend. Spend it wisely. And don't distribute it to many places. We don't want the peasants to have any of that now, do we? Great conversation all around today. Indeed, Spider-Man. Loving it. Loving it. Tristan, how are you doing? Long time no see. Long time no see, Tristan. Long time no see. Hopefully we see soon, right? Thanks for popping into the stream. Anywhere near, let's drop that. Imaginary numbers are a little different than imaginary money. But I'd like to cut on your jib. Speaking of bananas, I was taught this trick. If a person has the hiccups, ask them a mathematical question such as if a banana tree had 26 branches and 41 bananas. Per branch, how many bananas are in the tree? The hiccups usually disappear, really? Okay, Robinson, I'll try to remember that. So just ask them to multiply two numbers. Or probably it's just about thinking about something. Okay, you got me there. Session 7. Coolio. True, but when you define math so broadly, it becomes hard to talk about an example. That guy that said, you don't need math. I doubt he meant you can get through life without learning to count. He likely meant you don't need topology. I would love to learn topology. I need to get into topology. Maybe in another 20 years, gang, when we got all the modules out and we got our cookbook out and we got our exercise routine out and we got all the podcasts updated up to date and everything like that, we'll go through together and learn topology. Laugh out the mouth. Black market for that. That's math. The Kenzie and their model. Goldilocks. First time catching the stream. Welcome, Goldilocks. I hope you're enjoying your stay. It's a nice, beautiful Monday afternoon. And thank you very much for the Twitch Prime sub. By the way, thank you for the follows. Thank you for the subs, gang. I'm sorry if I missed them, but I get lost in the conversations and the questions and the good times. I do appreciate them very much. Coolio, session nine. Yeah, but that's why we should dig deeper and ask for specifics. Otherwise, I'll be assuming his math syntax is the same as mine or vice versa. Yeah. And that's like defining words, right? Potassium. That's hilarious. Elder God regarding the banana question. It's a lot of potassium. A lot of potassium. Graham, some people have a bad taste when they talk about math and so anything bad is linked to math in their head. But when you break it down, yeah, Graham, I agree, right? Totally agree. Agreed. Hence my semantic comment. Exactly. So should we change the definition of math? I don't know if we should change it. It's just a word, right? It's like, for me, whenever people say it, I just take it back to literacy, learning how to read and write, right? So that's the way I deal with it. And my students usually go, oh, yeah. And that's the only thing I'm caring about with when I talk with my students, right, to get that door open for them to be accepting a mathematics to think a bit of the language. That was a nice glass of water. I had to pound that back. The sun's got me all hot, came through. We just saw the sun just go through us, right? Fantastic. Fantastic. Not change. Just expand. Wow, we're almost at two hours, gang. What a fantastic Monday afternoon, Monday evening for our friends in the UK. I guess Monday morning or Tuesday morning for our friends in Australia if they're watching, right? Should we call the stream gang? Should we call the stream? Fun times, fun times. What a great stream. And only a timeout. One little timeout, someone thrown into a cage. That's it. Yeah, Tuesday morning, session seven. 2350. Elder God. It's not even after 12 for you. Right on. That's good. That's good. Smith-Gulio. I think it's better to leave an open definition. Constraining it will strife all discovery or cause some to scuff at things outside the box. Note that many branches of the subject border on philosophy but are written in the language of math. So which is which? Can it not be both? Good point, Smith. Very good point. It has to be both. It has to be both. It has to be all of it, right? Okay, gang. Let's call the stream. Thank you very much for being here, gang. Mods. Thank you for taking care of business. Thank you for the conversations. Everybody, really. For those of you that are new here, thanks for popping by. I hope you enjoyed the stream. And it was probably a heavy sentence for the crime. And it was probably a heavy sentence for the crime. Gang, if you want to know who we are, I'm on Patreon. I'm sharing the work there. If you want to support this project, Patreon is a fantastic way to support this project. I don't put anything behind paywalls, so you can just follow and keep up the date and as to what we're sharing. The videos we're uploading, the audio we're uploading to SoundCloud now, any pics and whatnot. And I have sort of a thesis on the description of Patreon, a page of what my work is centered towards, which is basically creating a math curriculum that can teach all of high school mathematics, right? I think if everybody was literate in the language of mathematics, the world would be a much more beautiful place for all of us, period, end of story, right? So if you want to follow the work, Patreon is a fantastic place to follow this work and to support this project. We are live streaming this stuff on Twitch. And if you want to follow this work live, participate in the chat, Twitch is where you want to be at. And my Twitch handle is twitch.tv or twitch.com backslash, chico, live, all one word. And for those of you that are subbing, following on Twitch, thank you very much for the subs and the follows. I appreciate it very much. I do announce these streams on Twitter, Gabs, Mines, VK, and Owl. Okay, about 30 minutes before we go live and I do share additional content and stuff on those platforms and announce videos and audio that we're uploading. Beginning of this year or in the last month, last couple of weeks, started uploading audios to SoundCloud as podcasts. I've been asked to do this for a number of years now and we're finally on SoundCloud and I'm having a heyday, fantastic time just learning about that platform and uploading these, some of these audios anyway up to SoundCloud. We didn't record this one. So this one will probably not go on SoundCloud because I don't have it with a lapel mic but I have 900 plus videos on YouTube, at least 500 of those I've recorded with a lapel mic. Okay, so I'm going to go through and slowly start uploading those previous videos that we've recorded up to SoundCloud as podcasts, as audio and you should be able to access them through whatever podcasting platform that you access stuff on. I just fixed it on iTunes so you should be able to find them on iTunes as well. Okay, and as far as the videos go, I'm uploading these videos to YouTube and Bitshoot. Everything goes to Bitshoot, technical hiccups permitting and everything goes on YouTube except things that YouTube is censoring. So it's going to become less and less things being uploaded to YouTube, unfortunately. But if you are on YouTube watching these things, the math videos will always go on YouTube for sure. If you're on YouTube and if you want to support this work, we do have YouTube membership available now and that became available at the beginning of this year. So a few things have rolled out at the beginning of this year and joining through YouTube membership is a fantastic way to support this project and I do premiere a lot of these videos on YouTube and I am live in the chat on YouTube when we do premiere the videos on YouTube. Okay, aside from that gang, thanks for being here everyone. Hey Chico Parker, how's it going? You caught us at the end of this stream. Thanks for being here again. I hope you guys have a fantastic next few days and most likely I will announce the next set of streams. Today is Monday, probably by Thursday. And by the way, by the way, heads up, we might do another DJ set next weekend. We're just trying to confirm things right now. So I'm going to hold off until we get confirmation from the next set of DJs that are into doing a DJ set with us and we'll announce it as soon as that's confirmed. If not this weekend, maybe next weekend. Okay, so hopefully we can get that going and we can do another at least a six hour DJ set. That'd be fantastic. Everyone's excited. Yeah, so I'm going to pass on the word. Let's get it going. Let's get it going. Okay, thanks for being here again and I'll see you guys in the next live stream. Bye for now. Cheers everyone and peace, of course.