But first, we need to talk about parallel universes.
And if you thought my other tangents were complicated, just you wait.
Okay, so Mario's position is a floating point number but it's converted to a short when the game uses it to test for collision with floor triangles.
In other words, Mario's position can basically be any decimal number but it's converted to an integer between negative 32,768 to positive 32,767 inclusive.
So, any fractional portion is truncated and numbers too big or too small are moved into this range using the modulo operator.
Graphically, that means the position used for floor detection is always inside of this box.
So if Mario's in that box, then his actual position and the position used for floor detection are the same, albeit maybe off by a single fraction due to the truncation.
But if Mario leaves that box, then his actual position and the position used for floor detection will separate since the position used for floor detection will just loop back around to remain in the original box.
So now I ask you this.
Here's the course.
So if Mario is standing way over here where there's no land but the position used for floor detection is on land, can he stand over here?
The answer is yes.
As far as the game sees it, Mario is in fact above land over here because the game actually checks for land over here.
So, for all intents and purposes, there is essentially land over here.
A copy of the original map.
And this is what we call a parallel universe or a PU.
And this applies to every one of these boxes.
So there's actually a grid of nearly infinite PUs.
Here is a to scale diagram of the PU grid.
As you can see, the PUs are actually pretty far apart.
But I'll be taking some creative liberties and drawing them closer together for the sake of clearer visuals.
Now, PUs aren't as glamorous as you might think.
The graphics are only found on the original map so that PUs are completely invisible.
Furthermore, PUs have no objects like elevators or item blocks, no enemies, no items like coins or stars, and not even any walls.
So really, it's pretty barren.
Furthermore, the N64 console will actually crash if you go to a PU and let the camera follow you.
But luckily, we can avoid that crash by fixing the camera in place on the original map before leaving it.
Though, that does make it even harder to tell what is going on in the PUs.
So, as you just saw, you can travel to a PU if you have enough speed.
But, it's not as simple as you might think.
If you h
