Why apply such complicated theorems to a game of catch? Apart from using math to help examine how the world works, it's also useful in the study of human movement. Juggling has played a role in human movement and perception studies in several important experiments.
One such experiment examined the role optical (or visual) information plays in maintaining a juggling pattern. Human movement scientists A. A. M. van Santvoord and Peter J. Beek knew that when someone juggles three objects, he can't possibly pay attention to all three at the same time. A competent juggler can continue catching balls while shifting his attention back and forth constantly. Santvoord and Beek set up experiments to see how much optical information a juggler would need to maintain a stable pattern. While most jugglers believe the peak of each toss is the most important part of a throw, Beek and Santvoord discovered that as long as jugglers could see about 100 milliseconds of the flight path of a ball, they could continue catching and juggling.
Beek and Santvoord also discovered that accomplished jugglers relied less on optical information than beginners. They theorized that experienced jugglers rely more on haptic information, which means they pay more attention to how their throws feel. An experienced juggler can feel if a toss isn't right and can adjust without looking. Some jugglers have proven that they can maintain a simple cascade pattern while blindfolded.