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> The separation of talent and skill is one of the greatest misunderstood concepts for people who are trying to excel, who have dreams, who want to do things. Talent you have naturally. Skill is only developed by hours and hours and hours of beating on your craft.

- Will Smith

This kind of exploration, banging your head against the wall, is exactly "beating on your craft".

No matter if the result is crappy by any metric, trying to wrap one's head around things and producing output - any output - over and over is oh so important.

And dare I say talent without practice is useless and a waste, because one's going to stay in the comfort zone, and usually get cocky about it, whereas relentless practice teaches humility.

s/art/literally anything/g in this comic:

https://www.deviantart.com/scotchi/art/keep-tryin-690533685

There is also an epistemological aspect to a lot of this. In school you are often taught true statements ("facts"), but that is not the same as knowledge. If I accurately predict that the next time I flip a coin, it's going to land heads; I did not know it would. I made a correct correct statement, but I did not know.

Knowledge is about understanding how and why things work. That is what I was attempting to figure out about these linear algebra-operations. My classmates were attempting to retain the facts for the test, that typically doesn't work particularly well, and long term retention is poor. I've done that too. I could barely tell you what it is I'm supposed to have learned in those classes. But I could still probably construct 3D rotation matrices by hand without looking them up, all these years later.

You also had a goal beyond "pass a test", which I think is more important still. After all, Geometry isn't generally something taught or tested as merely a collection of facts (but rather their application, a la "given this, prove that", and you have to intuit a path through applying other proofs to get to the final one), and yet it still sucks as a subject in school. Because there isn't a real "why".

A per-cursor form of talent is burning passion, focus and interest, which leads to better & more practice. The person who is willing to push hard into their field is probably %80 of what people call talent. And then when they encounter the obsessed after the fact, they call it talent because they're effectively the same outliers.

Beyond that, what you describe as talent should be called built in ability, much like IQ or similar, because current usage of talent is too muddled with the well practiced.

Twenty-five years ago, slightly before I was an undergraduate, I got hold of the PC Games Programmers Encyclopedia http://bespin.org/~qz/pc-gpe/ and built myself a software renderer. You can see it on github: https://github.com/pjc50/ancient-3d-for-turboc

Software matrix multiplication is a perfectly reasonable way of doing 3D graphics, when you don't have a GPU. They were just starting to become a consumer product at that time: https://fabiensanglard.net/3dfx_sst1/

Moral of the story is that you were intrinsically motivated to learn… in which case it doesn’t matter how you learn it as long as you follow that motivation.

Is there any other sort of motivation?

Extrinsic, from the outside. For example being paid for stuff.

Right, seems to me that's still intrinsic. The motivation somehow entering me from the outside, I still want to do the thing. (If I don't want to do it, then I'm by definition not motivated to do it)

There has been plenty of research that shows a distinction. Stuff like paying kids to read books leads to them reading less over time.

https://rady.ucsd.edu/faculty/directory/gneezy/pub/docs/jep_...

Behavioral economics is debunked pseudoscience.

Incentives are more in the vein of psychology than behavioral economics but the two fields are clearly adjacent. And this "debunked pseudoscience" led to a Nobel prize a few years ago. And many of the observations that led to this--relating to people not always being economically "rational"--are very clearly true.

I don't think anyone other than an economist would assume that people were economically rational. Is it really worth a prize to demonstrate a fundamental hypothesis underpinning your field of science is wrong?

It was apparently worth a prize to explain more rigorously why behaviors often deviate from an underlying assumption of maximizing expected value. And, yes, some of the economics community was quite resistant to the idea that the answer was anything more than people are stupid. (That may be a bit of an exaggeration but there was quite a bit of resistance in economics to behavioral economics being a field of serious inquiry.)

You can argue with the (somewhat squishy) motivational theory but money is pretty much the classic extrinsic motivator in the literature. There's also an idea of internalized extrinsic motivation however like peer recognition. (Basically external motivations without an explicit carrot/stick.)

The line is somewhat blurry but there's probably a difference between playing a game and doing a job you don't really like because you're paid to do it.

Nothing squishy about it. The more indirection the more extrinsic it is.

Squishy in the sense that many things are neither purely external or purely internal.

If someone was threatening to kill you you would be motivated to defend yourself, even going as far as hurting them… wouldn’t mean that you would want or desire to hurt them.

I had a similar story. I barely got through linear algebra in university. The professor never suggested that linear algebra was useful for anything (except passing the course). Apparently the goal was to manipulate symbols. Applications were something for technicians, not academics. Everything was so abstract and seemed arbitrary. Theorems were developed and proofs were presented without ever providing any sense of why you would want to do whatever it was the theorem did. I had absolutely no intuition about anything related to linear algebra, I only had memorization to go on.

Then a decade or so later I encountered matrices in computer graphics and suddenly I found that a lot of that stuff was actually useful and piece by piece it started to make sense to me.

The way that course was taught didn't work at all for me. I wasn't looking for motivation in the sense that I want to use it, but more about what was the motivation for developing any of it in the first place.

> Turns out, software matrix multiplication is not the best way of doing 3D graphics

ok, what is? all the 3d engines I've ever worked with do tons of software matrix multiplication. You generally need to know where things are for collision checking and other things so doing it all on the gpu is not an option

> You generally need to know where things are for collision checking and other things so doing it all on the gpu is not an option

Sure. You can do some of it in software. That's fine.

Point is I didn't use the GPU at all, and did all the rendering in software. No matter how you rotate or translate it, that's not a particularly efficient way of doing it.

Anyway, the GPU usually does it with matrix multiplications.

So what are some of the more efficient ways of doing it, if it's not too much to ask? :-)

To have the GPU do the work for you.

A series of calls to OpenGL is a heck of a lot easier than setting up 3x3 rotation and translation-matrices and implementing a library to do 3x1, 1x3, 3x3 matrix multiplications, scalar transformations, transpositions, calculating determinants, planar projections, perspective shifts, and what have you.

Quaternions?

https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotati...

https://stackoverflow.com/questions/8919086/why-are-quaterni...