The space-time window is an ongoing recording of the positions of the
balls being juggled. Juggling ordinarily happens in a plane and so can
be drawn in only two dimensions; in these diagrams we forget also the
height of the balls, recording only their horizontal position. The
other dimension is then used for time.

Imagine photographing a juggler from above, who is juggling glowing
balls and walking forward, using a very long exposure. A space-time
diagram is essentially the picture you would get.

For some reason these pictures have acquired the name "ladder
diagrams"; thankfully I have never had cause to climb anything that
looked so unlike a ladder.

For example, take the pattern "3". In this pattern, each ball goes
from hand to hand, moving at a constant horizontal speed until caught,
then at that constant speed in the other direction. Graphed in space
vs. time, it traces out a zigzag, zigging from left hand to right
hand and then zagging back.

There are two ways in which the space-time diagram differs from the
long-exposure photograph mentioned above. The first is that it is
adorned with numbers, marking the points in space-time at which a ball
is thrown with the number of the throw.  The other is that throws back
to the same hand have their arcs bowed out to the side (in reality
they would go on a flat line). This is a bit of artistic license which
prevents lines from being drawn one on top of the other and therefore
improves clarity.


