 Hi everyone, this is Chisholm. Welcome back to my channel. Now what I like to do in this video is share with you some of the tools that I have on my disposal when it comes to teaching mathematics, right? And this is sort of a routine that I use to talk about coordinate geometry, to teach my students coordinate geometry. And it's a routine that I use no matter how old my students are. I've used this little routine with students that I have worked with in elementary school. I've used it with students that I've had in the beginning stages of high school. I've used it in the later stages of high school, grade 11 and 12, right? And I've also used this with students that I've had in college or university, right? And I use this basically to give people a really good appreciation of how mathematics can be used in the real world and a better appreciation of spatial coordinates, right? To give them better appreciation of where they are in the world and how the position of other things in the world surrounding them can be looked at from the lens of mathematics, right? Which is basically coordinate geometry. And what I do is sort of slip in the concept of time in there as well. And the question that I ask my students when I'm trying to teach them this, right? And it could be just a very simple concept of just putting a point on a Cartesian coordinate system or taking a look at a function, taking a look at a graph and taking a look at how that function varies with time, right? And the question that I pose my students is basically this. I ask them, how many dimensions do we live in, right? And usually it catches my students by a little bit of surprise, right? Because if we're trying to put a point on a graph on an XY coordinate system and they're having a little bit of a hard time visualizing this or if we're talking about three dimensions or two dimensions even when we're trying to put even a polynomial function on a graph in an XY coordinate system all of a sudden I sort of pause everything if they're having a little bit of a hard time appreciating what's going on and I say, listen, let me ask you this. How many dimensions do we live in? And I pause, right? And I let them think about it. And some students look at me like, weird, why am I asking this? Some of them go, oh, we live in a three-dimensional world. Some people turn to me and say four dimensions which basically depending on the answer they give me I start this discussion, this little routine in different locations, right? But what I want to do with you right now is go through the whole routine, right? And this, as you can guess, sort of relates to some of the other videos we've put out regarding time, right? We put out a little video or a long video where we took a look at how the perception of time can vary with age and how mathematics can help us to have an appreciation of why as you get older, the concept, the perception of time may vary depending on your experiences, right? And in that video we sort of related it to ratios and how long you've lived, how old you are and how long you've lived and how many experiences you've had and stuff like that. And it was a nice little introductory concept to how mathematics can be used to appreciate the concept of time, right? The perception of time. And this definitely relates in a big way to what we talked about when we had a little discussion regarding Einstein's theory of relativity on the paper that he put out on the electrodynamics of moving bodies where he basically introduced the concept of space-time that we don't live in just a spatial world. We live in a space-time world because time is the fourth dimension when it comes to us appreciating the universe where we are, right? And that's sort of a huge introduction to this video, right? Which is definitely related to some of the things we're talking about and we will continue to talk about when it comes to zero and infinity because zero and infinity in a big way connect up to space-time, coordinate geometry and our understanding of time itself and definitely connect up to what we talked about regarding the perception of time how the perception of time can vary with age, right? So that's a sort of a pretty long little introduction to this little routine that I have that I work with kids in elementary school even, right? And basically the concept is this when my students have a hard time or not necessarily a hard time when I feel that my students don't really have a good appreciation of what coordinate geometry is and what the power of mathematics is when it comes to explaining to us where we are in the world, in the universe how that can play out in our everyday lives, right? And the routine I have is this, okay? The first question I ask and to a certain degree I don't bring this up out of the blue we need to be talking about graphs, coordinate geometry, points, x, y axes something like this, it has to be something related to something that's going to be put on a graph, right? So when I'm working with a student that needs to understand this concept, right? Or have a better appreciation for it, I sort of pause everything and I turn to them and I say, how many dimensions do we live in, right? And depending on the answer and how long I've worked with the students I sort of start this discussion in different locations but what we're going to do, we're going to start off at the base of it, right? To a certain degree, right? We could go a little bit earlier on but I'm going to start off assuming that we're talking about high school students in large part, okay? So my question to you is, how many dimensions do we live in, right? And we've already talked a little bit about that in the intro of this, right? And, you know, my students sometimes say, oh, we live in a three-dimensional world and they go, you know, they try to be funny and they go 25 dimensions or something like this and then when they do that, I sort of relate it back to string theory and go, well, actually it could be 10 or 11 dimensions or something like this some people have discussed using string theory and it could be, I think, I've even heard 26 at some point papers that I've read a long time ago, right? So my question to you is, how many dimensions do we live in, right? And if there's little pause, if there's a little discussion, right? We talk about it a little bit and then I ask them this, if you're going to be meeting a friend somewhere, right? What are you going to tell them? Where are you going to tell them to meet, right? So just imagine if you're meeting a friend downtown somewhere let's say you're going to meet your friend, right? Let's do a little break here. Let's put up a couple of roads here, right? And let's put a building here. That's a rectangular building. Let's put a square building here. Let's make it bigger. So let's put a, let's go. So let's assume we have a building up here, okay? Trippy building, hard to draw in this angle, right? So let's say we have a building here and we're going to meet up, meet with someone, right? And let's say this is the corner of 1st Street or let's call this X Street and let's call this Y Street, right? So if we're going to meet someone, let's say here on the 7th floor, okay? So we're going to meet someone here. Let's put a little floor here, right? I'm going to meet someone here. Let's say we're going to meet them and usually I say you're going to go watch a movie on the 7th floor of this building. What are you going to have to tell your friend? How are you going to meet there? What's the information that you have to convey to them, right? And usually, you know, my students say, oh, I just tell them to meet me at the building at the corner of XY Street on the south side or north side or northeast side, I guess this one, right? If we're north, it's straight up. Then I usually turn to them and say, okay, so you're going to sit there and everybody's texting. So I say, you're going to text your friend and you're going to say meet me on the corner of X and Y Street on the 7th floor, okay? So I usually confirm that that is what they're going to tell them. And then I ask them, is that all you're going to tell them, okay? And usually, most people, 95% of the people have asked this question to, they go, yep. I go, so you're going to text your friend and right now, if you're going to do it, you're going to grab your phone and you're going to text your friend and you're going to go meet me at the corner of X and Y Street on the 7th floor. We're going to go check out the movie or a movie or a show or go to a bookstore or go to a comic store, right? And they go, yeah. Really, 95%, if not more of the students I work with, they say yes. And then I turn to them and say, when are you going to meet them? They do a little pause. While they're having that little pause, I don't let that pause last too long, right? Very quick. I go, when are you going to meet them? And they go, boop. And within a second I go, we live in a four-dimensional world. There's an X-axis, there's a Y-axis, right? There's a Z-axis, right? And there's time. There's depth. There's the length, there's width, right? And there's time. There's height, if you want to think about it. That's height, the seventh floor. There's length, there's depth, width, whichever way you want to think about it. And time, it is a four-dimensional world, right? So when you're trying to meet someone, you don't just say, on the corner of X, Y, and this height, you don't just have an X or Y as Z, if we're going to call it Z height, right? You also have time. Those are the four, right? Four variables we have when it comes to appreciating where we are in the universe, okay? X, Y, Z, and time. Length, width, height, and time. One of these could be depth, if you want to call them depth, right? And then I ask him, what is the difference between X, Y, Z, and time? Is there a difference between length, width, height, and time? And I let that pause last longer, okay? And I let them think about that for a while and then they go, I don't know. I go, think about it, think about it, right? We have X, right? We can go this way that way. We got Y, we can go this way that way. We got height, Z, we can go up and down. And we have time. What's the difference between X, Y, Z, and time? Okay, and I let them think about more and I let them give me answers. And depending on how frustrated they're getting, right? I continue asking them questions, trying to lead them towards the answer because I think that's one of the... One thing that's really important when it comes to teaching mathematics is not giving answers all the time. Sometimes you have to give answers, right? That's the punchline, right? But it's really important to lead students on, to get them to get to the answer themselves, right? And make mistakes along the way so they can eliminate some of the answers for themselves, right? So I continue this back and forward with them, okay? And then I turn to them and say, well, X, you can go this way or this way. And then I start introducing numbers on there, right? And I say if this is a Cartesian coordinate system and this is zero, right? Then we can go negative, right? Now, we've talked about this Cartesian coordinate system a lot, right? Or somewhat. Actually, no, we've talked about a lot, right? When it comes to talking about X, Y, plan A and talking about series 3A and 3B, right? With graph polynomials and functions and we've done a lot of it in ASMR math, right? But for the X, you can go negative and positive. For the Y, you can go positive and negative, right? This way and that way. For height, you can go up and down, positive and negative. You can go in the basement, negative, right? Time is something that, as of right now, end of 2017, we don't know how to go backwards in time. We can only go forward in time, right? So time is one directional as far as we know, right? So the difference between X, Y and Z is that for X, Y and Z, length with height, we can go both directions, positive and negative, right? Or increase it and decrease it, right? Because you can't really have a negative height unless you have, you know, set your zero point on street level and this thing has parking in the basement, so you're in negative height, right? But when it comes to time, there's only one direction. We cannot go back in time, right? Right now that you're watching this video 30 seconds from now, the only way to go back to where we are right now is to pause the video and take it back. You can't travel physically back in time, right? We have a recording of things, but we can't go back in time, right? When we're experiencing life. So that's the big difference between X, Y and Z. X, Y and Z are both directional. You can go forward backwards. When it comes to time, you can't go backwards. It's one directional, okay? As far as we know right now. And that is the big difference between what the space aspect of space time is and the time aspect of what space time is, right? So we live in a four-dimensional world and that's the way we have to interact with the world in four dimensions. It is not just an X, Y, Z plane that we live in, existence that we live in. There's the concept of time as well, which is obviously links back to what we talked about when it comes to how the perception of time varies with age, right? When it links up to what we talked about regarding theory, Einstein's theory of relativity, right? The natural dynamics of moving bodies. When it comes to relating to the concept of zero and infinity, right? They all overlap. They all overlap, okay? So I thought I'd share this with you. It's just a routine that I have. I'm sorry if the delivery is a little scattered, right? Because when it comes to teaching this, it's very individual specific, my students. It really depends on where they are, their mood, their understanding of mathematics, how inquisitive they are, how interested they are in this, right? And I play around with that and lead them in certain directions, depending on their mindset, just to make them have an appreciation for this. And I beat this thing to a pulp. I bring this up. I bring this up. I bring this up to a level where their mindset, their understanding changes, right? Because I think this is one of the most important things that we really have to understand when it comes to understanding the language of mathematics, which is where we are in the world physically, right? How we perceive time, how we experience reality is really dependent on four dimensions, x, y, z, and... I just thought I'd share that with you. It's an important concept. I'm going to do a lot more of this stuff. I'm going to share with you some of the tools of my disposal, some of the things I do, some of the things I've used to get a point across when it comes to talking about mathematics. Okay. That's it for now. I'll see you guys in the next video.