Why can't we do the same thing with 4d? Why does the object just disappear when it bounces into the 4th dimension, can't we maybe see a projection of it onto the 3rd dimension?
It was really disorienting (the 4d, but also the eye-crossing), and like the post author says, just bundles of lines rather than solid shapes. Still very cool.
Ooh, I found it!
Yes, you can. This program just doesn't.
Ofc it is abstraction, I know that physicists aren't happy with heterodimensional settings at human scale.
Now contrast that to if you were plucked up vertically 'above' the game's level to look down upon it. Now you can see the entire 2D extent of the maze at once. Before, your vision was blocked by the walls, now you see the walls and what's on the other side of the walls simultaneously in a way that's entirely distinct from simply seeing through a transparent object.
Now, like seeing a 1D amount of information about a 2D maze while live inside it, we see a 2D amount of information about a 3D world around us (a picture demonstrate's this 2D amount of information - it's planar). Now imagine being lifted out the 3D plane of existence so that you could behold the entirety of the 3D world at once. That's the rough analogy.
Every 4d object would end up being a clear 3d cross-section where it intersects with our 3d world, plus a cloud of superimposed and increasingly hazier 3d cross-sections above and below us along the 4d ("w") axis, projected down onto w=0 3d-space.
Now apply the same analogy to our world: our 3D world is just an infinitely large 3D plane in a 4D world. When the objects aren't in our 'plane', we can't see them.
Edit: Didn't notice it was mentioned at the end of the comments, https://news.ycombinator.com/item?id=14472395, there's a free version linked from archive.org.
Aside from all the misogyny and the style of writing, you mean?
But I'd still like to see the difference.