 And we are live streaming, should be anyway. It takes a few seconds for it to confirm, cool? So we're live and we're I guess doing day two of a little bit of mathematics. Okay, just a drop in session. We're gonna do four sessions today. An hour of pop, okay. And the schedule is basically, we're doing one right now, which is 9 a.m. my time. Let me just open this up. Hello Tom, how are you doing? Welcome to our day of math, right? So we're gonna do one at 9 a.m., which is now. We're gonna do one at 11. Oh, I guess it goes into the last room, cool. I was just checking the events as soon as you go to the events. When I go live, I didn't notice about Twitch. It kicks you into the live stream. I was looking at the times when we're going to do, when I set them up. But I believe if you go to the events page, it's gonna be at 11.30 a.m., 2 p.m. and 4.30 p.m. So we're gonna do four sessions. Hello, hello index. How are you doing? And Casey, how are you? You're back. Hope you're feeling better, man, than yesterday. I know you retired, but you tried to go to bed early. You kept going back and checking out what was going on. And by the way, one thing about yesterday when we were talking about tours the end, we did sort of, we started talking about comic tour experimentation. A little thank you. Ah, you're welcome, you're welcome. How are you drinking your good tea? After our session yesterday, the second session, I wanted to make myself some ginger, Persian black tea. It's that time of year to get a nice ginger and make some ginger tea that's fantastic if you're feeling cold or whatnot, you wanna warm up a little bit. Yeah, peppermint. Peppermint is fantastic to write through some peppermint, not peppermint, but just mint leaves that we have as well. But just in case you were here, I think it was the second stream. We're talking about comic tour, so I wish you again a good evening. Good evening to you as well. Good morning from my end. It's starting out the day, Saturday weekend, doing a little bit of mathematics is, I like it, just very relaxing to a certain degree, right? So I hope people that need help do pop by because if anybody still has exams, they realize that, I guess, other parts of the world, people have already finished their exams. So it might be a little bit quiet depending on where you are, but in my part of the world, exams basically start in June and go almost all the way to the end of June. If we do this, well, we'll definitely do this next year as long as I'm around. If we do this next year, I'll start math drop-in sessions earlier. Okay, we'll do them maybe at the beginning of May. That way, people in other parts of the world, they're writing their exams, especially if you're in college or university, and by that time, hopefully, I would have had time to look at calculus a lot more and get my hands dirty with statistics a little bit more. We'll start it earlier next year, okay? But if you were here yesterday, towards the end, we talked about combatorics and someone asked the question, where in the real world would use combatorics, permutations, trying to figure out how many different ways you can order things and stuff like this, which really kicks into probability and statistics, right? And just out of the blue, the person said to provide an example where we would use this in the real world. And for me, I went back to something that I'm familiar with and something that I worked with a student a few days before too, but I haven't dialed into it too much. And I said, well, one of the places you could use combatorics that kicks into probability and statistics is for games of chess, specifically poker. And I've spent a long time playing poker and I played lots of games of chess and I used to know the stats on it a lot better. So I try to go back to my memory, pull out the stuff, but I made a mistake on that one, right? So I looked it up this morning just to do a little correction on what I wrote, right? And if you go to the wiki page, just do poker probability, okay? And if you scroll down and there's a table they've set up there and they start off with, the type of hands you can get, the distinct hands, frequency probability, cumulative probability and the odds and all that jazz. And then on the last column, on the right most column, it has mathematical expression of absolute frequency, okay? And frequency is combatorics. How many different ways we can form something, right? And this is the frequency. This is the number of different two pair hands you can make in poker, okay? And let me just write it down for you. It's take off my glasses and we're gonna use this few. Before we get into the salutations and stuff, I'd like to do the corrections as soon as possible. Doop, so we did this hand and it's 13, basically it's gonna be 13 choose two four choose two, 11 choose one and four choose one, okay? Hopefully that's coming out okay. Maybe I use a darker one for the next stuff. And oh, and this should be squared. I knew there was something I keep on forgetting on this. This is supposed to be squared, okay? Because you're picking, you try to match up the pair with the singles you choose. So basically the way it works is from there's 52 cards in a deck and there's 13 cards of each suit, right? So you're gonna pick two cards from the 13, right? And from there, you have to match up those two cards to make two pairs, right? And that's why it's squared. So you pick those and then you have one card left, one spot open, one, two, three, four, five. Your five card hand. This is the number of ways you can get the last card and these guys are the number of ways you can get these two pairs, whatever they might be, right? Just to clarify that out, and this is your last card. As long as it doesn't match any of these guys, which is why you have 11 here, right? So you're eliminating the two numbers, maybe numbers or face cards, whatever, right? Or he aces, right? So you're eliminating two from the 13 that you could choose from and you only have 11 more cards left that you could pick at random to fill up the spot. You can't have the two that you chose here to be one of these choices because I would make a full house, right? I just looked that up just to answer it for myself and remind myself, right? As we talked about one thing, yesterday's stream too, use it or lose it. If you don't use this information, you tend to forget it, right? You tend to lose the ability, you lose that power, right? But the beauty of mathematics is if you know your, the syntax of the language of mathematics, this is just the syntax applied to the game of poker, right? This is convitorics and that has a specific meaning saying 13 choose two, which basically means the 13 factorial over 13 minus two factorial, two factorial. This is the math part of it, right? That's the syntax of the language of mathematics. You can take this and apply it in the real world and this happens to be poker. So you don't have to know how mathematics is applied to every discipline, every system, right? As long as you know the core language, the syntax of the language of mathematics, you can apply that anywhere, right? So that I wanted to clarify is it's a beautiful way to look at mathematics and really appreciate why it's important to learn math, which is really the question that the person asked yesterday, why are we learning math, right? The comments here, catch up on the comments. And aside from that, welcome to another live stream. Hello monkey, how are you doing? I wish you again, good evening. I got here perfect timing, sweet, sweet, sweetie. So again, we're gonna do, you know, I set this up, there's shorter sessions I guess, and now we're a pop. And I realize there isn't too many people doing mathematics right now, I guess people have finished up. But if there's any questions that you guys have regarding mathematics, we can do, okay? Or we can talk about almost anything else you'd like to talk about. If anything comes up that we can put in another video maybe politics, economics, life, whatever it is, I'll get my notepad here, we can make a little note and we can tackle it later, okay? And one of the other things I should have specified regarding mathematics, these open discussions as well, which is one thing I do when I try to put my math content together, try to teach mathematics and I look this up and I try to make it relevant to the present to a certain degree or take some historical data, is basically what I do is I look for data and I take that data and I crunch the numbers and present a certain perspective and then from that I either end up making a video or I make a note of it, just a mental note of it that if the opportunity comes up, I use that example to get a point across when teaching mathematics, right? So that to me is math for me anyway, right? Aside from learning the syntax of the language. So if there's any type of data, that's a long intro to it, but if there is any type of data that you would like us to take a look at, these open discussions are open to that, right? These sessions that we do with mathematics are open to that and hopefully that'll open up a huge can of worms, right? In terms of, hey, can we do this? Can we learn this? Can we take a look at this data and maybe get a point across and we'll do the searches together possibly, okay? And if you do know the information where it can be found, you can probably post it on Discord. Let me do this, aha. Play ta ki, I got play. Ta hi, ta, ta ki ti online. I don't know that name, that game. This chord, there you go, oops, I made a space on it. Discord. And there's the Discord page that we've set up and if there's any data you'd like us to take a look at, then post links in the Discord, there's a mathematics section, right? And later on maybe we'll quit having, thinking about doing this, but I'm really busy until the end of the year, school year, but basically creating another folder in Discord in regards and basically calling it research. And this is something that I would really like to do. I know there's Casey and probably maybe other people here that are active on Discord as well that we've set up for Chicho. There's different forums you can have discussions on or we can have discussions on or post questions. I'm thinking about creating a new folder and calling it research topics or something like this. And as a community, we could take a look at certain types of data and create a math lesson or just take a look at that data and crunch the numbers and to see what the data tells us and hopefully I can take some of that and include it in a math lesson or an example that we can use when learning the syntax of the language of mathematics. So basically some of the stuff that I've been doing behind the scenes but do it in a more open fashion, right? Because I do believe in creative commons and making all this stuff open. Hello, luxurious, hello, luxurious, how are you doing? And by the way, sisters and any math questions, you can post it anytime, we'll break, do math and talk about whatever, okay? Aside from this, I was thinking about doing an update video just before this started. That sounds really, yeah, I really wanna do that, Casey. Because there's so much data. And one thing with what kind of math do you teach? I teach high school mathematics. I'm very focused on high school mathematics. And I used to, I have worked, actually this year as well, I worked with a couple of college students with statistics and stuff like this. I do quick math. I work with a couple of college students doing some statistics and stuff like this but I mainly focus on high school math and I've done a little bit of elementary school. Some parents that I have, that word of mouth gets out. And I do private, I do private in groups. And I don't really advertise. It's just word of mouth that goes around. I've had some parents contact me and I've taught their kids when they were in high school or they've heard that I do an okay job teaching mathematics, prepping kids for the real world, right? So there are some students that I've worked with that are in elementary school but elementary school mathematics, in my part of the world, is ridiculously simple. It's absurd how easy it is. And I usually fly through that stuff and in elementary school, I start teaching on high school mathematics, okay? And unfortunately, in my part of the world, what's happened is math education has deteriorated dramatically, dramatically. And I can't, I keep on saying this in the streams but I can't even overemphasize this. It is horrendous. And it blows my mind where I read statistics and saying, I'm in Canada, by the way. I read stats and reports saying Canadians do well in mathematics, Canadians does. That is an outright misinformation, disinformation. I even go as far as saying it's a lie, okay? Easiest but most important. Easy, for sure, elementary school math. Easiest, extremely important. Unfortunately, they're doing a horrendous job teaching it. They're confusing the living daylights out of the kids. So kids coming into grade eight into high school mathematics in my part of the world, most of them don't even know how to deal with fractions. Like I'm not kidding you. They don't even know how to deal with fractions. They don't know how to move around an equal sign. They really don't have a grasp of numbers. They don't even know their multiplication table, okay? It is so bad, so bad. And that's one of the reasons I decided as soon as the technology was available and what I do with technology, I try to incorporate that into my life and figure out how I can use that technology into my life to improve my life, right? To compliment my life. That's basically disruptive innovation. And as soon as I realized that live streaming was gonna be a way to interact, to continue my sort of passion to teach mathematics, right? I decided to do this because what that's doing is allowing me to relearn some of the stuff that I've forgotten because math curriculum in my part of the world has deteriorated to a level where they've taken out so much information that I'm not using it, so I'm losing it, right? Hello, Lexi, how are you doing? Welcome to live stream on a Saturday morning, doing a little bit of mathematics and open discussion. Would you be cool with talking about the multi-haul problem? Oh, the multi-haul problem, what is that problem? I know that problem. Though it's kind of basic statistics. There's a lot of interesting cognitive psychology concepts within it in that most people don't understand the basic costs of statistics even when a real-life situation is getting to them. Oh, that's the multi-problem is, oh yeah, this is the problem. That's behind the door, there's three doors. Oh man, I looked at this a long time ago. Let me lay it out, just remember what it is again, okay? So let me lay this out, let me erase this guy. Contour, oh yeah, great problem. Contour, I'm gonna talk about it. If I make any mistakes, please post comments. As soon as I finish laying it out, I'll read your comment and then we'll do any corrections if need be, okay? But this is the multi-haul problem. So there is a game show where there was, actually it's back again, I guess. I think I've seen my grandmother or someone watching it, right? It was basically, it was a TV show called, let's make a deal, okay? And basically people dressed up in costumes and the presenter was actually a very lovable character. He was sort of the jester, the joker. He was sort of, he liked to throw a little bit of fuel on the fire, right? Tease people, give them, make them deals that made them think, should they take the deal or not take the deal? And usually, people would dress up and the camera person would find someone who's dressed up really crazy and they say, oh, the gingerbread man or something, let's make a deal. And the presenter would go up to these people dressed up in a costume and they would be basically, if I remember the game correctly, there's three doors. Okay. Or three curtains. Okay, let me read the questions. Make sure I'm laying this down properly. Deal or no deal, kind of game show for sure, right? So there's door number one, door number two, and door number three, okay? And man, while I'm explaining this, I'm trying to remember the logic behind the mathematics and hopefully it'll come to me, okay? But basically, here's the presenter. I draw good stick figures. Here's the gingerbread man. Here's the gingerbread man. Dressed up as a gingerbread man. Here's the guy's mic, right? So this Monty guy comes along, big smile. He plays sort of the, what do you call it? Anyway, he tries to make it entertaining, right? So he comes up to the gingerbread man and says, listen, sometimes I guess it worked this way where the guy has money, right? Let's say he's got like $500, the five fingers for $500. And the presenter says, I'll give you $500 right now. You sit down, we'll go find someone else to stress nicely and we can make a deal. I think, I watched this one as a kid a little bit. Or you can not take the $500 and decide on opening one of these curtains and the gingerbread man would get one of the prizes in one of the curtains, right? And very seldom people took the $500 or whatever it is that he was offering. Sometimes it was $50 maybe, $100 or something, right? The devil's advocate, yes, that's the word. Thank you, comment, I'm checking the comments. So he would play the devil's advocate, right? And he did a fantastic job, right? And I'm doing it. So this person, you know, there'd be people in the audience and this is in the audience. So you see a whole bunch of people dressed in all kinds of wacko kind of ways, right? You got a whole bunch of people in the background dressed in crazy ways, cheering, yelling, yelling, you know, waving high at the camera and stuff like this, right? So it's a fun entertaining game. So this guy would say, no, I don't want the money. I wanna pick a door, right? And people all of a sudden would start yelling and screaming, pick door number one, two, three, pick one of those doors, right? So let's say the guy picked door number one, right? So the person picks door number one and in door number one, sometimes it would be a fantastic prize, right? So I don't, it was sort of on the low end, the game was sort of on the cheap end of the gaming stuff. So there wasn't like a Porsche or anything behind here, sometimes it was a video game, like a pinball game, pinball, pinball machine, right? Sometimes it was something else, right? And by the way, I'm just remembering, he would say, this guy would say, I picked door number one and then Monty would say, yeah, that's right, that's the way it worked. So he would say, this guy would say, I picked door number one. So here's this little door bubble or here's this little speech bubble, right? Let's do a little speech bubble here. Here's a speech bubble. He would say door number one, right? And Monty would go, hmm, you picked door number one, eh? I think he would offer more money for the guy to change his mind or something like this or something along that level, right? And then door number one would open up. I think there was a little bit more intricate stuff associated with it, right? And then sometimes there would be, that's one thing they loved having. They would love having a goat. I don't even know how to draw a goat. That's not something like a goat, but let's assume it was a goat, okay? I'm gonna read the comments because I think I'm missing some kind of interaction here with the game. Hold on a second, let me change the camera angle. I wish this question was coming up. I would have read up on it, right? Let's check it out. Typically there was no new car. There was behind the curtain and two goats, ah, yeah, two goats, so a drew one goat. People expected the probability of winning to be 50, 50 after choosing one incorrect door. And they would show curtain they didn't pick and give them the option to switch. Oh, okay, I gotta read this up then. I remember it incorrectly. This is a long time ago that I looked at this. So they would show them door number one. Okay, I'm gonna look this up, the Monty problem. Sorry gang, Monty, Monty Hall, Monty Hall problem. Here we go. And give them the option to switch. So they would say, oh, I gotta remember this. I can't remember it now. Thanks for trying to draw a pointer. I hate to be countered, but I forget the little intricate part about it, I guess. The Monty Hall problem is a brain teaser. So I'm just gonna read the Wiki page for the Monty Hall problem, right? The Monty Hall problem is a brain teaser in the form of a probability puzzle. Losing based on the American television game, loosely based on the American television game, show Let's Make a Deal and Made the Papa, Papa, Papa. 1970, it became famous after a question from a reader's letter quoted in Marilyn Vaughn, whatever, Ask Marilyn column in Parade Magazine, 1990. So it became famous in 1990. Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car. Behind the other, others goats. You pick a door, say number one, okay? And the host, oh, that's right. They don't show the door that they picked. They show one of the other doors. Who knows what's behind doors open. Another door says three, which is a goat. He then says, do you want to pick door number two? Is it your advantage to switch your vote? I just have to switch. Oops, two-thirds chance of winning the car. Well, consensus will stick to the initial choice. Have this, okay, so that's right. They don't show them the door that they picked. Let me read the comments and give them a switch. It's important that you phrase this problem correctly. Yeah, I wasn't phrasing it correctly, right? It's pretty simple. You have three doors and one of them has the prize. You pick one and on the other two, it's shown to have nothing. You're offered to switch and you should, because you won't win 60%. Yeah, that's right. The mathematics is straightforward but the wording of the problem is the important part. Chance after wrong, that's why it's kind of a prank. With the given chance of switching, okay, cool. So let's do this. So the guy, check this out. So Monty comes around, oh, I have switched the camera angle. My bad, did this last week, ah, you did this yesterday. So the guy says, here's door number one, right? So the guy says, I picked door number one. And Monty, being a devil's advocate says, oh, you picked door number one, eh? Here is, and then he turns to the audience and says, before we open up door number one and seal this deal, let's show Mr. Gingerbreadman what's behind door number three. So they showed our door number three and sometimes it's a goat. Sometimes it's something else. They say, you know, it's a pinball machine, right? I think anyway, sometimes it's a pinball machine. And they say, you know, instead of opening number one, you can take the pinball machine, right? And the guy says, no, no, no, I wanna see behind door number one. And then the Monty says, well, I'll give you one more choice. You can switch your choice from number one to number two. Okay, because maybe at the beginning they've told them there's something, you know, behind one of these is a goat, behind one of these is something better than a pinball machine or something, right? He says, I'll give you a chance to switch your vote, right, instead of door number one, you can pick door number two. And most people would say that because you're down to two choices, then you have a 50, 50% odd of winning the better prize, right? However, the way this works is because initially your choice was one out of three, that means if you pick door number one, it was one third of a chance of you being correct. And if the good prize that was behind door number two or number three, this was two thirds of a chance of being correct, right? Just because they showed this to you, it doesn't remove the possibility that two thirds, there's a two thirds probability of the better prize, not the goat being behind door number two than it is behind door number one, right? And this is called conditional probability, I believe in mathematics where we already know the condition or one of the conditions popped up, so the probability changes to a certain degree. Sometimes it stays the same, sometimes it changes if we know the conditions have changed, right? So that's as far as I can go with this without really delving into it and creating a full-blown lesson of bringing different examples into this to get this point across. But it is a fun exercise. I wish I remembered the question more accurately instead of having to read it. All right, let's check it out. But most people think there's a 50-50 chance after a wrong one being revealed. That's why it's kind of a brain teaser because of the misunderstanding. With the given chance of switching, yeah, it's conditional probability. Yeah, it's conditional probability. It's really cool, actually. Conditional probability and stuff like this. There's different formulas that you can use. It's basically the syntax for something like this. And you have to sort of appreciate the trick with doing mathematics, with doing work problems, with doing probability, combi-torques, and stuff like this as a race killer mentioned. Okay, and hi, race killer, how are you doing? You're back again for another day of math. It's important that you phrase the problem correctly. So one word in a word problem can mean the difference between using this type of formula to solve it or this type of formula to solve it. It changes the game, which is one of the reasons why a lot of people have a hard time with word problems and mathematics. For me as well, words sometimes confuse me to a certain degree. Sometimes I read things backwards. Sometimes I read a word that's not there. Sometimes I'm reading fast and I skip an end or an or. And those are the words, ends and ors and ifs in mathematics when you're trying to quantify a problem. Those are the words that really matter, okay? The gingerbread man doesn't matter, right? A Monty doesn't matter. What matters is the connecting words from one thought to another because those are the things that mathematics that pop out at you, right? So conditional probability sometimes you have just a syntax on it is, I can't remember it, but I'll try. You know what, I'll just do the base on it. Sometimes you do, if you want to write down what's the probability of flipping a coin, right? If you're flipping a coin, right? You can get heads or tails, right? So the probability of flipping a coin once, the probability of getting a head is 50%, 0.5, right? But sometimes when you write, you only want to find the probability of something, probability of A given that B has occurred, oops, that B has occurred, all of a sudden, this I believe becomes the probability of A and B divided by the probability of B or something like this. I'm probably getting this wrong, but there's a whole formula depending on what the condition was that they gave you, right? And again, as long as you know the syntax, what each part of this means, then you can do the mathematics based on the problem as long as you understand what the problem is referring to, right? It's sort of being wishy-washy about this, but the reason is, is because this thing changes depending on what type of systems we're looking at, right? It's pretty cool actually, very cool. The reason people must understand this is because people don't explain it correctly. That's what my professor said. He kept telling us the English translations into math is the most important, 100%. 100%, a lot of people explain it in a way that 50% is correct, yeah, yeah. They don't explain that there's conditions to it, right? There's like the mathematics. Once soon as you quantify something in the real world, you can't be wishy-washy with things. That's the beauty of mathematics. When, you know, that's why mathematicians, you know, I may be very, very much over-generalizing this thing, but that's why people who speak the language of mathematics who really appreciate what mathematics and is using math in the real world, they can't really become politicians because they can't really be wishy-washy. They're really straight up direct. That's my experience anyway in large part and I'm really generalizing here. So my apologies, but I do tend to generalize a lot. I've actually had students where, you know, work with students where they're getting, you know, they're in 80, 90%, you know, that's their marks that they're getting in math, right? When it comes to doing the syntax and doing problems that they understand or appreciate, but then when it comes to certain sections where they're taking English and trying to trick them, right? And they read these problems. They end up failing those exams and they're like, oh, they get totally destroyed and emotionally, you know, up and down. So rollercoaster ride and they're like, oh, man, I'm really bad in math and da, da, da, da. And I explain to them, look, man, it's not your mathematics, that's the problem. It's the English, that's the problem. So if English happens to be their second language, I just tell them, don't worry about it. Just improve your English slowly. You'll get these problems. If their natural language is English, then I have a talk with them and with their parents and say, listen, your kid is good at mathematics, okay? You should take some of that energy that they're putting into the sciences and focus on learning the language that they're communicating in because English is gonna prevent them from progressing in certain fields if they want to, even if it's math related, even if it's science related, okay? Sorry about mucking up that Monty problem a little bit. I got really excited about it. I was like, oh, Monty problems, I've seen this for a long time. Super point differs through race killing. Racer kill. Oh yeah, I read that incorrectly, yeah? Racer, oh it's race, it's not race killer, it's a racer kill. Brimstone, racer kill, I don't know what racer kill refers to. Yeah, racer killer, I guess that wouldn't be a nice thing to say, right? You know how to do a quad formula? Yeah, the quadratic formula for sure. X is, it's the only formula I remembered after high school. Dante, how are you doing? Hello, hello. The quadratic formula is one of the few formulas that I remembered retain after graduating from high school and university. It just rolls off the tongue, right? X is equal to negative B plus or minus square but B squared minus four AC over two A, right? Never forget that formula. We end up in the sciences, we end up using it a lot, right? That's why you remember it, you tend to retain it. I've forgotten, I think there was time in my life that I forgot what the area of a circle was but I still remembered the quadratic formula, right? Because we ended up using it a lot. And the quadratic formula is just one piece of the puzzle, one part of the puzzle where the way they teach it to you when they say it's used to find the X intercepts where it comes into play. There's a huge, this is actually a really cool channel now. Thanks brother. Amilette is turning to be a real cool channel now. My favorite formula is PV equals NRT, PV equals NRT, NRT. Oh my God, from chemistry. I've used that and I can't remember what it is. PV equals NRT, T must refer to the temperature in Kelvin most likely. R is resistance, voltage, PV is voltage, I can't remember that. When I used to tutor for mathematics, when I was talking, when I was taking calculus back in the day, teaching students to translate sentences into formulas, formula and logic symbols and teaching them basic logical rules like module poems show them how to translate work problems in mathematics to filter useful information and logically reach conclusions. Oh okay, I've just gone with experience when I teach it to my students. I go, oh, what does all mean in mathematics that I do? Because I'm mainly focused on high school math, but that's cool, I'll keep this in mind actually. As you can tell, my English isn't very powerful, it's just powerful enough for me to do what I need to do. And I spent, I didn't, as far as English, just went on the pressure volume and temperature, that's right, pressure volume and temperature, cool. V is volume, P is pressure, okay, cool, cool, cool. I totally forgot about that stuff. Man, I miss chemistry, I love chemistry. But just to let you know, just since we're on the topic of English, okay. I think momentum was always my favorite from it. Momentum, I really like it because it was so easy. Yeah, P equals MV, and conservation of momentum, right? Before you introduce friction and heat loss and distortion into it, of course, right? But when it comes to English, my English was horrendous. Coming out of high school was horrendous. Coming out of university was horrendous. When I got my first job as a geophysicist, it was horrendous, okay. I mentioned this before, but I remember doing my first geophysics project by myself and writing a report. So I would, you know, someone else, at that time I wasn't writing proposals, so the job came to us. And, you know, I went out and collected the data. I was a very good collecting data, processing data. I was good at the mathematics aspect of it. So I got the stuff. I was good in the graphic design. I made the maps and stuff like this. So I put all the diagrams together and I wrote my report and I gave it to my higher-up to review my mentor, really. Within an hour, he came back and he threw the report on my desk and said, what the hell is this? I went, what? And I picked it up. And I had never, ever submitted in an essay or a report or anything in high school or university that had so much read all over it. Every page was crossed out and read. It took me from here because I was very proud of writing my first report, handing it to down here where I was like, man, I am out of my league, right? So that's where my English was when I got my first job as geophysicist and over the years I got better and better. You know, about 10 years ago when I started blogging, I took about two, three years dedicated into learning how to write and improve my English. Really, really important. What is the most complicated equation you know? You can show us. You know what? The most complicated stuff is Maxwell's equations. Okay, Maxwell's equations. I looked into this a long time ago. I was looking into the works of Tesla. And who was the person? I was watching lectures from, I forget the guy's name, so I'm not gonna mention any names. But if you do Tesla, there's a couple of guys online, they're old school, they've done a lot of work on Tesla, on electromagnetics, magnetic methods. Like for me, I got my degree in geophysics with a minor in mathematics and I specialized in electromagnetic and magnetic methods. Okay, that's what I specialized in. I even had one of my thesis for my bachelor's thesis. No, not Tesla car. The real Tesla, Nikola Tesla, right? My bachelor's thesis was even accepted in SAGIPE. And that was the largest geophysics conference and it's held, I believe, in California. I was invited in to do a presentation. I was like just out of university, like crazy out of my league, right? But I specialized in electromagnetic methods, right? And all the electromagnetic, magnetic formulas and stuff we learned all the way through university, all the way through my geophysics career that was using these equations. There were all the shortened versions of what really those equations were. I found that out when I looked into Nikola Tesla and read some articles and watched a whole bunch of lectures, right? At some point, I would like to go back and relearn all that stuff with the full equations because they were basically truncated equations if I remember correctly. That stuff will take your head for a spin and I think there's a lot of information there to be had, okay? Can you show us? I can't show you. I haven't looked into this stuff a long time ago. It's, I wish I could show you right now. And at some point, we will go into it. I promise you that. But that's gonna be a while down the road. My apologies. I would have to do a review. I would have to do it justice. I don't wanna do another multi-problem where I start off and I forgot the little details. And the wording, as Racer Kil mentioned, the wording of the problem, this is Racer Kil, the wording of the problem, the way you present the information is very, very important. We're trying to get math concepts across. So some things, that's the reason I'm not really tackling calculus and hardcore. Probably the statistics yet because I really wanna make sure I'm correct in the words that I use, right? And I'm going down the right pathways, okay? Are you a French speaker? I'm not. I speak, the only language I can read and write in is English, okay? My affluent in English, okay? In English, I guess. I can communicate while in English. While enough, at least anyway. And I also speak Farsi, Persian, and Armenian, okay? And I speak the language of mathematics and I can hold my own on a poker table. And on the craft table because that's a different language itself. That's a different language itself. Were you struggling with English because you weren't speaking at home? Yeah, for sure. My first language, natural language, was Armenian. I learned Farsi. When I came to Canada, I didn't speak a word of English. Can you, no, I can't read. I used to be able to read a little bit but I never learned and I was trying to learn in teenage years but there was too much going on during the teenage years. Okay, because you weren't speaking. One thing I'll let you know about English, my experience with English. Not Gucci. I'll give you a story about me in English, okay? So when I went to, let me erase this stuff here just in case we start something else. So when I came to Canada, I didn't speak a word of English. I used to think, how are you meant hello? Okay, so I'll go around and say, how are you? How are you? It's hilarious, really. And I was sort of a trickster to a certain degree. So I like how I'm fine. Didn't really, nothing, things didn't phase me too much and if they did, I dealt with it. So I was learning English and I was only 10 years old when I came, right? So halfway through grade five. So I was learning English in grade five, six, seven. So by the time I finished grade seven, I could talk with people but my writing reading was horrendous, right? My level English was really low. And then I went to high school and in high school, they told us we had to take a second language and the second language that was offered during the time when I was in high school was French only, right? So I was struggling with English. I'm still trying to learn English. My mathematics was super powerful, right? The mathematics in Iran that they taught in Iran in grade five was equivalent to the mathematics that they were teaching in Canada in grade 10. Okay, so I remember when I arrived in Canada, I went to math class in grade five and I sat down and they were doing math. And I didn't remember, this is like first couple of weeks being here, I didn't speak English, I didn't know what people were saying but I knew what they were writing on the wall on the chalkboard, the teacher writing mathematics and he was writing three plus two equals five. Like, I was like, what's going on, right? They were writing just like numbers being added and subtracted seven minus negative three equals 10. I was sitting there looking around going, this is weird. Like, what's going on? Like, I had done that in grade like two. The mathematics I was doing in grade five in Iran was functions, right? So there was a huge gap and there is right now too. The mathematics like in grade eight in Iran, right? I had a family member in grade eight in Iran that they had started doing calculus, right? Back then, at the end of the seventies, right? That's when we came to Canada, right? End of the seventies, in Canada, you couldn't find a high school in Canada taught calculus in grade 12, let alone grade eight, right? So there was a huge gap there. So my math was powerful but my English was horrendous when I went to high school, right? And when I went to high school, they said, okay, you need a second language, you have to take French. And I told them, listen, barely no English. Like, you know, I can communicate, I can talk, but I don't, my essay writing, my spelling, all this stuff is bad. So learning another language now is gonna be extremely difficult. And they said, oh, it's just, they use the same letters. Like, no, like I know two other languages. And at the time when I came, I knew how to read and write Farsi. I've forgotten now. And I knew a little bit of Armenian read. And I said, well, why can't I learn Farsi or Armenian? And they turned to me. They said something to a high school student, to a teenager that you know administration, no teacher should ever say, okay. They turned to me and they said, we don't recognize those languages, right? And me being Chico, I was, I am who I am, right? My name, whatever it might be, this is me that you see, right? And this is me that you see when I was in grade eight, the core philosophy. I've changed my mindset on many, many things about how society, the world works and stuff like this. But my demeanor is a way that I confront authority, right? And they turned to me and they said, administration, yeah, 100%, they don't recognize. So I turned to them and I said, well, I don't recognize your language, right? I don't recognize French. So I took French from grade eight to grade 11 in high school, okay. I learned some of the basics, fenetra, right, window, whatever. But in grade nine, I, in school, what I did was, I learned what I wanted to learn and anything that was rammed down my throat that I didn't want to learn, I cheated. And in grade nine, I had a cheating method in high school that was basically foolproof, almost, right? I never got caught and one day I'll show it to you, okay? So in grade nine or grade eight, probably, I started creating this cheat thing that I had that would come with me, okay? And basically from grade eight all the way to grade 11, for French, I cheated. And I didn't refuse to learn that language. I learned the basics just to get along. And I ended up getting like, I don't know, 80% in it. That's how ridiculous high school education is, right? You can learn nothing and still get a good mark. Okay, put minimal effort and still get a good mark. That's why I always get surprised when I explain this to my students saying, listen, high school is not hard. The amount of work you have to put in university if you want to really do it right, one month of high university work, if you're doing it right, if you're getting the most out of your money because it's your time, right? Your time, right? That's the way it should be. If you're studying something, put your full attention on it. You know, the amount of work you do in one month or two months of university is probably equivalent to all of high school math, right? Or at least one semester if you do it correctly. One semester I took four math courses at university. Two of them I didn't even have the prerequisites for. They were applied mathematics, it was high level math. It was insane, right? I had no right to take those courses, but I did and I did okay and I passed them. And I relearned what I, so if you do it hardcore in university, four months of university should be equivalent to all of high school, right? So that's my story about learning English and French. Going off topic of mathematics, but as I've said before, I'll share as much as I can to help share my experience and help any of you guys that are struggling through university or high school or whatever it might be. Man, get through it. Life awaits you at the end of the door, right? Okay, that's super shitting on administration. Cool, so we're about an hour. How about we call it, call this the session, the first session. We've got three more sessions coming up. The next one's 11 30. And what I'm gonna do right now, oh, Casey's messages. I've never, let's read this, Casey's comment. I had a similar experience being forced to take German. Luckily the teacher was very reasonable and she left me a few other, let me and a few other people just doodle and chat as long as we didn't disrupt, oh, that's fantastic. Lucky, I didn't have that experience with French anyway. I had some amazing teachers. I always, I got along with almost everyone. I didn't, there was a handful of people in my life that have come across certain demeanor that we have conflict with, but in general, I'm okay with most people. There are certain types though that we do bank heads. It is what it is, right? It is what it is. But one thing I wanted to let you know before we end this session, before we come over to the next session, I edited the how to take notes video, okay? And as soon as we end this session, I'm gonna let it loose on YouTube, okay? It took me a long time to edit it. My desktop computer is officially, needs a serious upgrade. So it kept on crashing. It took me three days to edit it. So I didn't get to the cryptocurrency one. The cryptocurrency one I'm gonna get to in two weeks because for the next two weeks, my students are in exams. I have to spend a lot of time with them and stuff and have a lot of other things going on, okay? So I won't get a chance to edit the cryptocurrency video. That'll come up in two weeks, most likely. But I'm gonna let loose the how to take notes video. It took me a day to edit it, a day to debug to figure out a way and a round way to be able to process it. And then it took me another day to muck around with it and process it. I let it process and it took 15 hours to render, okay? It's only an hour long, but because I have videos popping up when I'm showing notes, because what I do in that video, we went through my notebook, behind the scenes we did it and showed it, went through my notebooks, some of the notes that I've taken over the years over the last few years anyway. I went through like six of the notebooks I have more. And every time we hit certain type of note I've created content, not every time, but some of the times created content, I had a video popping up. So you can see the notes that I took for that video being created. So for anyone that's into creating content to ask me how I create content on what I do and all this jazz, that, this video being loaded on right now, on YouTube, it should give you an insight into what I do to a certain degree. And again, this is, it is very personal, just to let you know, okay? It is very personal the way I organize. I play with things, but as I said before, I am who I am now. I was who I was in grade eight, right? I am, I am Cheecho, right? So things really don't faze me. I don't, I'm okay sharing personal information as long as it helps other people to experience life in a better way, right? And get an idea of how other people operate because I know our education system does not do that, right? So that video is going to be loaded on. And just because we're loading that on today, I'm gonna let that float for a couple of days on YouTube, just be the main video today, tomorrow, probably Monday as well. And then I'm gonna start loading on all of these, open discussion mass stuff that we're doing to YouTube. And the odds are I'm gonna load on one session at a time, okay? And sometimes Twitch is cutting the streams. And if Twitch is cutting the streams, you know, they're becoming two sessions, two videos that are gonna be loaded on that happened with the second stream yesterday that we did, right? So today is gonna be the video being loaded on YouTube, how to take notes. And then we're gonna come back at 11.30 and do another live stream. We're gonna come back at two o'clock, do another one. And then 4.30, do another one. I believe those are the times if you wanna check the evidence page, okay? So that's it. I'll see you guys at, I believe 11.30 for next stream. Thank you for being here, by the way. Thank you for the questions. And thank you for the multi-question and the corrections and all that jazz. Thank you for having me back. I'll see you guys in about an hour and a half. Bye for now.