TweetFollow Us on Twitter

June 95 - THE VETERAN NEOPHYTE

THE VETERAN NEOPHYTE

Paper Juggling

DAVE JOHNSON

[IMAGE 094-097_Neophyte_final_h1.GIF]

I've been juggling seriously since the summer of 1979, when I saw a performance of the Pickle Family Circus in a park one gorgeous Saturday afternoon. I already knew how to juggle three balls -- shakily -- but that was the day Ireally discovered juggling. I had never seen clubs juggled up close and in person before (clubs are those bowling pin-like things that are thrownspinning end over end through the air), and in particular I had never seen jugglers throw things back and forth between each other (calledpassing ). The Pickle Family did lots of both.

I was stunned. I was bowled over. I was frozen in myseat, gaping and incredulous. I couldn't believe that what I was seeing was possible. Ihad to learn how to do that.

Fortuitously, the circus offered workshops in various circus arts, including juggling, so I immediately signed up. The following morning, I learned the basics of passing balls, forced my roommate to learn to juggle three balls so that I'd have someone to try it out with,and embarked on a long and fruitful juggling binge. Thefire that was lit that day burned white hot for over fiveyears, and will remain fitfully smoldering as long as I canstill lift my arms, close my fingers, and count to 3.

My favorite kind of juggling nowadays is getting together with other jugglers and passing clubs. We arrange ourselves in various formations about the floor, start juggling all together, and throw the juggling clubs back and forth in varied and complex -- but mostly predetermined -- ways.

Which brings me to the main topic of this column: how multiperson juggling patterns work, and one way to write them down on paper. I'm going dangerouslyfar out on a limb here, assuming that it will be interestingto you, even though it has precious little to do with programming computers, and even though you're probably not a juggler. This particular limb is propped up a little by the very high proportion of computer people, mathematicians, engineers, and other scientists among jugglers. (There have been long-winded and unresolved discussions about why this should be so, but whatever the reason, it's a fact.) It's also been my observation (at Apple at our weekly juggle, and at the Worldwide Developers Conference) that computer people, in their endearing analytical way, often stand around for a long time trying to figure out the patterns.

Once you understand the rules of how the objects interleave and the jugglers interconnect, you can search for new patterns on paper, whether or not you know how to juggle. It's like a puzzle, or like a mathematical game. It's even conceivable (though just barely) that a knowledge of juggling patterns could be useful to you. I saw a citation on the rec.juggling newsgroup a while back for a paper called "Juggling Networks," published in the proceedings of a conference on parallel and distributed computing. From the abstract:

. . . these constructions are based on a metaphor involving teams of jugglers whose throwing, catching, and passing patterns result in intricate permutations of the balls. This metaphor affords a convenient visualization of time-division-multiplex activities that should be of value in devising networks for a variety of switching tasks.

There have been several mathematical papers that deal with juggling in one way or another, and even so eminent a personage as Claude Shannon, the father of information theory, was an amateur juggler and was interested in the permutations and combinations in juggling patterns. He wrote a paper called "The Scientific Aspects of Juggling," and I heard that when he appeared at a juggling convention he drew thunderous applause from the assembled jugglers (another indication of how many jugglers are science types).

Club passing is by far my favorite kind of juggling. The jollies I get from it are all over the map; it's deeply satisfying for me on many, many levels. Part of it is social, of course. Like sex, it's just more fun with others. And a big part of it is the cooperation, being a part of this complicated group pattern that's built and maintained by everyone together. I suspect it's a lot like jamming with a band in that sense: we all agree on a framework -- 12-bar blues in E or a seven-club four-count with triples, as the case may be -- and then go for it, the members either struggling to keep up or embellishing wildly, according to their level of skill. Sometimes we'll hit a "groove," a day and a pattern and a distribution of people that just feels right, the beat solid, the hands sure of their grip.

Club passing can feel like being part of some giant, whirling, clockwork contraption, with everything ticking and clacking along. Talk about being a cog in the machine! The spinning clubs form this sort of living, writhing, flying tangle with its own weird existence, a kind of "energy net" connecting the jugglers involved. The old saw "what goes around comes around" has a particularly pointed truth in club passing: if one juggler throws a pass badly -- say without quite enough spin, or a little off target -- it causes the receiving juggler some, well, discomfort. That discomfort often manifests itself in another bad pass, causing the next receiver to struggle, and so on. It's often actually visible; you can see the disturbance making the rounds, until it either gets smoothed out by jugglers who manage to keep their cool, or amplifies itself so badly that the whole pattern comes crashing down around the jugglers' heads. (Interestingly, the disturbance often travels independently of the clubs themselves, in a different direction or at a different speed, like a wave passing through water.) And passing clubs fosters --requires , actually -- a sort of heightened awareness of the other people involved. Often a quick, nearly imperceptible motion on the part of one juggler, a tiny hesitation, or the beginning of a wrong throw, corrected almost before it happens, causes another juggler to react reflexively. Typically both burst out laughing, mostly because it's unbelievable that such a tiny signal is transmitted at all.

And then there's the patterns game: a significant portion of the time spent "juggling" is really spent standing around, fiddling with the clubs, and trying to come up with new formations, new ways to arrange ourselves and the clubs in space and time so that everything fits together. The landscape of possible patterns is vast and complex, but also highly structured in mysterious ways. As in other iterative systems (computers and economies spring to mind), the underlying rules are relatively simple but the results can be very complex and widely variable. It's a kind of combinatorics and is, I think, actually covered by the mathematics of group theory.

I wrote a computer program that implements one particular kind of juggling notation, introduced to me by a juggler named Martin Frost and known ascausal diagramming . This notation can be handy for doodling around trying to find new multiperson passing patterns. (Actually, Istarted writing the program. It's still rickety and unfinished, and will probably always remain so -- it was more an experiment in QuickDraw GX programming than anything else. Nevertheless, it's included on this issue's CD, for your edification and/or derision.) The program implements a kind of active graph paper, allowing you to draw only "legal" throws, and constraining your diagrams in appropriate ways (such as preventing you from drawing throws that go back in time, for a start).

Figure 1 shows the diagram for a juggler doing a basic three-object pattern (called acascade ), and will serve to show both how the notation works and how juggling works. First the diagram: Time marches off inexorably to the right, divided into nice, even steps (calledcounts ). A juggler is represented through time as a row of Ls and Rs, representing the juggler's left and right hands, alternately throwing things. A thrown object is represented by an arrow from the hand that throws it to the hand that catches it. The pattern wraps around at the dotted lines, and repeats endlessly -- or until someone drops something. (The program always shows two repeating cycles like this, with the repeated parts "faded.") Note that the arrows (throws) form an unbroken line traveling through time from left to right, and that each hand has exactly one "input" and one "output."

[IMAGE 094-097_Neophyte_final_h2.GIF]

Figure 1. A three-object juggle

Contrary to what you might think at first glance, the overall path the arrows make doesn't directly trace the path of an individual club. If it did, this would just be a diagram of throwing one club back and forth between two hands. (That's a necessary prerequisite to juggling, but is definitely not juggling.) Instead, each throwdisplaces a club that is always assumed to be held, waiting,in the receiving hand. Think of the juggler as holding a club in each hand, while the third is in the air. The incoming club displaces the club that's already there, forcing the juggler to throw it elsewhere. In a cascade, the displaced club is thrown back to the opposite hand, where it in turn displaces the club that's there, which goes back to the first hand, displacing the club that's there, and so on, ad infinitum. (Note that although I'm saying "club" here, all these principles apply equally well to balls or rings or rubber chickens.) So the chain of throws is really a conceptual one, not a material one; it's a chain of cause and effect through time.

Figure 2 shows two jugglers passing with each other (the repeated cycle was cropped for space reasons). Note that they juggle in time with each other, like musicians keeping a beat. (When juggling with clubs, you actuallyhear the beat, when the clubs slap into the jugglers' hands.) Both jugglers throw a club to each other at the same time, both from the right hand (though it could just as well be the left). Throwing a club to another juggler "breaks" the juggler's continuous line of throws, but the other juggler's club arrives in the nick of time, knitting the pattern back together. This is a requirement: any club thrown to another juggler must be replaced by an incoming one. Otherwise, juggling can't continue; the juggler just stops, a club in each hand, waiting. (Actually, there are common situations that force a juggler to "stall" like that for a count or two, but we'll limit ourselves to the nonstalling patterns here.)

[IMAGE 094-097_Neophyte_final_h3.GIF]

Figure 2. A four-count

Because of the close timing, both jugglers must agree on the pattern before starting. The pattern in Figure 2 is called afour-count because there's a pass every four counts. (Another name for this pattern is every other , referring to the fact that every other right-hand throw is a pass.) The four-count is a very common pattern, and for most club jugglers this is the default, "idling" pattern. Since there's so much time between passes, it's possible to do lots of fancy free-form tricks (affectionately known as "throwing trash") in the midst of the pattern. Of course, "so much time" isn't really much time at all: a club juggle is roughly 160 counts per minute, so there's just over a second between the passes in a four-count.

These diagrams show nothing about spatial relationships,by the way. The usual situation has the jugglers facing each other 6 or 8 feet apart, but the same patterns can be done standing side by side, back to back, or even with one juggler standing on the other's shoulders. These diagrams show only the "connectedness" of the pattern through time, and in fact you can draw patterns that work fine on paper but are difficult to actually do because of mid-air collisions.

Figure 3 shows another pattern that demonstrates some other important concepts. In this case, every right-hand throw is a pass (which makes this pattern atwo-count ). Although the jugglers are juggling to the same beat, note that they are out of sync; one juggler's right-hand throw is simultaneous with the other's left. Note also that each pass spends twice as long -- two counts -- in the air. In all the previous diagrams, the throws have beensingles , meaning that the club spins around once during transit. The passes in Figure 3 aredoubles; since they're in the air twice as long, they have time to spin around twice before being caught. (The left-hand "self" throws are still singles.)

[IMAGE 094-097_Neophyte_final_h4.GIF]

Figure 3. A two-count with right-handed doubles


A warning about these multiple-spin throws: It's tempting, on paper, to make heavy use of long arrows (throws that spend lots of time in the air between jugglers). A little physics tells you, though, that the time in the air is proportional to the height of the throwsquared . So a double needs to be thrown four times the height of a single, and a triple must thrown nine times higher. A quadruple -- a "quad" -- must besixteen times the height of a single, and that's about as far as you can reasonably go with any sort of accuracy (or safety!). I generally stop at triples.

Now take a look at Figure 4 (again, cropped for space). This shows a three-person pattern called a feed . In this case one person (juggler 2) acts as the feeder and the others are feedees . The feeder is passing twice as often as the feedees; the feeder is doing a two-count, while the feedees are each doing a four-count, interleaved with each other in time. The feeder switches back and forth between the two feedees. This is another very common pattern, and can be added to indefinitely: Juggler 3 could pass with a new juggler, juggler 4, on the first count, at the same time jugglers 1 and 2 are exchanging clubs. That makes juggler 3 a feeder as well, feeding 2 and 4.

[IMAGE 094-097_Neophyte_final_h5.GIF]

Figure 4. A feed


I think by now you can see how the patterns fit together. It's like building a network, where everything has to eventually connect up and balance out. Go ahead, give it a try. A favorite pattern of mine is a three-count, with a pass every third count; both left and right hands pass. How about a feed where the feedees do three-counts? How many three-count feedees can one feeder possibly handle? Try a ten-club feed (the feeder does two-count doubles, as in Figure 3, and the feedees each do four- count doubles). Admire the attractive and tidy braids that result. Go wild. There are some interesting and nonobvious things about this notation that are probably worth pointing out. You can tell how many clubs there are in a pattern by taking a vertical slice through the diagram anywhere, counting the throws you intersect, and adding two clubs per juggler. (Note that Figure 3 is a seven-club pattern!) Also, if you start anywhere and follow the line of arrows around, wrapping back at the first dotted line, they always form closed paths, eventually arriving back where they began. Some patterns form one long continuous cycle; they're knit from a single strand, like a sweater. All the examples here are like that. Other patterns form distinct "orbits," where there are two or more strands making up the pattern; the three-count is an example. Each strand is an independent line of cause and effect, really an independent subpattern, that has no effect on the other parts of the pattern. You can actually decompose such patterns into their constituent parts, and juggle just one strand of the pattern at a time.

Also, the fate of any particular club isn't obvious at all in these diagrams. You can trace it, if you like -- a club leaves a hand two counts after it arrives -- but it's a bit of a pain (hmm, that might make a good addition to the program). Of course, tracing the paths of individual clubs isn't of primary interest to jugglers (though it's fun sometimes), in the same way that the path of an individual dollar is rarely of interest to economists and the trials and tribulations of an individual electron don't concern circuit designers. In contrast, I'd bet that the paths of the individual clubs are of great interest to the folks who wrote the network paper cited earlier. This notation would probably be a poor choice for them.

Finally, of course, theexperience of juggling is nowhere to be found in these diagrams. In contrast to their clean, orderly lines, passing clubs is a very physical thing, full of grimacing effort, plagued with fumbling and mistakes, and occasionally bone-whackingly painful. It's more like chopping wood than like doing math; it's more like pounding nails than like tying macramé, despite the nice braided look of the diagrams. But when things get cooking, when everyone is warmed up and throwing well, when the pattern grows and takes shape between our hands and fills the air with intricate, swirling, impossible motion, there's nothing else quite like it in the world.

RECOMMENDED READING

  • "Scientific Aspects of Juggling," in Claude Elwood Shannon Collected Papers (IEEE Press, 1993).
  • "The Academic Juggler," in Juggler's World, Vol. 45, No. 4 (Winter 1993-94). A discussion of the origins of juggling notations.
  • The Juggling Information Service on the World Wide Web at http://www.hal.com/services/ juggle/. You'll find juggling software, FAQs, archives of net discussions, movies, and lots more.
  • Operating Instructions, A Journal of My Son's First Year by Anne Lamott (Ballantine Books, 1993).
  • June 29, 1999 by David Wiesner (Clarion Books, 1992).


DAVE JOHNSON first met his wife, Lisa, in a stage combat class, learning to swashbuckle in dramatic fashion. Dave took fencing in college for a couple of years, always secretly wishing there were more yelling, ducking, slashing, and diving, instead of the tightly controlled, linear, minimalist motions of good foil fencing. Then he discovered the world of stage combat, and he's never gone back. He and Lisa are currently enrolled in a new class: Elizabethan Swordplay, using rapier and dagger. En garde! *

Thanks to Lorraine Anderson, Jeff Barbose, Martin Frost, Bo3b Johnson, Lisa Jongewaard, and Ned van Alstyne for their enlightening review comments.*

Dave welcomes feedback on his musings. He can be reached at JOHNSON.DK on AppleLink, dkj@apple.com on the Internet, or 75300,715 on CompuServe.*

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Yasu 4.0.0 β - System maintenance app; p...
Yasu was created with System Administrators who service large groups of workstations in mind, Yasu (Yet Another System Utility) was made to do a specific group of maintenance tasks quickly within a... Read more
Skype 7.37.0.178 - Voice-over-internet p...
Skype allows you to talk to friends, family and co-workers across the Internet without the inconvenience of long distance telephone charges. Using peer-to-peer data transmission technology, Skype... Read more
EtreCheck 3.0.5 - For troubleshooting yo...
EtreCheck is an app that displays the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to... Read more
Amadeus Pro 2.3.1 - Multitrack sound rec...
Amadeus Pro lets you use your Mac computer for any audio-related task, such as live audio recording, digitizing tapes and records, converting between a variety of sound formats, etc. Thanks to its... Read more
NeoFinder 6.9.3 - Catalog your external...
NeoFinder (formerly CDFinder) rapidly organizes your data, either on external or internal disks, or any other volumes. It catalogs all your data, so you stay in control of your data archive or disk... Read more
WhatsApp 0.2.1880 - Desktop client for W...
WhatsApp is the desktop client for WhatsApp Messenger, a cross-platform mobile messaging app which allows you to exchange messages without having to pay for SMS. WhatsApp Messenger is available for... Read more
Hazel 4.0.6 - Create rules for organizin...
Hazel is your personal housekeeper, organizing and cleaning folders based on rules you define. Hazel can also manage your trash and uninstall your applications. Organize your files using a familiar... Read more
Apple iBooks Author 2.5 - Create and pub...
Apple iBooks Author helps you create and publish amazing Multi-Touch books for iPad. Now anyone can create stunning iBooks textbooks, cookbooks, history books, picture books, and more for iPad. All... Read more
MYStuff Pro 2.0.26 - $39.99
MYStuff Pro is the most flexible way to create detail-rich inventories for your home or small business. Add items to MYStuff by dragging and dropping existing information, uploading new images, or... Read more
MarsEdit 3.7.8 - Quick and convenient bl...
MarsEdit is a blog editor for OS X that makes editing your blog like writing email, with spell-checking, drafts, multiple windows, and even AppleScript support. It works with with most blog services... Read more

How to get past Vulture Island's tr...
Vulture Island is a colorful and quirky mish-mash of platforming and puzzles. It’s creative and fresh, but sometimes the game can throw a curveball at you, leaving you stuck as to how you should progress. These tips will help you explore smoothly... | Read more »
The new Clash of Kings is just for Weste...
If you’ve played the original Clash of Kings, you’ll probably recognise the city building, alliance forging and strategic battles in Clash of Kings: The West. What sets this version apart is that it’s tailor made for a Western audience and the... | Read more »
Frost - Survival card game (Games)
Frost - Survival card game 1.12.1 Device: iOS Universal Category: Games Price: $3.99, Version: 1.12.1 (iTunes) Description: *Warning: the game will work on iPhone 5C and above and iPad Pro / 4. Other devices are not supported* | Read more »
How to build and care for your team in D...
Before you hit the trail and become a dog sledding legend, there’s actually a fair bit of prep work to be done. In Dog Sled Saga, you’re not only racing, you’re also building and caring for a team of furry friends. There’s a lot to consider—... | Read more »
How to win every race in Dog Sled Saga
If I had to guess, I’d say Dog Sled Saga is the most adorable racing game on the App Store right now. It’s a dog sled racing sim full of adorable, loyal puppies. Just look at those fluffy little tails wagging. Behind that cute, pixelated facade is... | Read more »
Let the war games commence in Gunship Ba...
Buzz Lightyear famously said, “This isn’t flying, this is falling – with style!” In the case of Gunship Battle: Second War, though, this really is flying - with style! The flight simulator app from Joycity puts you in control of 20 faithfully... | Read more »
How to get a high score in Fired Up
Fired Up is Noodlecake Games’ high score chasing, firefighting adventure. You take control of a wayward firefighter who propels himself up the side of a highrise with blasts of water. Sound silly? It is. It’s also pretty difficult. You can’t... | Read more »
NBA 2K17 (Games)
NBA 2K17 1.0 Device: iOS iPhone Category: Games Price: $7.99, Version: 1.0 (iTunes) Description: Following the record-breaking launch of NBA 2K16, the NBA 2K franchise continues to stake its claim as the most authentic sports video... | Read more »
Dog Sled Saga (Games)
Dog Sled Saga 1.0.1 Device: iOS Universal Category: Games Price: $3.99, Version: 1.0.1 (iTunes) Description: A game by Dan + Lisa As a rookie musher, foster a dogsledding team whose skills will grow if they're treated right. Week by... | Read more »
60 Seconds! Atomic Adventure (Games)
60 Seconds! Atomic Adventure 1.2 Device: iOS Universal Category: Games Price: $2.99, Version: 1.2 (iTunes) Description: 60 Seconds! is a dark comedy atomic adventure of scavenge and survival. Collect supplies and rescue your family... | Read more »

Price Scanner via MacPrices.net

21-inch iMacs on sale for up to $120 off MSRP
B&H Photo has 21″ iMacs on sale for up to $120 off MSRP including free shipping plus NY sales tax only: - 21″ 3.1GHz iMac 4K: $1379 $120 off MSRP - 21″ 2.8GHz iMac: $1199.99 $100 off MSRP - 21″ 1... Read more
13-inch 2.7GHz/256GB Retina MacBook Pro on sa...
Amazon.com has the 13″ 2.7GHz/256GB Retina Apple MacBook Pro on sale for $151 off MSRP including free shipping: - 13″ 2.7GHz/256GB Retina MacBook Pro (sku MF840LL/A): $1348 $151 off MSRP Read more
Apple TVs on sale for up to $50 off MSRP
Best Buy has 32GB and 64GB Apple TVs on sale for $40-$50 off MSRP on their online store. Choose free shipping or free local store pickup (if available). Sale prices for online orders only, in-store... Read more
Apple refurbished 13-inch Retina MacBook Pros...
Apple has Certified Refurbished 13″ Retina MacBook Pros available for up to $270 off the cost of new models. An Apple one-year warranty is included with each model, and shipping is free: - 13″ 2.7GHz... Read more
Duplicate Sweeper Free On Mac App Store For O...
To celebrate the launch of Apple’s latest macOS Sierra, Stafford, United Kingdom based Wide Angle Software has announced that its duplicate file finder software, Duplicate Sweeper, is now available... Read more
13-inch Retina MacBook Pros on sale for up to...
B&H Photo has 13″ Retina Apple MacBook Pros on sale for up to $150 off MSRP. Shipping is free, and B&H charges NY tax only: - 13″ 2.7GHz/128GB Retina MacBook Pro: $1174.99 $125 off MSRP - 13... Read more
Evidence Surfaces Pointing To New A10X Chip F...
Citing a job description for a Project Lead position at Apple’s Austin, Texas engineering labs, Motley Fool’s Ashraf Eassa deduces that development is progressing well on Apple’s next-generation in-... Read more
Check Print’R for macOS Allows Anyone to Easi...
Delaware-based Match Software has announced the release and immediate availability of Check Print’R 3.21, an important update to their easy-to-use check printing application for macOS. Check Print’R... Read more
Apple refurbished 11-inch MacBook Airs availa...
Apple has Certified Refurbished 11″ MacBook Airs (the latest models), available for up to $170 off the cost of new models. An Apple one-year warranty is included with each MacBook, and shipping is... Read more
Apple refurbished 15-inch Retina MacBook Pros...
Apple has Certified Refurbished 2015 15″ Retina MacBook Pros available for up to $380 off the cost of new models. An Apple one-year warranty is included with each model, and shipping is free: - 15″ 2... Read more

Jobs Board

Sr. *Apple* Mac Engineer - Net2Source Inc....
…staffing, training and technology. We have following position open with our client. Sr. Apple Mac Engineer6+ Months CTH Start date : 19th Sept Travelling Job If Read more
*Apple* Retail - Multiple Positions-Norfolk,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Restaurant Manager (Neighborhood Captain) - A...
…in every aspect of daily operation. WHY YOU'LL LIKE IT: You'll be the Big Apple . You'll solve problems. You'll get to show your ability to handle the stress and Read more
Lead *Apple* Solutions Consultant - Apple (...
# Lead Apple Solutions Consultant Job Number: 51829230 Detroit, Michigan, United States Posted: Sep. 19, 2016 Weekly Hours: 40.00 **Job Summary** The Lead ASC is an Read more
US- *Apple* Store Leader Program - Apple (Un...
…Summary Learn and grow as you explore the art of leadership at the Apple Store. You'll master our retail business inside and out through training, hands-on Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.