When Balls Collide - Understanding the Skill of Juggling

By Jack Kalvan and Arthur Lewbel

A scientific look at the skill of juggling. For the juggler who’s interested in science, or the scientist who’s interested in juggling, this is a comprehensive examination by two experts in the field.
We look at the pros and cons of different juggling patterns and analyze various constraints jugglers face, including: hand speed, timing, throwing errors, and the spatial constraints of objects in the air.
We make some conclusions about optimal patterns, what constitutes good form, how jugglers avoid collisions, and the human limits of juggling.
We also look at the many ways jugglers change the constraints to make it more interesting.
Other topics in the book include: juggling definitions, different props, historical juggling, juggling records, the physics of thrown objects, Shannon's juggling theorem and other useful equations, juggling instruction, “siteswap” notation, and training advice.

• Language: English
• Publisher: Lulu.com
• Release date: Apr 1, 2020
• ISBN: 9781716142048

Book preview

When Balls Collide - Understanding the Skill of Juggling

When Balls Collide

Understanding the Skill of Juggling

By Jack Kalvan & Arthur Lewbel

Copyright © 2018 by Jack Kalvan and Arthur Lewbel

All rights reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever, except by reviewers, without express written permission of Jack Kalvan or Arthur Lewbel.

eBook version created: Apr. 2, 2020

First Printing: July 11, 2018

ISBN 978-1-71614-204-8

Design and Illustrations: Jack Kalvan

Front Cover: Jack Kalvan (2009 photo by Jon Held)

Contents

Acknowledgements

Preface

1. Perfection Four Times a Second

2. What Is Juggling?

2.1 The Present and Past Definitions

2.2 Learning and Records

2.3 Props

2.4 Patterns

2.5 More Patterns

3. Juggling Through the Ages

3.1 Juggling in the South Pacific

3.2 Deception and Misconceptions

4. Not Enough Time on Your Hands?

4.1 Shannon's Juggling Theorem

4.2 Other Useful Variables

5. The Physics of Thrown Objects — Newton and You

5.1 The Old Bridge Problem

5.2 Hand Acceleration

6. Air Traffic Control — The Importance of Throwing Well

6.1 Good Form

6.2 How Balls Collide

6.3 Throwing Error

6.4 Ideal Patterns with No Error

7. How Humans Cope with the Constraints

7.1 Timing of Throws and Catches

7.2 Pattern Dimensions

7.3 The Juggling CATCH-22

7.4 What a Good Pattern Looks Like

7.5 Quantifying Human Error

7.6 Actively Avoiding Collisions

7.7 Predicting Catches

7.8 Juggling and Learning

8. Putting It All Together

8.1 Notes About Patterns

8.2 Juggle Struggle: The Obstacles to Adding One More

8.3 Will Anyone Ever Juggle 15 Balls?

9. Changing the Constraints

9.1 More Hands

9.2 Multiplexing

9.3 Bounce Juggling

9.4 Changing Gravity

9.5 Different Throws and Catches

9.6 Different Skills and Other Props

Appendix A. How to Juggle Three Balls

A.1 One Ball: Learning the Basic Throw and Catch

A.2 Two Balls: Almost Juggling

A.3 Three Balls: Where Real Juggling Begins!

A.4 Mastering the Three Ball Cascade

Appendix B. Juggling Notation

B.1 Siteswap Notation

B.2 Extending Basic Siteswap

Appendix C. Training Advice for Jugglers

C.1 Break It Down. Take Small Steps.

C.2 Practice Juggling, Not Dropping.

C.3 Pay Attention to What You Are Doing.

C.4 Relax Your Body and Mind.

C.5 Physical Preparation

C.6 Making Things Uncomfortable

C.7 Choosing Props

C.8 Future Improved Training Techniques

Appendix D. Other Technical Stuff

D.1 An Interesting Property of Parabolas

D.2. The Optimal Value for P

D.3 Graphs with Some Interesting Data Points Added

Bibliography

About the Authors

Acknowledgements

The authors would like to thank: Mike Day, Laura Dickerson, Erik Åberg, Jeri Kalvan, Jay Kalvan, Hazel Rebold, and Jackie Reynolds for proofreading and helpful suggestions.

Thanks to Penn Jillette, Dick Franco, David Cain, Eivind Dragsjø, Selyna Bogino, Peter Davison, Dan Berg, Jonglissimo, Roger Dollarhide, and Alan Howard, for providing photos.

Thanks to Bruce Tiemann for some siteswap information and patterns.

And thanks to all the great jugglers everywhere, who continue to push the limits of human dexterity and creativity.

Preface

As far back as history records, people have enjoyed throwing and catching balls, as well as hitting, rolling, and bouncing them, and trying to get them into all sorts of holes.

Several people playing with one ball is often called a sport. A person who can masterfully handle a single ball may not only be respected as an athlete, but also earn millions of dollars a year doing it. Still, the vast majority of people who play ball sports do so for fun, not to make money with their skill.

Possibly because juggling is relatively uncommon, it is less understood. Non-juggling spectators often assume that jugglers practice with the goal of entertaining people. But, as with other ball sports, the majority of jugglers practice their skill just for fun. They have no aspirations of joining a circus. They don’t juggle to entertain others or make money, but purely for personal joy and the satisfaction of improving their skill.

The few people who do make juggling their profession may perform beautifully choreographed routines of technical skill and artistry, or they may combine juggling with comedy, or dangerous feats. Among circus performers, jugglers are highly respected as having mastered one of the most difficult circus skills. A lifetime of dedication is required to become a top-quality juggling act.

Top jugglers who masterfully handle many balls at once may never reach the levels of fame and fortune of the master football player. Nevertheless, juggling always gets people’s attention. It amazes and captivates people, and they rarely fail to stop and watch.

Sometimes jugglers’ feats don’t seem humanly possible. Spectators often view it as magical, and want to know, what’s the trick? But unlike magic, when you see a juggler doing something very impressive, he's actually doing it! There’s no secret, but there is a great deal of technique and practice that makes it possible.

This book defines what jugglers physically do. We analyze the multiple obstacles and constraints that jugglers must overcome to keep many objects in the air. We’ll use math at the level of high school algebra, geometry, and physics, and a few graphs, but it is not necessary to understand all the technical details to enjoy this book.

To enhance your appreciation of this book (and your life), we highly recommend learning to do the basic three ball juggle. It’s a fun skill that you can learn quickly. Most people achieve some real juggling success on the first day. If you don’t have easy access to a professional juggling coach, fear not; we have provided easy instructions in Appendix A. In addition, plenty of instructional videos can be found online.

Whether you see juggling as a relaxing pastime, an athletic pursuit, a visual art, entertainment, or a mathematical diversion, it is far from mindlessly throwing things in the air. We hope that this book will give you a better appreciation of this beautiful and fun skill.

Luly Perezoff, c. 1960

1. Perfection Four Times a Second

A performer on stage deftly tosses seven balls into the air, and miraculously she is able to keep them all in motion, catching balls and throwing them back up at a rate of over four times per second. The juggler’s attention is focused near the top of the juggling pattern, but she can see most of the balls peripherally. As she watches ball number 4 reaching the top of its flight, ball 1 is being caught, balls 2 and 3 are on their way down, balls 5 and 6 are going up, and ball 7 is being thrown.

Every fourth of a second, a ball is caught, another is thrown, and the juggler must sift through all this motion again to determine exactly when and where the next ball will be caught, and how the ball in her hand should be thrown.

The sportsman’s advice to keep your eye on the ball, is impossible to obey, as attention must be split among many balls. Looking up, the juggler does not see her hands; she already knows where they are. She has learned to extrapolate landing positions from flight paths seen earlier in the pattern and get her hand to the right location at just the right moment to make another catch.

While each catch is being made, the other hand is preparing to throw, because a fourth of a second later, it will have to be empty to catch the next ball. Each ball stays in a hand for less than a third of a second, during which time, its energy must be absorbed and its motion must be redirected with extreme precision.

If the throw angle is off by just three degrees, the ball will land too far from its target to be caught. In fact, each throw must be much more precise than that, to avoid colliding with other balls.

Once thrown, each ball flies through the air for a little over one second, narrowly avoiding collision with six other moving balls in the pattern, before being caught again. And if the ball doesn't arrive at its target within about one sixth of a second of the right moment, it will cut into the time that was meant for handling another ball, and the whole pattern’s stability will be in danger.

If the juggler fails to catch a ball, or throws a ball too hard, or too soft, or too soon, or too late, or from the wrong location, or at the wrong angle, or at the wrong height, then the juggling pattern will be demolished, often in a spectacularly obvious explosion of wayward props.

Then there are the additional challenges of starting and stopping. The juggler must learn how to hold all the objects, with each finger holding balls