THE ACADEMIC JUGGLER

A Short Lesson In Thought & Gravity

By Arthur Lewbel

"Is thinking required for juggling?" In some sense, a juggler with near-perfect accuracy wouldn't need to think. When we juggle, we rapidly analyze and remember the exact path of each object in the pattern, then move our hands and arms appropriately to successfully make each catch and throw. We need to think about every catch because throws are never exactly the same.

Automatons that juggle don't "think" about catches at all. An example is Claude Shannon's W.C. Fields machine. This machine, which is built from an erector set, can bounce juggle three balls off a drum in a cascade nonstop for a half-hour or more. A machine like this doesn't "think" about the catches at all. The more accurate the throws, the less feedback (that is, mental processing) is required to make catches and maintain the juggle.

Since absolutely perfect throws are impossible even for a machine, any successful juggler (human or machine) must allow for some kind of error compensation in catches. In Shannon's machine, errors in throws are corrected by having short grooved tracks in place of hands. No matter where in the track a ball lands, gravity makes it roll to the back of the track before being thrown. In this way, Shannon 's machine makes corrections with every catch.

Modern industrial robots incorporate far more sophisticated feedback mechanisms than a grooved track. For example, such robots can "feel" when a peg has become stuck diagonally in a hole, and "know" enough to jiggle it to get it in, rather than forcing it. If industrial robots were programmed to juggle, they could probably compensate for far worse throws than Shannon 's erector set can.

Like robots, human jugglers also make unconscious corrections with every catch. For example, good club jugglers always slide a club to the knob before throwing it. However, we also consciously make much more elaborate adjustments. For example, we may subtly push an entire juggling pattern up, down or to one side to compensate for a single bad throw, then slowly drift the pattern back into place.

Numbers juggling pushes the limits of human precision in the aim and timing of throws. The more this limit is pushed, the more our ability to use our brains to compensate for bad throws becomes relevant. When machines that juggle large numbers of objects are constructed, they will likely be less capable than humans of compensating for bad throws, and will have to adjust by making throws more consistently and accurately than humans can. Even if machines one day become technically better jugglers than people, they may never match our versatility, adaptability and spontaneity. It will always be more fun to watch human jugglers!

We'll end with a short lesson about gravity. Rather than give details, I'll just state some figures that show how much trouble gravity is for jugglers. These will be approximate, because they assume the throws are vertical, they ignore the effects of air resistance, and they're rounded for simplicity.

Let T be flight time in seconds, H be the height of the throw (measured from where the object is thrown to the top of its flight) and V be the velocity of an object as it leaves the hand.

The following table shows H and V for different flight times T:

A typical 5 ball cascade is about 4 feet high. The first column of the table shows that a 4-foot throw spends about 1 second in the air, and is thrown at 16 feet per second (about 11 mph). For comparison, if we got Roger Clemens to lie on his back and throw a 98 mph (144 feet per second) fastball straight up, it would go up 324 feet, yet only spend 9 seconds in the air.

The relationships between T, H and V are approximately V = 16T feet per second and H =4T squared feet per second. This last equation is probably the most important one. It says that to double the amount of time an object spends in the air, you must quadruple the height to which it's thrown.

(The author invites your suggestions and comments on academic juggling. as well as bibliographic information on the science of juggling. Write: Arthur Lewbel, Somerville, MA.)