Juggling reinforces some powerful lessons ­ the most important being that risk and failure, so clearly revealed in the drops, is a necessary part of learning. As Ms. Frizzle, the teacher in the "Magic School Bus" book and TV series advises, "Take chances, make mistakes!"

 

Success results not from avoiding failure by giving up, but from embracing failure, seizing errors as opportunities to learn from ones mistakes. This is a hard lesson, and juggling demonstrates it beautifully. Marion Lee Caldwell observes in his essay in the Summer 1995 Juggler's World that other lessons juggling reinforces are patience, tenacity, self confidence, and breaking up complicated tasks into manageable steps.

 

The same attributes of juggling that make it useful for students are also valuable for scientists interested in studying how people learn. The earliest scientific study of juggling that I have found is an article on this subject that was published in 1903 by E. O. Swift in the American Journal of Psychology. In this paper Swift describes teaching some volunteers how to juggle, carefully charting their progress and methods of learning. Similar studies of juggling have appeared sporadically in psychology and other journals ever since.Interest in how juggling is learned, along with all other aspects of how learning is accomplished, increased in the 1970s as part of the artificial intelligence fad among computer scientists. Seymour Papert's 1980 bestseller, Mindstorms devotes some 10 pages to juggling.

 

In 1903, Swifts objective data consisted of little more than counting catches in each juggling attempt (though subjects' attitudes and feelings were also recorded). Recently, technology has been used to obtain better data on how our bodies and minds learn to juggle. For his Ph.D. thesis, Peter Jan Beek filmed jugglers and reviewed the tapes frame by frame to chart how the juggling patterns changed and stabilized as skill increased. Software and hardware exist to aid this process but it remains laborious work.

 

One of Peter's more interesting results is that the fraction of time that each hand spends full (that is, the time a hand spends with a ball in it, divided by the total time between one throw and the next from that hand) tends to be a sim­ple fraction. The fraction 3/4 is preferred for five and seven balls, while with three balls both 3/4 and 2/3 are common. The physics of juggling essentially allow this ratio to be almost anywhere between 0 and 1 and computer programs that simulate juggling (such as site swap viewers) often let users set this ratio to any desired value. It just turns out that human physiology makes 3/4 comfortable.

 

More recently Tony Santvoord, a student of Peter's, completed his own thesis on juggling. To get a truly complete record of the process of learning to juggle, in one part of his thesis Tony replaced real juggling with virtual juggling. He wired a computer to have two mice, one for each hand. Each mouse controls a hand on the computer display. As subjects learn to juggle the animated balls on the screen, the software keeps track of every mo­tion of the mice, so the entire process from beginner to accomplished virtual juggler can be replayed and analyzed in any way one desires.

 

Tony found that many of the "spatiotem­poral" attributes of human juggling remain the same, whether the juggling is done with real balls in the air or virtual balls on the computer. These attributes include things like the amount of variability from one throw to the next and the same preference for having hands full about 3/4 of the time.

 

Juggling can help kids "learn how to learn." In the same way, the data collected in juggling laboratories help scientists understand how we all learn.

 

Bibliography

What follows is a partial, alphabetic listing of academic references on juggling and learning. I'd like to thank Thomas Sparough for providing many of these references.

 

· Austin, Howard A. (1976), A Computational Theory of Physical Skill, Ph.D. Thesis, Dept. of Electical Engineering and Computer Science, M.IT., Cambridge.

 

· Beek, Peter Jan (1988), Exploring the Dynamics of Juggling. In A. M. Colley and R. Beech (eds) Cognition and Action in Skilled Behavior, pp. 229-246, Amsterdam: North Holland.

 

. Beek, Peter Jan (1989), Timing and Phase Locking in Cascade juggling, Ecological Psychology, vo\. 1, #1, pp. 55-96.

 

. Beek, Peter Jan (1989), juggling Dynamics, Ph.D. thesis, Vrije Universiteit, Amsterdam.

 

. Beek, Peter Jan and Michael T. Turvey (1992), Temporal Patterning in Cascade

Juggling, Journal of Experimental Psychology. Nov. 1992, vo\. 18, #4, pp. 934-947.

 

· Beek, Peter Jan, and Anthony A, M. van Santvoord (1992), Learning the Cascade juggle: .A Dynamical Systems Analysis, Journal of Motor Behavior, March 1992, vol. 24, # 1, pp. 85-94.

 

· Fagerstrom, M. L. and E. Patrikis (1980), Effects of Gender Grouping on Performance of a Novel Task, Perceptual and Motor Skills, vol. 50,pp.1235-1238.

 

. Hautala, R. A. (1985), Juggling Scarves: A Learning Tool That Aids or Hinders Learning, Perceptual and Motor Skills, vo\. 60, pp. 447-451.

 

. Hautala, R. A. (1988), Does Transfer of Training Help Children Learn juggling? Perceptual and Motor Skills, vol. 67, pp. 563-567.

 

· Knapp, C. G., G. Clyde, and W. R. Dixon (1950), Learning to juggle: I. A Study to Determine the Effect of Two Different Distributions of Practice on Learning Efficiency, Research Quarterly, vol. 21, pp. 331-336.

 

. Knapp, C. G., G. Clyde, and W R. Dixon (1952), Learning to Juggle: II. A Study of Whole and Parts Methods, Research Quarterly, vol. 23, pp. 398-401.

 

· Knapp, C. G., W R. Dixon, and M. Lazier (1958), Learning to Juggle: III. A Study of Performance by Two Different Age Groups, Research Quarterly, vol. 29, pp. 32-36.

 

. Papert, Seymour (1980), Mindstorms: Children, Computers, and Powerful Ideas, Basic books Inc.: New York. On pages 105-115 of this book, Papert applies his theories on using structured programming as metaphor for learning skills to teach juggling.

 

· Penderson, J. (1947), Experiments in Ball Tossing: The Significance of Learning Curves, Journal of Experimental Psychology, vol. 2, pp. 178-224.

 

. van Santvoord, Anthony A. M. (1995) Cascade Juggling: Learning, Variability, and Information, Ph.D. thesis, Vrije Universiteit, Amsterdam.

 

· Shannon, Claude E. (1993) Scientific Aspects of Juggling in "Claude Elwood Shannon Collected Papers," edited by N .J.A. Sloane and A. D. Wyner, New York: IEEE Press. pp. 850­864. A short history of juggling, the basic physics of juggling, Shannon's juggling theorem, a "jugglometer," and more. This was written sometime in the early 1980's, but remained unpublished until 1993.

 

. Swift, E. J. (1903), Studies in the Psychology and Physiology of Learning, American Journal of Psychology, vo\. 14, pp. 201-224.

 

· Swift, E. J. (1910), Relearning a Skillful Act. An Experimental Study in Neuromuscular Memory. Psychological Bulletin, vol. 7, pp. 17-19.

 

. Trussell, E. (1965), Prediction of Success in a Motor Skill on the Basis of Early Learning Achievement, The Research Quarterly, vo\. 36, pp.342-347.

 

For a more complete bibliography, send me a self addressed, stamped (with sufficient postage for 8 ounces), 10 by 13 inch or larger manila envelope and I will mail it back to you filled with 40 pages of the math and science of juggling, including a bibliography of over 50 references on the subject and copies of some particularly useful articles. Past Academic Juggler columns are included. The address is below. When you write, please include a letter about yourself telling why you are interested in the material. Also, if you find or write any academic references to juggling that are not included in the bibliography, or if you use this material in some other way, please let me know. Arthur Lewbel, Lexington, MA.