Juggling By the Numbers

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Posted by timothy on Friday December 21, 2012 @05:08PM from the first-they-came-for-the-tab-sites dept.

theodp writes "The BBC News' Laura Gray reports on a juggling notation system developed in the 80's called Siteswap (aka Quantum Juggling and Cambridge Notation) and how it has helped jugglers discover and share thousands of new tricks. Frustrated that there was no way to write down juggling moves, mathematician Colin Wright and others helped devised Siteswap, which uses sequences of numbers to encode the number of beats of each throw, which is related to their height and the hand to which the throw is made. 'Siteswap has allowed jugglers to share tricks with each other without having to meet in person or film themselves,' says James Grime, juggling enthusiast and math instructor for Cambridge University. Still unclear on the concept? Spend some time playing around with Paul Klimek's most-excellent Quantum Juggling simulator, and you too can be a Flying Karamazov Brother!"

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Maybe you did, but, by DeTech · 2012-12-21 17:19 · Score: 1

You should not juggle the cat.
1. Re:Maybe you did, but, by nospam007 · 2012-12-21 17:27 · Score: 1
  
  "You should not juggle the cat."
  This guy can do it.
  http://www.yogakitty.com/youtubeemf.html
2. Re:Maybe you did, but, by kerohazel · 2012-12-21 18:10 · Score: 3, Funny
  
  Some people juggle geese.
  
  --
  Skype is too convoluted... Now I'm reverse-engineering the Kyoto Protocol.
3. Re:Maybe you did, but, by wallsg · 2012-12-21 19:23 · Score: 2
  
  Is that like tossing dwarfs?
4. Re:Maybe you did, but, by Anonymous Coward · 2012-12-21 23:06 · Score: 1
  
  Nobody tosses a dwarf. They must be juggled. This is why dwarves always travel in groups with at least three companions.
5. Re:Maybe you did, but, by SternisheFan · 2012-12-22 02:07 · Score: 1
  
  My friend used to flip his cat "Alley" all the time, doing a full somersault, and the cat loved it! He'd jump back up into his arms to do it again.
Boppo on youtube by avandesande · 2012-12-21 17:52 · Score: 1

Talking about juggling is pretty boring- check out some of his vids on youtube.

--
love is just extroverted narcissism
1. Re:Boppo on youtube by Threni · 2012-12-22 02:19 · Score: 1
  
  Juggling is boring though, performed by annoying, attention seeking arseholes who always get in your face. That's why I support anything that will encourage jugglers to experiment with knives, chainsaws and fire. Here's hoping.
2. Re:Boppo on youtube by PopeRatzo · 2012-12-22 02:31 · Score: 2
  
  Juggling is boring though
  It's boring to watch, but not boring to do.
  About 20-some years ago, my martial arts instructor (who is now 87) decided that I needed to learn how to juggle. Nothing fancy, just three balls. I told him I didn't know Chinese juggled and he smacked me. I got up to 4 objects and then learned to pass with another juggler. I think it helped me as a martial artist and as a musician. It also was a great source of amusement for my daughter when she was little. I could juggle and she'd fall asleep, proving that juggling is in fact boring to watch.
  
  --
  You are welcome on my lawn.
I can juggle three ... by The_Dougster · 2012-12-21 17:58 · Score: 1, Interesting

and it took a long time to be able to do that. Four is a *LOT* harder. I cannot even fathom trying to learn all of these advanced maneuvers.

--
Clickety Click ...
1. Re:I can juggle three ... by narcc · 2012-12-21 20:00 · Score: 1
  
  No kidding. It took an hour a day for a solid month before I could juggle three balls at all. A bit longer than that to be able to manage it longer than a minute with any kind of consistency.
  Seeing a skilled juggler now is boggling. Kudos to the skillful Slashdot jugglers!
  
  --
  Required reading for internet skeptics
2. Re:I can juggle three ... by Anonymous Coward · 2012-12-21 20:27 · Score: 0
  
  Learn to do two with either hand, then do two in both hands all at once.
3. Re:I can juggle three ... by Neil_Brown · 2012-12-21 21:44 · Score: 2
  
  Four is a *LOT* harder.
  Four is a lot harder... I found (and still find) four harder than five, since juggling four in a cascade pattern is basically juggling five but "passing the gap" — making sure that the gap, where the fifth ball should be, is harder for me than actually having that fifth ball in place.
  A very useful (as much as any juggling is "useful"...) technique for four is to learn to juggle two in each hand simultaneously, in both rotations and in columns. Asynchronous columns of two balls in each hand (no pun intended but, in the juggling world, "take two balls in your right hand" is a common phrase!) helps with coordination greatly. If you can juggle two ball rotations in each hand, you're not too far off being able to juggle three balls in one hand — just increase the height of the rotation to give you the extra time, and then lower the pattern down as your coordination and technique improves.
  Sod knows how I ended up being a lawyer, but I still have "can juggle three machetes whilst blindfolded" on my CV :)
4. Re:I can juggle three ... by hankwang · 2012-12-21 23:48 · Score: 1
  
  It took an hour a day for a solid month before I could juggle three balls at all.
  Sounds familiar. Then I met a woman (who ended up becoming my wife) and explained her the basics and within twenty minutes she was able to keep three balls in the air for ten throws or so.
  That day, I decided to restrict myself to practicing skils that I actually have some talent for. :-)
  
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  Avantslash: low-bandwidth mobile slashdot.
5. Re:I can juggle three ... by BlackPignouf · 2012-12-22 00:43 · Score: 1
  
  It took me about a month to learn how to juggle with 3 balls.
  I didn't have a teacher by then, and only saw a guy doing it in the street.
  The good news is that I did pretty much all the mistakes one can do by learning. :)
  In all modesty, I think I became a very good juggling teacher. I taught a few hundred people how to juggle, and it took anywhere from 2 minutes (really) to an hour.
  Anyone can do it, and you really got to begin with the basics (that is, with one ball, going from L to R and R to L).
  I'm blind in one eye, but I managed to flash 8, to shower 6, throw 35 with 7 balls and do some siteswap with 5 balls.
  It's still a huge pleasure to juggle with 3 balls, and what's interesting is that there is an infinite amount of tricks, and there's always something new to learn.
  Right now, I'm trying to juggle 3 completely behind my back :D
  I also like to generate random siteswap patterns, print them and go to the park.
  You might want to try Mill's mess. The movement is so beautiful and perfect, it really is a huge pleasure to do it again and again.
  Another interesting trick is "The box".
  Take a look at jugglemaster (http://jugglemaster.net/) and begin with the basics.
  As for learning 4, I just love 441. It's a great rhythm, and you really get the feel of 4 balls even though it's a moderately easy 3 balls trick.
  Enjoy!
6. Re:I can juggle three ... by BlackPignouf · 2012-12-22 00:53 · Score: 2
  
  As I mentioned in another post, I taught juggling to a few hundreds people.
  My best students were all women.
  My best student could juggle "endlessly" after 2 minutes.
  I couldn't believe it, but she really didn't know how to juggle at first, and I saw the complete usual learning curve in a time span of 2 minutes.
  I showed her the "Mill's mess" after that, and she managed to do it after 3 tries. It looked sketchy, but it was definitely the right movement and rhythm.
  BTW, twenty minutes is longer than my teaching average. I usually begin a session by telling my student that it's only gonna take 10 minutes.
  They don't believe me at first, but after 10 minutes, they look like children in front of a huge cake. :D
7. Re:I can juggle three ... by BlackPignouf · 2012-12-22 01:03 · Score: 2
  
  Four is a lot harder... I found (and still find) four harder than five, since juggling four in a cascade pattern is basically juggling five but "passing the gap" — making sure that the gap, where the fifth ball should be, is harder for me than actually having that fifth ball in place.
  
  Then don't do that!
  Why would you learn 55550 before 5 or 4? As you said, it's harder than 5 or 4, but it doesn't help to learn either one.
  It's also sketchy, and tends to go out of rhythm.
  If you want to learn 4, try 441 first.
  If you really want to juggle 4 balls on a 5 cascade pattern, try 5551. It feels great, its rhythm is stable, it's much easier than 5 but it kinda looks like 5.
8. Re:I can juggle three ... by hankwang · 2012-12-22 01:05 · Score: 1
  
  I usually begin a session by telling my student that it's only gonna take 10 minutes.
  Instead of the success stories, I would be more interested in how many students are like me and the guy I replied to: hours and hours of practicing to get anywhere.
  Mind you, people like me are also behind the rest in dance classes, car driving (with stick shift and Dutch bicyclists everywhere) and everything else that requires motoric coordination skills.
  
  --
  Avantslash: low-bandwidth mobile slashdot.
9. Re:I can juggle three ... by BlackPignouf · 2012-12-22 01:13 · Score: 1
  
  I was by far my worst student. It took me a few hours a day and a month to learn 3.
  Since then, it never took me more than 1 hour to teach juggling to someone.
  The only student who failed was my nephew (he's 4) who got bored after 5 minutes of trying.
  I supposed you didn't have a good teacher. Everybody can learn how to juggle.
10. Re:I can juggle three ... by SternisheFan · 2012-12-22 02:17 · Score: 1
  
  For the beginner, don't use balls as you'll always be chasing the dropped ones. Use bean bags, or three hackey sacks. Start off holding two in one hand, one in the other. Throw one of the two into the air and, as it begins to descend, throw the one in your other hand into the air and catch the first one. Repeat. In the beginning you'll notice a tendency to throw them away from yourself, and walking forward trying to catch them. Try to keep your throws close to your body. When you catch one, that's called a "jug", catching 2 or more more is "juggling".
11. Re:I can juggle three ... by Neil_Brown · 2012-12-22 05:24 · Score: 1
  
  Then don't do that!
  Fair advice :) I'd just skip 4 and go to 5, but I didn't express that too clearly!
12. Re:I can juggle three ... by Jmc23 · 2012-12-22 08:23 · Score: 1
  
  Depends if you really lack motor coordination skills. What it sounds like is you either have your left and right confused or one side of your body is doing the work for both sides. The former more common in women, the latter in geeky guys. Basic unfamiliarity with a motor movement is never too time consuming when you have adequate feedback (working eyes and 3d vision help!).
  Took me about 2 weeks before i stopped throwing the balls at the wall in front of me. 4 balls is simple when you're divided. 5 balls is my goto when it gets nippy in the winter, better than turning up the heat.
  
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  Don't complain about syntax, grammar, or spelling. There is no.hell like input on android.
13. Re:I can juggle three ... by HalfFlat · 2012-12-22 09:55 · Score: 1
  
  Much like BlackPignouf, it took me a month of daily practice to learn how to do the standard three cascade, and having been through that, I've found it very easy to teach others how to do it. (Probably, familiarity with a whole suite of failure modes helps.)
  I persisted with juggling, and had a lot of fun with more complicated patterns, pass juggling, and so on. But it is all a case of directed persistance overcoming a complete lack of any natural ability.
14. Re:I can juggle three ... by RiderOfGiraffes · 2012-12-23 03:41 · Score: 1
  
  Then don't do that!
  Fair advice :) I'd just skip 4 and go to 5, but I didn't express that too clearly!
  What he means is - don't juggle four in that way! Juggle four by doing two in each hand, in a vertical plane parallel to your shoulders, the throws happening asynchronously. It's *way* easier than juggling 5, and similarly *way* easier than juggling 4 in a 5 pattern with one missing. These SiteSwaps with 3 help a lot:
  ... 333 42 333 ...
  ... 333 4440 333 ...
  ... 333 441 333 ...
15. Re:I can juggle three ... by Neil_Brown · 2012-12-23 03:52 · Score: 1
  
  Juggle four by doing two in each hand, in a vertical plane parallel to your shoulders, the throws happening asynchronously.
  If just for the sake of juggling four, or as the basis for tricks with five, then sure — as a means of progressing to a five ball cascade, I'm not sure that would help at all? For me, that was great for co-ordination training for three in each hand, but not as something on its own. But I guess everyone juggles for their own reasons!
16. Re:I can juggle three ... by ColinDWright · 2012-12-23 03:58 · Score: 1
  
  The original complaint was that four is a lot harder than five. This is manifestly false.
  On the other hand, if your target is to get to five, then I *still* think it's faster to learn a four fountain, then learn simpler tricks with four, then learn some SiteSwaps with four, then move to working directly on five, rather than working just on doing five.
  Yes, different people have different reasons for learning, and different people will learn best in different ways, but trying to do four in one of the harder patterns, and then claiming that four is harder than five, is simply perverse.
17. Re:I can juggle three ... by Neil_Brown · 2012-12-23 07:47 · Score: 1
  
  trying to do four in one of the harder patterns, and then claiming that four is harder than five, is simply perverse.
  
  Fair point :)
18. Re:I can juggle three ... by juggler314 · 2012-12-23 08:10 · Score: 1
  
  I used to teach people to juggle in college - and had similar stories - most people could manage at least a decent showing of the standard 3 ball cascade within a half hour at most - but every once in a while I'd come across someone that just couldn't learn - not sure why. .
  Interesting to note that I would start with just tossing one ball from hand to hand - as soon as you can do that consistently, try two (as in left, right, catch, catch, right left, catch catch, etc). again do that until they look the same in both directions and the heights stay the same and you don't drop them. Then go for all 3, usually starting is the hardest part, and you'll try it a few times before you get the first throw decent.
  Sometimes you have to have people stand right in front of a wall to teach them not to throw forward...
  I taught myself while home sick from school - took about a week. This was pre internet and I had no references at all other than 3 balls.
19. Re:I can juggle three ... by juggler314 · 2012-12-23 08:11 · Score: 1
  
  Oh and at the time I could manage 6 - sort of, but I could do 3 in my right hand fairly well. So after someone complained about it being hard I'd do it one handed (in the same cascade pattern, not just up and down like a shower). Shut people up real good.
I had no idea that it had a name by bjoast · 2012-12-21 18:43 · Score: 1

but I've been using it for years with friends. It's easier to just say "744 with five balls" than to come up with some random name for the move/pattern.
1. Re:I had no idea that it had a name by Neil_Brown · 2012-12-21 21:45 · Score: 1
  
  If you do not have access already, get hold of a copy of Charlie Dancey's Compendium of Club Juggling — you've obviously got siteswap mastered anyway, but, as a collation of some fantastic (and some simply fun) moves for club juggling and passing, it takes some beating.
13 11 9 7 5 3 1 by Anonymous Coward · 2012-12-21 18:48 · Score: 1

One of the coolest ball juggling tricks I've ever seen is the 13 11 9 7 5 3 1. That's a 7-ball pattern where for a brief moment all 7 balls are in the air in a vertical column. Siteswap notation helped fuel a revolution in "numbers" juggling (more than 3 objects). Before siteswap, nobody really knew what to do with large numbers of balls so numbers juggling was generally limited to the basic cascade pattern. The advent of siteswap helped people realize that there were actually interesting patterns, and once a juggler knows something is possible, he will keep trying until he can do it. Now there's a whole new generation of jugglers who think tricks with 7 balls is the norm.
1. Re:13 11 9 7 5 3 1 by RedHackTea · 2012-12-21 19:08 · Score: 1
  
  4 8 15 16 23 42 Lost
  
  --
  The G
2. Re:13 11 9 7 5 3 1 by BlackPignouf · 2012-12-22 01:08 · Score: 1
  
  I agree, but for siteswap numbers higher than 9, we usually use hexadecimal notation : db97531
  Otherwise, how do you tell the difference between 13 and 13 :D?
3. Re:13 11 9 7 5 3 1 by fph+il+quozientatore · 2012-12-22 03:16 · Score: 1
  
  So can I say that I can juggle 13?
  (I know, this pattern should be called 31 rather than 13)
  
  --
  My first program:
  Hell Segmentation fault
4. Re:13 11 9 7 5 3 1 by BlackPignouf · 2012-12-22 03:50 · Score: 1
  
  31 can be called 13.
  I think it's called an "excited state", and you need a 3 as introduction and a 1 for the finish :D
5. Re:13 11 9 7 5 3 1 by fph+il+quozientatore · 2012-12-24 08:36 · Score: 1
  
  31 can be called 13.
  When I learned the notation, I was told that the convention is choosing among all cyclic permutations the largest in lexicographical order. So "31" rather than "13" should be the norm. All the often-mentioned siteswaps seem to follow this convention.
  
  --
  My first program:
  Hell Segmentation fault
6. Re:13 11 9 7 5 3 1 by ColinDWright · 2012-12-24 09:56 · Score: 1
  
  31 can be called 13.
  When I learned the notation, I was told that the convention is choosing among all cyclic permutations the largest in lexicographical order. So "31" rather than "13" should be the norm. All the often-mentioned siteswaps seem to follow this convention.
  That's not always the best thing to do. For example, 45141 is a ground state three ball SiteSwap, one of my favorites. If you write it as 51414 it's not longer possible to go directly into it from cascade.
Late and wrong... But at least it's nerdy. by Anonymous Coward · 2012-12-21 19:49 · Score: 0

This wasn't news 10 years ago. I was looking at site swap juggling generators in 1986 and wrote one in pascal... Because I could.
They changed juggling (and have been extended even to multi person juggling).
If I juggled a lot I'd probably know of the guys mentioned by the Beeb, but they definitely didn't invent site swap. The Karamazov brothers were also great fun to watch, back in the day... I guess I hope they still have some good multiperson routines!
What do they have to do with siteswap?
"The notation was invented by Paul Klimek in Santa Cruz, California in 1981, and later developed by Bruce "Boppo" Tiemann and Bengt Magnusson at the California Institute of Technology in 1985, and by Mike Day, Colin Wright, and Adam Chalcraft in Cambridge, England in 1985 (whence comes the alternative name)."
-Wikipedia
1. Re:Late and wrong... But at least it's nerdy. by RiderOfGiraffes · 2012-12-23 03:44 · Score: 1
  
  Yeah - the guy mentioned on the Beeb was Colin Wright, who definitely was in one of the groups that invented SiteSwap.
Screensaver by AliasMarlowe · 2012-12-21 19:59 · Score: 1

Actually, the Juggler 3D screensaver is fairly popular at home (it's an X screensaver, maybe there's a Windows equivalent). I'm not sure if it uses the same numbering system, but it always indicates a string of numbers in the upper left to describe the particular juggling pattern being shown.

--
Those who can make you believe absurdities can make you commit atrocities. - Voltaire
Juggling is just the tip of the iceberg by spankey51 · 2012-12-21 21:18 · Score: 1

Juggling has a very long, rich, lineage and a well established community-base. Interestingly, It and many other circus-esque artforms involving "object-manipulation", can now in some ways be considered as paralleling/part of a larger movement/subculture that is quickly evolving and gaining steam - It can be thought of as a festival-culture similar to the jam bands of the 60's and onward crossed with martial arts, dance/jazz improvisation, circue-du-soleil and open-source information paradigms. The community at large has many individuals actively working on theories similar to siteswap that systematically define the dynamics of disciplines similar to, but outside of, conventional juggling.
I've had the great fortune of spending the last 10 years working inside this amazing community as an amateur theoretician, my focus is on another type of object manipulation called Poi.
Other examples of object manipulation include: yo-yo's, Contact Staff, Diablo, Hooping, etc. In each case, the discipline involves the skillful manipulation of instruments. Juggling has many MANY different sub-categories that involve the implementation of things like choreography, fire, multiple performers working in synchronization, etc. and the myriad aforementioned disciplines do as well.
My main focus as an amateur theoretician in this field as of late has been the study of spinning as a complement to the abstract language of music. Acoustic harmonics, melody, etc., have a remarkable ability (as we're all fully aware) to function as a language that communicates abstract geometric concepts to the listener. Spinning, juggling, object-manipulation at large can be adapted to serve as a spatial equivalent to the acoustic, implementing form, line, and motion to communicate the very same abstract geometries to a viewer.
A great way to illustrate how we think about this as a complement to music:
Singing: Bio-acoustic - The body alone produces sound as the carrier of the abstract language.
Dancing: Bio-spatial - The body produces line, form, and movement as the carrier.
Musical instrumentation: Instrumental-acoustic - A tool is used to produce the carrier sounds.
Spinning: Instrumental-Spatial - A tool is used to produce line, form, and movement as the carrier.
Siteswap aside, there are actually many more substantial (albeit terribly disorganized) sets of theories which we have been developing and that are actually beginning to resemble music-theory in many ways - complete with their own variations on spatial harmony, melody, arpeggios, measures, rhythm, landscape and song-structure, inflection, etc. As I mentioned earlier, perhaps the most interesting element is watching what appears to be a new variation on the language of music evolving everyday; and it is certainly a humbling experience as a practitioner of one of its disciplines. I'm pretty sure that the catalyst for this rapid progression comes from the internet, specifically social networks and youtube - The sense of progress has always seemed very intense to me and many others because we are essentially participating in a massive crowdsourcing of the development process. I suppose that's what the internet does for everything. When Jazz started to take off in 1900, the USA was primed for its arrival and it spread like wildfire - I strongly suspect that spinning is following suit now that the concerts and music clubs have started to transform into, or at least share substantial space with raves, music festivals, music videos, and so fourth. Performing arts have never been as visual as they are today and this I feel has primed the entertainment/arts for a turn back toward the spatial. Mix that with innumerable blogs, tutorial videos and enthusiast-forums and you have this giant boiling melting pot of young, creative performers

--
-ubuntu others as you would have others ubuntu you.
1. Re:Juggling is just the tip of the iceberg by spiralx · 2012-12-23 06:12 · Score: 1
  
  I've also been doing poi for almost a decade now, although not nearly at the ferocious pace I learnt at in the first four years or so. It's interesting how it has developed over the years, people now learn a whole different way than I did, back before concepts such as flowers, isolations and hyperloops were developed... was lucky enough to be around some of the people who came up with these things when I was very much into it. It's still one of the few things that calms my ADD twitchiness and anxiety, and it's nice to be able to physically push yourself to learn new ways of moving and dancing.
Fascinating by hackertourist · 2012-12-21 23:44 · Score: 3, Interesting

The idea that creating the right language can make such a difference may be dismissed as obvious by the /. audience who are familiar with this effect in programming languages.
But it shows the power of having someone look at a problem from a new or unusual perspective. In this case a mathematician managed to encompass most of the act of juggling in a simple expression. It must be incredibly satisfying to get an Eureka moment of this magnitude.
I went to a lecture on Siteswap years ago... by Anonymous Coward · 2012-12-22 00:21 · Score: 1

I saw a fascinating lecture explaining the notation, including how it can be used to prove whether a particular pattern is physically possible or not.
He even got the audience to come up with a five ball pattern that fitted the criteria and managed to juggle it. It wasn't pretty though - it's a bit like musical notation, there are lots of things that will fit but don't actually work aesthetically. If someone can find a way to grade patterns on 'appeal' they'd be rich...
The system was developed in the 80's by obarel · 2012-12-22 00:32 · Score: 0

How is that news?
I was juggling like crazy in the 90's, but that's still almost 20 years ago.
All I saw was "James Grime" after a few moments. by Anonymous Coward · 2012-12-22 04:49 · Score: 0

I love the Numberphile channel on YouTube! So interesting! :-)
not exactly news by Anonymous Coward · 2012-12-22 06:37 · Score: 0

Every juggling convention between ten and five years ago was featuring at least one workshop on siteswap.
Heck, every 5 balls beginner's workshop I've been to over the past few years did go over the useful siteswaps
(mainly 5551, 552 and 55541 obviously, since 531 is actually harder to juggle).
It's so old news in the juggling community that people took THAT and ran with it for passing patterns (look up Prechac's notation on the web).
There was even a lot of controversy back in the day, as non mathematical-oriented jugglers insisted that siteswap jugglers were somehow *less* artistic... which isn't an accurate statement at all, considering that juggling *is* a technical art.
1. Re:not exactly news by hattom · 2012-12-22 08:54 · Score: 1
  
  ...and 55541...
  you mean 55514 not 55541
2. Re:not exactly news by Anonymous Coward · 2012-12-22 21:26 · Score: 0
  
  yep... shows that's the one I can't juggle with any consistency. It's actually harder than pure 5 for me.
Team Shreddie Crunch by hattom · 2012-12-22 08:45 · Score: 1

http://juggling.tv/12550 - Team Shreddie Crunch 2
A great sample of mainly siteswap and numbers juggling by some of the British best technical ball jugglers. (Link to the more recent video).
There are plenty of good examples out there, but this is one of the best.
Disclaimer - I'm friends with most of these guys, just lucky enough to have lived in the part of the world with the possibly the highest concentration of technical jugglers.
Mills Mess by Anonymous Coward · 2012-12-22 09:39 · Score: 0

It's funny that the article mentions trying to document the pattern Mill Mess as a reason for the development of siteswap notation, since the siteswap for MM is just 3. MM involves crossing and uncrossing the hands, which siteswap does not describe.
Claude Shannon (yes, that Claude Shannon) created a juggling theorem that relates the timing of a pattern's timing to the number of objects juggled and the number of hands doing the juggling: b/h=(d+f)/(d+e). It describes the same relationships that siteswap notations indicate.
1. Re:Mills Mess by hattom · 2012-12-22 10:54 · Score: 1
  
  It's what happens when a long story about the original motivation for him wanting to develop a method (a story which does indeed feature mills mess) gets edited for an article.
  I guess you could say that mills mess is what started him thinking, and by the time he'd got something simple and usable out of the idea - it was no longer about where the throws were made (eg mills mess), but when/what they're made (eg siteswap).
  So of course, siteswap has nothing to say about mills mess - but that should explain why it's mentioned in the article at all.
2. Re:Mills Mess by Anonymous Coward · 2012-12-23 01:37 · Score: 0
  
  Claude Shannon ... juggling theorem that relates the timing of a pattern's timing to the number of objects juggled and the number of hands doing the juggling: b/h=(d+f)/(d+e). It describes the same relationships that siteswap notations indicate.
  Actually, it doesn't. It talks about the relationships between dwell times, flight times, number of balls and number of hands, almost none of which is what SiteSwap is about. In particular, Shannon's theorem is only really relevant when talking about a pattern where all throws are the same, so either cascade or fountain. It doesn't talk about throwing balls to different heights from each other. (Technically, throwing balls that are then subsequently thrown a different number of beats later - exactly what SiteSwap is about.)
true religion clearance by Anonymous Coward · 2012-12-23 13:55 · Score: 0

You really make it seem so easy with your article. Before I read this I thought I would understand that topic completely
Book on the topic... and the Squeeze Principle by Anonymous Coward · 2012-12-26 14:47 · Score: 0

A book on the topic is Burkard Polster's (http://www.amazon.com/The-Mathematics-Juggling-Burkard-Polster/dp/0387955135). He also has a short pdf summary available online that's not too bad (www.qedcat.com/articles/juggling_survey.pdf).
One of the coolest theorems is that if a sequence of numbers is "jugglable", then the number of balls required is the average of the numbers in the sequence. So the pattern mentioned by someone above --- 13 11 9 7 5 3 1 --- requires (13 + 11 + 9 + 7 + 5 + 3 + 1) / 7 = 7 balls. A consequence of this is that if the average of some sequence of numbers is not an integer, then it is not jugglable. I've often proved this to maths classes as a fun way to introduce the Squeeze Principle, which they then go on to use in the context of power series.
1. Re:Book on the topic... and the Squeeze Principle by ColinDWright · 2012-12-27 04:39 · Score: 1
  
  It's worth noted that this does not work in the other direction - just because the average is a whole number, that does not necessarily mean that the sequence is a legal juggling trick. Standard example: 432 is not legal, but 423 is.