4 ms·

Matrices are funny. You can encounter them as a teenager reading 3D graphics tutorials on the internet, learn that they can compactly represent scalings, rotati

Matrices are funny. You can encounter them as a teenager reading 3D graphics tutorials on the internet, learn that they can compactly represent scalings, rotations, and translations, and that several transformations can be conveniently “stacked” using this thing called matrix multiplication which looks like this… and that’s it, now you can use them for a cool practical purpose, but the tutorials never derive or attempt to justify why mmul looks like that, often because the author doesn’t know either! Or you can learn about them in school and be given neither a real-world use case nor a rationale or derivation for mmul. Or you can encounter them in college, and there the experience depends on whether it’s a good or bad kind of a linalg class. But even there – after all the painstaking definitions and lemmas and derivations – it’s easy to end up not grokking how mmul does what it does even if you grasp all the building blocks – vector spaces, bases, how matrices can represent bases and systems of linear equations and linear operations on vectors and how they’re all kinda equivalent.

boricj 4y ago
It reminds me of a funny story back when I was a student. We had a week-long group project in the first year whose theme was "a 360° pong". Our group decided that it meant the paddles had to travel in a circle around the playfield and I've decided that matrices and stacked 2D transformations were the way to go. The other students gave me blank stares, I basically said "trust me, you don't need to understand them to use them" and off we went coding. We ended up with the most impressive pong clone out of all the groups, as nearly all of them had axis-aligned rectangular paddles going around a rectangular path, whereas ours had a stretched half-circle paddle going around a circle path always facing the center of the playfield, alongside extra features like walls and a level editor. First class the Monday morning after, the math teacher announced that the next topic was matrices. We stared at each other in the group and grinned manically. If anyone wants to stare at an old C codebase from 10 years ago by a bunch of first year students: https://code.google.com/archive/p/pong-norris/ https://code.google.com/archive/p/pong-norris/
aj7 4y ago
And a lot of dynamics is e to a matrix.

boricj 4y ago

It reminds me of a funny story back when I was a student. We had a week-long group project in the first year whose theme was "a 360° pong". Our group decided that it meant the paddles had to travel in a circle around the playfield and I've decided that matrices and stacked 2D transformations were the way to go. The other students gave me blank stares, I basically said "trust me, you don't need to understand them to use them" and off we went coding. We ended up with the most impressive pong clone out of all the groups, as nearly all of them had axis-aligned rectangular paddles going around a rectangular path, whereas ours had a stretched half-circle paddle going around a circle path always facing the center of the playfield, alongside extra features like walls and a level editor. First class the Monday morning after, the math teacher announced that the next topic was matrices. We stared at each other in the group and grinned manically. If anyone wants to stare at an old C codebase from 10 years ago by a bunch of first year students: https://code.google.com/archive/p/pong-norris/ https://code.google.com/archive/p/pong-norris/

aj7 4y ago

And a lot of dynamics is e to a matrix.