4D Unknot

In four dimensions, you can’t tie your shoelaces — because 4D knots don’t work. Any 1D curve in 4D space can be continuously deformed to the unit circle, which is an unknot.

The looping animation below demonstrates how to undo a trefoil knot in 4D, where rainbow colors code the 4th dimension. The animation pauses when curve segments appear to intersect, but the segments’ different colors reveal their separation in the fourth dimension.

2D is too small to allow complicated neural circuits, and 4D is too large to enable knots; perhaps unsurprisingly, we find ourselves in a 3D world.

Unknotting a trefoil knot in 4D, where rainbow colors code the 4th dimension