@alex: yeah it is, and it is Cartesian in the video. Rich just used time as an illustration.
@rich: loved the 2D/3D analogy - very nice.
Oooh, and my
HTC Desire arrived today
Doesn't 4d normally refer to the 4th Cartesian dimension rather than spacetime?
eg. a 4d hypercube is to a cube what a cube is to a square.
Love the family guy ref
In 3D there are two rings which (unless you are Jesus in Family Guy) cannot be made to intersect without being pushed through each other.
Now imagine the 4th dimension as time... Each ring only exists in the lower three dimensions for a limited range of times. Initially both rings share the same position in time so their 3 dimensional structure prevents their intersection, to get round this you can just move one further forward in time, where the 3 dimensional struture of the other ring is no longer present, move the ring into the 3D position at which it needs to be, then move it back in time so they are intersecting in three dimensions at the same time point.
It is exactly analagous to two rings of different sizes in two dimensions. It is impossible to put the smaller ring inside the larger ring in 2D without making the lines intersect, but by moving one in the third dimension (where the other ring isn't present) repositioning it, then moving it back onto the starting 2D plane it is trivial to put one ring inside the other.
Does anyone else not have a clue what went on there?