For an appendix to the video, here’s some further explanation:
- The `tan` function is actually very important in math and game development. The reason I skipped over it here is because the only noticeable effect breaking it had was changing FOV and the scale of menu animations.
- The reason the game is at all playable is because the Source engine likely uses wrappers or custom implementations of many functions which I can’t hook. Anything precalculated or any GPU code is also obviously off limits, so this only really messed with some dynamic parts of the engine. Some other math (like movement) is also primarily done with vector operations, which often avoid using many of these functions.
- The audio and lighting are messed up because of the modifications to the `sqrt` and `pow` functions, which handle the square root and exponentiation respectively. Source has a sound system that adjusts reverb to the scale of the room you’re in, and that uses `pow` for its calculations. We’re effectively inverting the function, which means that small rooms are loud and bigger rooms are fine. Lighting is a similar story - the fog distance and light intensity are also products of exponentiation.
- I’ve seen some comments suggesting that I should’ve tried using bad approximations for these functions, but rather unsurprisingly, that would still cause less chaos than pi being 4 or sine and cosine being swapped. I even tried turning sin/cos into a triangle wave, but that changed virtually nothing besides making physics a bit jittery.
- The ""physics engine"" I made in 10 minutes is really not as impressive as it sounds. It’s just doing ray-AABB intersection checks for all physics props and either simulating gravity if something is in the air or not doing anything depending on if there’s a collision. There’s some more code for picking up and throwing things, but that’s about it.
- I somewhat regret not adding this appendix to the video with some neat animations and a voiceover explanation, but if you have any other questions, comment them below.

"All Aperture technologies remain safely operational up to π = 4."

"If the laws of physics don't apply in the future, god help you."

"Two plus two is... ten. IN BASE FOUR! I'M FINE!"
-GLaDOS, probably.

Wheatley was right that if he ever got off his management rail or turn his flashlight on he would die lmao

“Ln of x is now log base 3” 4 trillion trig students dead, 45 gaborillion injured

Portal two but I did the calculations

The way portals still work perfectly fine is insane to me

8:48 "yeah physics didn't quite work so i just made physics at home"

0:44 unit circle jumpscare

Portal but you looked into the operational end of the device.

I was a math tutor in college, and one time I tutored a guy in remedial algebra. We spent the first 15 mins of every session arguing about whether math was useful in real life, and how he thought the algebra was a waste of time, but bro was a COMPUTER SCIENCE MAJOR WHO WANTED TO GO INTO GAME DESIGN like bro you got another storm coming

If you told me this was an early-access Bethesda game, I would believe you.

minor inconvenience

Here's a fun function replacement: Replace all the trig functions with their hyperbolic counterparts.

"I disabled the physics and replaced it with my super simple physics engine"

And he said it like it's no big deal

π = 4: "You think I'm bad? Make way for my big brother!"
π = 5: "Sup!"

you should've just done what astrophysicists do:
π = 1
π^2 = 10

"Morty! I belch rounded down this dimension's fine-structure constant from 1/137.035999177 to a clean 1/137! I just hate long decimals, Morty, I FUCKING HATE THEM! Besides, it's such a small margin, what's the worst that's gonna ha-"

…Today, I learned how to tilt the cartridge — of a game that was only ever released on a DISC (and in digital form)! :D