Catch and Release

There was always some space above my hands calling me.
— Siv Cedering Fox, The Juggler

Somewhere in the dexterity of the juggler, in the wheeling patterns traced by the flying objects, art and science come together.  The balls go up, the balls come down, arc and zenith, catch and throw.  It is the physics of gravity, the biology of reflex; it is the legerdemain of the magician, the play of the clown.

There was a time, long before our nights were illuminated by television, when jugglers were a mainstay of live entertainment.  No circus or vaudeville program was complete without at least one juggling act.  W.C. Fields began his career as a comic juggler, balancing blocks on his feet and on his bulbous nose, and establishing an international reputation as the best on the vaudeville circuit.  Fred Allen billed himself as “The World’s Worst Juggler.”  The world’s best was Enrico Rastelli, who could juggle 10 hoops simultaneously, who practiced daily for hours, and whose name, even a half-century after his death, still conjures reverence among practitioners of the art.

But the movies, with their more grandiose visual tricks, killed vaudeville and mortally injured the circus, and the illusion of defying gravity slipped to the status of a parlour trick.

Recently, though, the skill has enjoyed a considerable amateur revival, primarily on university campuses.  In the past five years the membership of the American-based International Jugglers Association has increased six-fold.  Juggling is in vogue particularly among computer scientists and mathematicians, who are by nature lovers of patterns and by inclination solvers of problems.

Joe Buhler, who teaches mathematics at Reed College in Portland, Ore., has taught hundreds of his colleagues and students how to manipulate the falling objects.  “Whenever I go to a math conference,” he says, “there comes a point when it’s obligatory to do a little juggling.”  Picture the mathematicians relaxing after a long day of Boolean algebra and non-Euclidean geometry, tossing pins to one another.

Professionally, the jugglers’ new home is the small comedy cabaret, smoky and dark, where the act is enhanced by the proximity of audience and stage.  In Canada, with a bust in small comedy clubs quickly following the boom, venues are few, but in the United States the juggler is in demand.

Tony Molesworth — juggler, comedian, ventriloquist, magician, and a man with the dubious and utterly coincidental distinction of having closed three clubs in a row — is a regular at Yuk Yuk’s in Toronto.  He juggles on a unicycle, eats fruit and vegetables as they fly past his mouth, and holds conversations with Jake the Ball, a Molesworth creation who complains about being in the act, feigning motion sickness as he’s being bounced back and forth.

For the professional, the art is a livelihood.  But for the amateur it’s a form of recreation — the continuous tossing and catching of more objects than hands involved.  There is nothing that motivates the amateur juggler other than the simple sense of accomplishment, the satisfaction that comes with, in the phrase of Marcello Truzi, keeping things up in the air.  The juggler can be his own audience, gravity his only referee.

But present in that simple act of play are motor reflexes, cognitive skills and spatial perceptions so complex they are peculiar to humanity.  There are animals, seals for example, that can be trained to perform marvellous feats of balancing, but only man can juggle.  (However, in their recent article in the French scientific journal La Recherche, mathematician Joe Buhler and his colleague Ron Graham report rumours that certain chimpanzees capable of “speaking” by using sign language have also been taught to juggle.  With the manipulation of language comes the manipulation of objects?)

Once a religious ritual, juggling has been mastered for thousands of years.  The earliest known record is preserved in paintings in the Beni-Hassan tombs of Egypt, dating from 1900 BC, depicting a woman juggling three balls, the spheres frozen forever above her hands.  Yet very little has been written about it, and while the human hand may be adroit, human language is clumsy when it comes to describing the nuances of the skill.

Nor is the action, despite its apparent rhythmic regularity, susceptible to mathematical dissection.  “It’s true one gets the impression that there should be something there to describe,” says Buhler, “but juggling seems particularly impervious to mathematical analysis.”  One reason is that juggling has no language beyond show-and-tell; it has no notation that would allow the act to be described easily, so the teaching of various tricks is almost always done by demonstration.

Attempts have been made to describe mathematically what is happening when objects are thrown from one hand to the other.  U.S. mathematician Claude Shannon — the “father of information theory” — arrived at the formula

b/h = (d + f)/(d + e)

to describe a technique called the cascade, in which b represents the number of balls, h is the number of hands, f the flight time of each ball, e the time each hand is empty between balls, and d the time each ball spends in a hand.

Shannon’s formula quantifies things that jugglers know intuitively.  For example, it states that the number of balls that can be juggled depends in part on the time each ball is in flight.  This, in turn, is dependent on the force of gravity, which limits how high a ball can be thrown.  The current world record for the largest number of objects juggled stands at 11, and it is unlikely that anyone on Earth will ever be able to juggle more than 12 or 13.

In mathematics this is known as juggling kinematics, a field of inquiry peppered with talk of rotational stability, patterns of topology and axes of moment.  And not content merely to discuss the various techniques that Earthbound humans employ, in their paper Buhler and Graham delight in speculating on how juggling would be performed on a planet inhabited by three-armed beings.

On planets with lower gravitational attraction, such as the moon or Mars, objects could be thrown higher, and would fall more slowly, than on Earth, thereby increasing both the flight times and the number of objects that could be juggled.

With the exception of weightless objects in free fall (meaning what goes up does not come down) virtually anything that can be lifted can be juggled: cannon balls, flaming torches, knives, playing cards, bouquets of flowers, ashtrays, Rubik’s cubes, plastic swimming pools.

The women of Nuku’alofa on the South Sea island of Tonga, which probably has more jugglers per square mile than anywhere else on the planet, juggle day and night, primarily with limes and tui tui nuts. The Brothers Karamazov of San Francisco perform an act in which they pass a running chainsaw back and forth.

The three most common categories of juggling objects, though, are balls, clubs and hoops.  Of these, hoops are reputedly the easiest, and are the objects used to set world records.  Because of their spin, they are stable when thrown to great heights, and because they are thin they lessen the likelihood of mid-air collisions. As well, the juggle is easy to finish because an arm can be thrust through the centre of each hoop. Catching five whirling knives in each hand is not so easy.

But for the non-mathematician the appeal of juggling lies, not in the permutations of patterns, but in the play.  It is like magic in reverse, in which the sleight-of-hand is revealed rather than concealed. The question is not, as the mathematicians phrase it, “How is it done?” but “How can he (or she) do it?”

It is a question that has been repeated since the Middle Ages, when juggling was practiced by joculatores, wandering acrobats, artists of chicanery, and clowns. Hence juggle comes from jocular, or comic, and juggling almost always spins its art and science with comedy.

• Globe and Mail August 28, 1982