And I was a little bit surprised to learn how up in the air the potential notations and conventions for teaching students about vectors was. Like a lot of the actual notation and terminology we have for vectors and cross products dot products the way we think of them in 3D ultimately stems from quaternions. You know, even the fact that we use i, j, and k as letters to represent the x, y, and z directions. And if Hamilton had his way, we would still teach engineering students primarily about quaternions and then things like the dot product and cross product would be viewed as subsets of what the quaternions do and what quaternion multiplication is. And I think there's a compelling case to be made for the fact that we would use that if we could visualize four dimensions better. But the reason that quaternions never really won out as the notation du jour is because they're confusing because no one really understood them. There's all sorts of hilarious quotes from Lord Kelvin and the like about how quaternions are just needlessly confuddling when you're trying to phrase some fact about the universe. Like Maxwell's equations were originally written much more quaternionically than we teach them to students now. And arguably they're much more elegant that way, but it's confusing because we can't visualize it. So I think if you had some alien civilization that came but they had a very good spatial conception for four dimensions, they would look at our vector notation and think that it was not capturing the deeper realities of math. Arguably, who knows? What do you think is the main thing that drives people away from math? Always hard to answer on these kind of things, but I really suspect that as soon as you wrap something in a certain kind of judgment of there's a notion of being correct or incorrect or an implicit statement there's a notion of being good at math. Some people are math people, some people aren't math people. As soon as you get someone identifying that they're not a math person, first you know insinuating that even makes sense and then insinuating that they fall into that, like of course you're not going to like it. Of course your natural mind churnings aren't going to go in the direction of some puzzle because you'd much rather think about things that you're good at and that make you feel happy. All of the latest stuff about growth mindsets and Carol DeWack and Joe Bowler are really behind that. You know, the idea that if you're trying to tell a student something about how they're doing with math rather than framing it around, oh you must be so smart, right? Frame have worked very hard or you must have put a lot of time into that. There's a lot of much less judgmental things that we have out there, like reading. Even though there's some notions of reading comprehension tests for students in school and you know you're reading at an eighth grade level, people usually aren't like, oh I'm not a reading person, right? Like I, those words like some people that just make sense to them but for me those letters I don't know how they come together. When it comes to contest math like the AMC, I think those can be really good for high schoolers as a bank of problems. I think they can be really bad for high schoolers as an insinuation of there's some like top-tier math folk and they can do these problems really quickly. But if you give the same questions to the student and you say rather than being forced to go through all of these in 75 minutes, you say let's spend 30 minutes on just one of them, right? Really delving into it. They're really solid problems that kind of engage in the spirit of problem solving and you know removing that judgmental aspect, removing that time aspect, I think you know that can help out a lot. A lot of people ask about certain things that I've made promises for but haven't necessarily delivered on. In a recent video, you know, I did one on divergence and curl and I mentioned at the end an example of using complex numbers to model fluid flow and a certain model for flow around a wing. And you might notice I have yet to actually put out a video on that and I've certainly seen a number of commenters you know hampering on me for that fact. If there's ever a thing that I promise and then I don't make a video on it, it's probably because I spent a good amount of time trying to write a script for it that I just didn't feel was compelling for whatever reason. And I think maybe the granddaddy here is the probability series, which at the moment I have five videos that I've made that are you know released to patrons. I don't, I just don't feel great about them and I kind of want the stuff that I put out to you guys to be something I feel is you know if not original, something that wouldn't be out there otherwise from other creators. And there's a lot of good probability material online. I will probably do something to release the material that I have, either just as it is but on some second channel with the acknowledgement, hey this isn't the greatest work I think I've done, or trying to rework them and make them standalones. But as far as you know essence of blank content, I feel much clearer about how I would want to extend the linear algebra series rather than spinning my wheels on certain scripts and animations that I ultimately don't think are going to deliver something to you guys that I would feel proud of. Do you have any questions, Jabril? I'm just reading from, reading from some Reddit ones here, but we do something live. How much compromise if any do you have to give with like what you can animate versus like what your script is trying to convey? Usually if I can't animate a thing, and it's a mathematical thing, it's not like a frivolous cartoonish type thing, I change the tool so that it can animate that thing right and then that might take more time. And it's possible that subconsciously that means I resist topics that I know would be more difficult to animate. I don't think that happens, I like to use that to encourage creation of new things right, like on the divergence curl didn't have good fluid flow stuff but it was fun to play around with that. For quaternions right now I think there's a lot of 3D related things that I wanted to sort of upgrade because the previous way I was doing a lot of 3D animations was clunky and not as extensible as I wanted it to be. So usually that is a good excuse to just improve the graphics tool. We have somewhere a question on here, what sort of music do you listen to?
