Videogame design requires logical skills, definitely. But arithmetic, not really; you might think of videogame programming instead. A game designer has to carefully specify events in a simulation and their contexts, for instance what unique conditions must be met for a character to grab a ledge (including character states, user inputs, timings, distances and angles), but they shouldn't have to worry how the angle between the character's shoulders and the ledge is computed; this is programmer's role.

@@EcoAku Totally agree! I kind of paired them both together in my example.

you mean they won't let me sit and play video games all day? WTF!

That makes me all the more interested

Blox117 that’s the job for testers, and the majority of the time is to play prototypes instead of finished products

probably a computer class, not math class. Or add computers to math class. It's much more intuitive in graphics that with formulas on chalkboard.

everything is more intuitive with computers tbh.

I actually never learnt vectors in math (yet) i do them next year However, i learnt them in physics class and engineering class (yes my school has an engineering subject) so i found vectors to be fun as ik where to apply them Such as adding forces on a structure

vectors should be introduced in geometry

check out my lectures on engineering maths and units to get A's kzfaq.info/get/bejne/f8l0eNqm1bebgqc.html

@Dr Deuteron I know that now, what i meant is, it would have been nice if i had known when i saw complex numbers at high school

Math is not Physics or Engineering. Many applications of particular areas of Mathematics weren't known/discovered until years/decades/centuries after their inception. Pure Math isn't a field about applications of formulae or specific processes, but rather, it is system of logic and reasoning. The applications of mathematics come in the form of other fields entirely; the aforementioned physics, engineering, etc, and trying to pigeonhole mathematics education by forcing applications for topics is an easy way to cripple expansion and exploration in the field and the skills it is used to develop.

@@EpicAsshole : Introducing mathematical topics with some sense of practical use will help students to build their intuition about the subject. Not only will they solve mathematical problems with intuition, it will be much easier to abstract mathematical ideas when there is a strong foundation to do so. In essence, intuition for foundation, abstraction for advanced use. A high school does not need much proof of a formula, rather they need understanding it. An engineer does not need the same mathematical proof background level in comparison to a mathematician, therefore learning should be more need basis.

@@comprehendnature2404 Beyond basic arithmetic, it is quite difficult for most people to really generate any sense of practical use without a fairly strong foundation in the topic; you have the direction of abstraction reversed. Beyond the basics of mathematics, you generally have to be familiar with the abstract concepts before you can apply them to concrete topics and novel problems, as for more advanced topics, the typical person cannot derive the abstract understanding from concrete phenomena.

@@EpicAsshole nailed it. You should understand the idea first and then apply it when necessary. Not the other way around

Yeah that would be awesome

Remember how often he used the word "normal?" In 3 dimensions, the normal vector is a vector that points "out" of a 2D plane that cuts through the 3D space. Such a 2D plane can be fully described by two (non-colinear) vectors, such as you'd get by picking one corner of a triangle and "pointing" toward the other two points. It turns out (and certainly not by fluke) that the cross product takes two vectors as input and produces a third vector that is perpendicular to both. Since we've required our two input vectors to be non-colinear, the only direction that can be perpendicular to both of them is "out" of the plane they define, which (again not by fluke) is exactly what we need for our normal vector. A couple of fun quirks: 1) There are actually two vectors that point "out" of a plane -- one facing "up" and one facing "down." Getting those backwards in a 3D graphics setting can lead to "interesting" results, as your lighting is effectively turned negative .. assuming the object is drawn at all. There's an optimization called backface culling that (using the dot product!) compares your viewpoint to the normal and if you're "behind" a particular triangle, it won't be shown (its assuming the object is solid and therefore there should be another triangle closer to you that would obscure this one anyway.. If you ever get your camera "inside" and object and it just blinks out of existence, this is probably why.) 2) Because the cross product returns a perpendicular vector, and the dot product returns zero for perpendicular vectors, it implies (AxB).A=(AxB).B=0. This is actually a very useful fact in lots of linear algebra (knowing things whether things are explicitly perpendicular or not is often far more important than knowing how far off of perpendicular they are.) Finally, I don't really remember the relevance of the cross product in other dimensions. But computing a normal in 3D is pretty darned important on its own!

Yeah,I would love it if you made another video on cross products of vectors

@@altrag Hmm cool, really liked the first fact; was new to me.

It would make sense if you were a physics professor. Many concepts from pure mathematics don't necessarily have a lot of practical applications, but that doesn't make them any less interesting.

@@helloimnisha what? Of course that makes them less interesting. Much, much less interesting in fact. It might still be interesting for people that inherently enjoy math. But for the rest of us, we simply learn and use math for it's usefulness.

@franciscodanconia45 any link about similar resoruces?

really?

@@RAGHAVENDRASINGH17 unfortunately, yeah. I'm more of a theoretical physics guy, so I'm less informed about the real world stuff. But as a 1st year physics major, I should know a thing or two about such things. I feel bad, tbh.

@Metric Tensor Nope. I don't regret taking physics as my major. I love it! Something about physics really draws me in, which even I can't properly explain. I even changed my channel niche to spend more time with physics. However, being a freshman, I can't really give you a solid answer, since the euphoria may not last long. But since I don't mind the sufferings as a physics major, things might not change for me that easily. :)

@Metric Tensor first, are you a college major or in highschool?

@Metric Tensor ok so it makes things easier. Right now, I can only tell you what I'll probably do in the future or what I intend to do. It's obvious that engineers get paid more than physicists. So after PhD we generally have three options: 1) Industry job, where most people go for an engineering job. It's quite lucrative, but then you'll probably lose the passion for physics and just getting a job finishing eng major would've been better. 2) Academic, where you get to be a professor and do more research (as a part of post doc and beyond). Funding for research is generally low, due to competition. If you become an experimentalist, generally high fundings. Reverse is true for theoretical physics. 3) Finance, where you get to manipulate the market and predict prices using maths. I'm not sure, as I just got introduced to this topic very recently. But some physicist guy did it in the past or something to make more money. High risk, high reward. So, as far as I know, these are the options. So whatever you think suits your style. If you have a burning passion for something, do it. Roads will show slowly itself. If you only care about money, then either don't take physics or do extra work for side hustles like me.(I trade options and make KZfaq videos.) As for my future plan, since I'm interested in QM and ML, I plan to create a business related to Quantum computing, but that probably won't be possible anytime soon (I'm also doing a major in CS btw). But in general, I just wanna do research on QM and create business out of whatever I find interesting in the future. But since I'm doing side hustles right now, I'm not worried about getting jobs, as I can just invest whatever I earn today and reap it's benefits later. But it's quite tiresome to do double major and have side hustles. I have to make a lot of sacrifices. Sooo yeah, that's my plan with physics in nutshell. I'm not really the most suitable person to give you the information, since I'm just a 1st year student. But I hope this helps. :)

Turns out we’ll have to reinvent math to fit quantum mechanics.... Or maybe is dark matter changing the laws of universe when stuff arises to the ‘macro’ scale?

Hmm..interesting

OOO interesting

Huh. Interesting

Hmmm.. interesting

InTeReStInG

Well, technically they could. If you apply voltage to a solar cell it lights up just like and LED, but I know that at least on on-grid systems the electronics of the DC-AC inverter prohibits the energy from going the other way. I never worked with off-grid systems, so I don't know how it's done in that case.

Since the sun is out of sight, the irradiance level at nighttime is nowhere near what it is during the day. The fact that the dot product with the line of sight to the sun is negative at night, is irrelevant. The panel can radiate energy to the cosmic background, but it will be a hell of a lot less than the power it would absorb during the day. Plus, panels have diodes in them that stop reverse current, so they automatically turn off if you attempt to let them "produce negative energy". This is a real concern for solar thermal panels, unlike solar electric panels, as they would radiate away their heat at nighttime, if not encased in glass. The glass acts as a bandpass filter that lets in 5800K sunlight, and blocks the emission of low frequency infrared that the panel's 300K black surface would emit on its own.

So this didn't start off as a youtube channel actually. In the beginning I was interested in starting a business, not being a youtuber necessarily. The first several videos that you see on this channel were instead on a website that I coded where I offered some videos for free and then put others behind a paywall in an attempt to make some side income (at the time I didn't even know about using youtube to earn a living). Since the entire website was video based I decided I should throw some videos on youtube in an attempt to advertise the website. Fast forward a few months and those videos started to get some real views (way way more than the website) and I was getting comments pretty much daily. The comments (mostly positive) made it much more real and I loved the feeling of having people I've never even met tell me these videos actually helped them in their personal life. It didn't take long for me to have more fun posting videos on youtube for free where I got real interaction/views compared to making a little money through a side website which didn't have that kind of interaction. As much as I loved making the videos though I knew I had to make money from it somehow cause they took a lot of time (I was not in the youtube partner program at the time), so I started watching videos on how to make a living with youtube. I began to sign up for affiliate programs, I reached out to advertisers, and I signed up for the youtube partner program. The growth in the beginning was slow and I was making maybe $100 a month. I got my first relatively 'viral' video eventually and that month I got closer to $800 which was an amazing feeling and I started to see the power of youtube. From there I just kept making videos in my spare time, trying to learn new software and just improve the video quality overall. I've always loved teaching math and this was a great way to expand on that. While I was building the channel I was working as a tutor so honestly my entire life was just teaching math/physics lol. In the end I wouldn't say I wanted to be a youtuber, I kind of grew into one after learning more and more about it, realizing I do in fact enjoy making the videos and interacting with the community (and the fact that I can now live off of youtube definitely made it a great investment of my time).

Zach Star Wow, thanks for the response, a great read, and truly inspiring!! I love your videos, and hope to see more content! :)

To be honest, a good full computer graphics course should probably a mix of both sprites, GUIs, animation and linear algebra.