3 ms·

One way to visualize 4d is using scale as the 4th dimension. Objects that are far along the 4th axis will appear too small or too large.

by akomtu 3y ago

IIAOPSW 3y ago
Another way is to realize waves of different frequency are literally orthogonal vectors. Also, RGB colors form a literal color space. So at the cost of sacrificing normally colored objects, you can have rainbow banding in the 4th direction. Imagine along the 4th dimension there's a hallway with evenly spaced lightbulbs tinted in RGB such that looking down the hallway you see rainbows. If you are moving in the direction of the 4th dimension, these rainbows will appear to be moving like waves rushing towards you from the vanishing point. If you are moving perpendicular to it, the bands of rainbow colors will remain constant relative to your motion. In general, the apparent speed of the background color banding patterns will be proportional to the component of your motion in the direction of the 4th d. The rings of rainbows are easily spaced, so looking at the scene you can tell how far along the W axis it is by seeing how tightly the rings are bunched (must be approaching vanishing point if they seem close) and also by just eyeballing how often the rainbow has repeated between your position and the object, judging distance as if you were counting floor tiles.
GuB-42 3y ago
That's actually how we visualize 3D with our 2D retinas and monitors. It is a perspective projection: objects that are far away (in 3D) appear smaller (in 2D). Making a perspective projection from 4D to 3D, and then from 3D to 2D for display is simple mathematically, and it could be done in wireframe mode instead of what is currently, I think, a simple orthographic projection. In fact, it is very possible that the author tried it but didn't like it enough to include it.

3 ms·

One way to visualize 4d is using scale as the 4th dimension. Objects that are far along the 4th axis will appear too small or too large.

by akomtu 3y ago

One way to visualize 4d is using scale as the 4th dimension. Objects that are far along the 4th axis will appear too small or too large.

IIAOPSW 3y ago
Another way is to realize waves of different frequency are literally orthogonal vectors. Also, RGB colors form a literal color space. So at the cost of sacrificing normally colored objects, you can have rainbow banding in the 4th direction. Imagine along the 4th dimension there's a hallway with evenly spaced lightbulbs tinted in RGB such that looking down the hallway you see rainbows. If you are moving in the direction of the 4th dimension, these rainbows will appear to be moving like waves rushing towards you from the vanishing point. If you are moving perpendicular to it, the bands of rainbow colors will remain constant relative to your motion. In general, the apparent speed of the background color banding patterns will be proportional to the component of your motion in the direction of the 4th d. The rings of rainbows are easily spaced, so looking at the scene you can tell how far along the W axis it is by seeing how tightly the rings are bunched (must be approaching vanishing point if they seem close) and also by just eyeballing how often the rainbow has repeated between your position and the object, judging distance as if you were counting floor tiles.
GuB-42 3y ago
That's actually how we visualize 3D with our 2D retinas and monitors. It is a perspective projection: objects that are far away (in 3D) appear smaller (in 2D). Making a perspective projection from 4D to 3D, and then from 3D to 2D for display is simple mathematically, and it could be done in wireframe mode instead of what is currently, I think, a simple orthographic projection. In fact, it is very possible that the author tried it but didn't like it enough to include it.