
mystran
 KVRAF


4657 posts since 11 Feb, 2006, from Helsinki, Finland
by mystran; Sat Feb 27, 2016 11:00 am
Re: Analogue Modeling Tutorial
Here's what I want to say about math: it's not hard.
It's mostly just scary, because it's usually written in a weird notation and there is a lot of different rules of what you can do, and you can't do anything unless there is a specific rule that says that you can do it (and that's pretty much everything you really need to learn). You might want to learn enough rules to get where you want to, and then figure out which ones you need to use, but none of the rules are hard! There's just a lot of them, so it takes some time to get used to choosing the best ones for any given situation, but for the most part you could just try them all at random until you get what you want.
Understanding why some particular rule (or shortcut that results from some other rules, or whatever) is valid can sometimes be very hard and make your brain melt. But the good news it that you practically never need to actually understand why. You just need to know that "some wise men" have already melted their brains figuring out why it's valid and now you can just accept that it's valid and use it for what it's good for.
What I mean is that when you need to do trigonometry, you can take a table of very many trigonometric formulas, you try to find something that might (or might not) get you to the right direction, and then you just use that (or something else if the first one doesn't work out), and you never need to worry about why those trigonometric formulas work, because some wise man somewhere already melted their brain proving that they do.
After a while you might realize that you can easily derive all those formulas yourself and you'll realize that your brain in fact didn't quite melt in the process. Congratulations, there's probably another set of rules that will make your brain melt if you think about them too hard and if that's not the case you can become a real mathematician and start thinking about the sets of sets of rules or some such nonsense to keep your brain melting process active.
But until then, just get a good book of formulas and every time you're stuck, try something random. I might not be the fastest approach, but if it takes too long just let your favorite math software do it for you, that's essentially how they work (obviously with some heuristic logic in terms of which rules should be tried first, to try to get the answer in finite time, but still).

ps. Here's a fun personal experience: I've been using quaternions for representing 3D rotations for howevermanyyears I can't even remember, because they just work remarkably well for that. But it wasn't until very recently (week or two ago) that I was casually walking in the park (not even thinking about anything 3D) and finally realized that just like you can treat a complex number as a vector on a plane, you can treat a quaternion (sortof, there's some weird geometry into it, so don't use this description when you are writing your quaternion routines) like a screw that you push through a sphere (essentially such that the sphere rotates as you push it further).
The bottom line is, don't be scared of trying to understand math, just focus on figuring out which rules are useful and which rules are not. Then learn where to look when you need more rules. It's all pretty easy when you don't try to think about it too much.