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Half dance, half juggling, half mime, half magic....I'm a contact juggler, not a mathematician
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 Posted: 23 Apr 2010, 18:35

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http://www.cornell.edu/video/?videoID=695

Juggling Notation
I know this is a disgusting, icky, bad subject to post on cj.org, but this video is simply too good not to go unnoticed anywhere in the juggling world. Cornell professor Allen Knutson gives an hour lecture on siteswapping, space-time diagrams, and state diagrams, the standard mathematical notations for toss juggling. Using various combinations of these notations, jugglers can represent the rhythm of every possible single-plane juggling pattern. Basically that means, if a juggler figures out a trick, he simply has to write down a series of numbers, and other jugglers can look at those numbers and repeat said trick.

I mentioned two caveats: it's only based on rhythm, and it's limited to a single plane. What this means is that these notations don't distinguish between different varieties of tosses (outside, inside, crossed arms, behind the back, etc.), but even with those shortcomings, this is still a really powerful tool in any toss juggler's arsenal. When you're learning toss tricks with 5 balls, it's often actually easier to learn them by siteswap notation than by watching a slow-motion video.

Contact juggling notation
Years ago, Jose (some of you may have seen the trick named after him, "Ungodly Jose"), tried to make a CJ notation, which JK_the_CJer turned into a piece of juggling simulation software. He had a nice website of his own which is probably still up if anyone cares to look for it. There's a fun little discussion about CJ notations between Drew and Remy here:
http://www.contactjuggling.org/phpBB3/viewtopic.php?f=22&t=759.
From this, and really just from thinking about it, it's easy to see that creating a standard notation for body-rolling in CJ is really bloody difficult. First of all, we'd need a (numerical?) method of signifying every stall point. Even if we had that, we'd have the same problem as siteswapping, which is to say that it is totally single-planed and rhythm-based. Contact juggling is a lot more dependent on rotations, plane-breaking, and flourishes than toss juggling, so these limitations really make things difficult.

However, it doesn't make them impossible! Let's talk about dimensions. Vanilla siteswapping encodes 2.5 dimensions of data, time, distance, and direction. By direction, I mean whether a ball is thrown to the same or an opposite hand. Direction is a totally binary metric, emergent in whether a distance is even or odd, so I'm only giving it half a dimension. Add extensions for synchronicity ("two-handed" notation, another .5 of a dimension) and multiplexing (multiple balls, another whole dimension), and that gives us 4 whole dimensions to work in. Please forgive my liberally incorrect use of the word dimension.

------------------------------------------
Body Rolling notation
So how can convert this to contact? One (admittedly limited) view of one-ball body rolling is to say the ball is always either stalled or rolling. Further, those rolls are always between one stall point and the next. This is a two-state (binary) variable, pause or pulse, much like morse code. The simplest descriptive notation for body-rolling would require a name/number/symbol assigned to every stall point imaginable. This is impossible, but let's start with a few easy ones:
palm=2
inside-elbow=3
outside-elbow (the basic one)=4
center point of chest roll=5
center point of btn roll=6

We don't need to assign left or right, because everything can work in a mirror, but we do need another binary metric for whether a roll crosses sides or not. Let's say this is denoted by an 'x'. It's pretty useful that our body is symmetrical, so all we have to do is talk about one side of it. Generally speaking, a ball is either moving up, down, in, or out (that is, up or down as normal, in being towards the chest, out being towards the fingers.) Let's denote those U(p)/D(own)/I(n)/O(ut).

Further, a roll can either go straight to a stall, or it can twist in some fashion. If you stand up straight, with your arms straight above you, fingers pointing to the sky, every rotation is either clockwise or counter-clockwise. This isn't a very useful way to say it though, because cradle->palm around the pink is clockwise for one hand, and counter-clockwise for the other. Instead, I'm going to arbitrarily pick a forward and backward direction. F(orward) is the rotational direction cradle->palm around the pinky, and B(ackward) is the rotational direction palm->cradle around the pinky. We can also use S(traight), which is cradle->palm or palm->cradle going up and over the fingertips.

On a further note, let's assume a roll uses as few rotations or fractions of rotations as is necessary to get from one stall point to the next.

To recap:
x - cross or transfer between two parts of the body that are not directly connected to one another, or switchg from one side of the body to the other
_
U - up / from the feet to the forehead
D - down / from the forehead to the feet
I - in / roll toward the chest
O - out / roll toward the fingertips
_
F - forward, rotational direction cradle->palm around pinky
B - backward, rotational direction palm->cradle around pinky
S - straight, no rotation, as in palm->cradle around fingertips
_
2 - palm
3 - inside-elbow
4 - outside-elbow (the basic one)
5 - midpoint of chest roll
6 - midpoint of btn roll
-----------
Let's put it all together. The numbers are the stall points, so let's stick them at the beginning. Let's signify a break (so as to not confuse 1 & 2 and 12) using "&" unless it's an 'x' transfer. Remember all notations are assuming you're standing straight up, with your arms straight and fingers outstretched and pointing at the sky.

1&2US = The windshield wiper
1x1IS = Basic back-to-back roll
1&4IS = Basic cradle-> outside elbow stall
1&3IB = Cradle->inside elbow stall, half spiral around the pinky side
1&5IS = First half of chest roll
5&1OS = Second half of chestroll
1&5ISx5&1OS = Whole chest roll without changing direction

Now of course this doesn't take into account different things like body positions (prayer, cage, etc.) or moves where the other arm is involved (wrist-touches, string-work, etc.) The prayer/cage/etc dilemma may be solved by adding [P] or [C] or whatever else before a trick is done to signify if you should be in a particular position, and frankly I haven't the foggiest idea how to notate that second problem.

1x2OS = Cradle to palm over the fingertips
1x2OS2&1US1x2OS2&1US = "Wilting butterfly", Cradle->palm over fingertips, windshield wiper, cradle->palm over fingertips, repeat (can also be signified as 1x2OS2&1US...) because of the repeat
1x2OS2&1US...[P]1x1US... = Wilting butterfly into prayer.

Now, you'll notice there's actually a lot of redundancy here, because every second number of a move needs to be equal to the first number of the next move. So let's just eliminate that first number of a new move if there's a string of tricks.
1&5ISx1OS2US3IB4_F = 1&5IS/x/1OS/2US/3IB/4_F/ = Chestroll from and to cradle, windshield wiper, palm->inside elbow stall, inside elbow stall->outside elbow stall.

Notice the underscore "_" I put in because inside elbow->outside elbow does not have a clear directional orientation.

Of course, this is hopelessly complex, and I believe that because so many of these things are of reduced dimensionality (binary or limited choices), we can find a way to encode them without making hopelessly long strings of numbers and letters. Maybe font colors, or arrows under the letters, or overlines & underlines/ or something of that nature will work.

Is this useful? A bunch of people (http://www.contactjuggling.org/phpBB3/viewtopic.php?f=2&t=2670), Drew included (respect Drew, y0), says it is not only not very useful, it's also very boring and probably needs to come with a video anyway. StickMan (anyone heard from him in the last few years?) suggested it's useful to have a personal notation for bodyrolling, but that it's difficult to have a universal notation because everyone has different names for things. I think we can come up with a common vocabulary, especially if it's published on the wiki, that would make a universal notation useful, if still boring. I also think there are few enough "dimensions" that we can represent it pretty concisely, and well enough that we don't need to post a video along with it.

Why is this useful? Siteswapping was popularized because in the early internet age, it was really hard to send videos back and forth to people, so they just shared strings of numbers. Since then, jugglers have found siteswapping really useful for creating juggling simulation programs and for coming up with new tricks. I think a CJ bodyrolling notation can be useful for similar reasons.
----------------------------------------
Multiball notation
Rolling is really tough to annotate, and so is spinning. I think basic, single-plane (no stacks or pyramids!) palmspinning can probably be notated with ease, but from there it gets difficult. Once we get into multidimensional spinning it gets hopelessly complex, but thankfully it gets a tiny bit easier with morphing structures. This is because morphing structures are changes from one solid, morphed state to another state, rather than fluid directional transitions for each of multiple balls.

In this old thread (http://www.contactjuggling.org/phpBB3/viewtopic.php?f=22&t=8, we can see Drew, Pich, and a few others throwing together some morphing structure notations. Appendix 4 of Drew's invaluable Multiball Contact book gives a lesson on a more mature version of that notation, which thankfully seems to have been adopted by this community (just look at Richard's recent post on celestial demons, and Ed's reply.)

--------------------------

Anyway, the video just inspired me to post this. I'd love people to write up improvements, or even yell at me for the uselessness of this system.

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 Posted: 23 Apr 2010, 18:48

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You're thinking of moves. It doesn't work that way.

Multiball it can work that way, but with one ball, not easy at all. probably best just to leave it be. Watch my next video, and try to add a notation to the one ball moves... your head will burst, because I'm not thinking of moves, I'm thinking of Fractals.

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 Posted: 23 Apr 2010, 18:54

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Look!_This_ChÃ¥nges! wrote:
You're thinking of moves. It doesn't work that way.

Multiball it can work that way, but with one ball, not easy at all. probably best just to leave it be. Watch my next video, and try to add a notation to the one ball moves... your head will burst, because I'm not thinking of moves, I'm thinking of Fractals.

Hey, yeah, I'm well-aware of the limitation. I said in the earlier post "One (admittedly limited) view of one-ball body rolling is to say the ball is always either stalled or rolling." My juggling has only recently made the jump from "moves" to "movement", but I still think this is a useful way for people to learn how to do contact. Just as with toss juggling, though, all it will give you is a skeleton outline. What you do with it changes everything.

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 Posted: 23 Apr 2010, 22:05

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So the problem is, your plane isn't flat the way it is in juggling. You would need to map every linear equator on the body and head to be able to fully map out, and even still, the notation would be unclear because some lines (say, in my body rolling) merge into others, etc...

Each line one all parts of the body would have to be named in at least 3 dimensions.

At least in Side Swap there is 2 hands, therefore 2 possibilities which notation can be taken. On the one ball & body, there are infinite points, sides and faces which could become a very complicated mathematical equation.

But, yunno, I might just be an ole fuddy duddy, I don't know how to calculate geometry very well. But I plan to forward this discussion to my friend Mark who DOES know a whole lot about this, since he did his PHD on geometric mapping, and is a juggler.

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 Posted: 23 Apr 2010, 22:36

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Dawn, good part about this system is that you don't actually need to map the body in 3 dimensions. You can picture your skin as a misshapen 2-dimensional sheet that's been stretched around your body, and all we need to do is talk in terms of how the ball rolls over that 2-dimensional sheet. We obviously don't care what's underneath your body. The issue is that, of course, your body pretty much loops in on itself (that is, a ball can roll around my wrist for ever and ever and not reach the end), so we also have to figure out how to notate rotational directions.

Also, while there are infinite points, these are rough sketches. Of course you can stall a ball anywhere if you practice long enough, but in the end, the ball moves on a path on your body. We can chop up that path into convenient pieces and use those pieces to teach newbies or to explore new paths. Siteswapping has to deal with multiple balls, distances, and hand-crosses, and is ill-equipped to deal with different styles of tosses. We should be able to get a similar notation based on stalls and rolls, but of course missing the nuance of experts =]

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 Posted: 24 Apr 2010, 01:50

Joined: 12 Apr 2006, 15:06
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Location: France
This reminds me :

that's the formula for shaping a fish...
X = day and Y = month.

Well I guess most of us should return to school because its gonna be tough

"Half dance, half juggling, half mime, half magic....I'm a contact juggler, not a mathematician"

Remember that statement ?

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 Posted: 24 Apr 2010, 06:07

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I've got a question, which I fear will sound rude, but which is not meant to be. What is actually gained by having a notation for the moves? Surely you can get the same information from giving the moves a name. Admittedly, not everything has a name and some things have more than one name, but these don't seem like insurmountable problems, whereas a string of numbers just seems confusing, harder to learm and, as some have said, a bit boring.

Ed, what did you mean by?
Look!_This_ChÃ¥nges! wrote:
I'm not thinking of moves, I'm thinking of Fractals.

Inspite of my sceptism for this idea, I'd like to suggest a possible change to Lirnyk's notation. Lirnyk, you point out that your list of stall points cannot be exhaustive, which would mean that with a number system like yours, whenever somebody wanted to code a new stall point it would just have to be the next number up. There would be no relation between the number and the part of the body. I think it would be better to have a number specifiying a body part, e.g 1 for hand 2 for elbow, and then a letter specifying how the stall was done. Something like

2a inside elbow
2b outise elbow, the basic one (I'm guessing you mean with elbow bent, forearm parallel to chest...?)
2c outside elbow, the less basic one (arm straight?)
2d jacknife
2e ... 2z stuff I've not thought of

I dunno, that might help, it might just make things more complicated/confusing than it is already.

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 Posted: 24 Apr 2010, 08:33

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5 Penny Twammer wrote:
I've got a question, which I fear will sound rude, but which is not meant to be. What is actually gained by having a notation for the moves? Surely you can get the same information from giving the moves a name. Admittedly, not everything has a name and some things have more than one name, but these don't seem like insurmountable problems, whereas a string of numbers just seems confusing, harder to learm and, as some have said, a bit boring.

Don't worry about sounding rude, it's a perfectly valid question. I think it's A) A lot more useful for representing a choreographed routine than move names would be. Because it'd take into account those little rolls in between what we consider "moves", I can wake up in the middle of the night, think of a really cool little string of moves, write 'em down and head back to bed. Also B) It would be useful if anyone were to create a CJ simulator like JK's old software, of which there have been rumblings since Drew's clever iBall he put together. You just enter in the moves, and it spits out a basic video of what the trick should look like.

That being said the numbers are confusing, harder to learn, and a bit boring.

I like your addition for each number signifying an area, and then a letter (or something) signifying which stall point in that area. Definitely better.

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 Posted: 24 Apr 2010, 08:48

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I'd love to be able to explain my theory in text, but unfortunately it's really hard to put into words.

A basic form is this: every action has an equal and opposite reaction. Chaos theory says that if we take the smallest information possible, and repeat it ad infinitum, ANYTHING can happen. that anything, is a fractal pattern. it looks random, but when viewed as a whole, it makes perfect sense. this to me is fractal thinking. two tiny bits of information I use: I have a ball, and I have a body.

Ball and body are opposite. but because they are opposite, my fractal theory says they are the same. EQUAL.... and.... Opposite. They Harmonise together to make something perfect, or fractal. and they can be interchanged at ANY point. Look at Nature. everything in Harmony together, (except humans) but still survival of the fittest.

in even simpler terms, I do something, and then try to contrast it as much as possible.say body still and ball isolated. the contrast is to move the whole lot. then the contrast of that is to stop again. but what about half stopped (the ball) and half moving (the body)? so many combinations.

But that's only step one.

After that everything goes crazy. we get into Quantum physics, and start seeing the world in a different light.

*sits back and waits the questions he can't answer yet* This is all VERY new to me, and I'm still trying to define it myself. I should also say that this theory has imprinted a firm belief in Zen Buddhism in my head as well

Yesterday, I put this theory to use with a stick, something I don't often play with. I blew my own mind.

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 Posted: 24 Apr 2010, 10:05

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Mmmmmm CJ simulator. I think this would be wonderful, and that one could spend an entire CJ career programming the damn thing.

While I like morphing notation, I'm not so sure about notating stall points, though I can see the merit. Let's give it a shot.

GIVEN: All body positions are potential stall points.

Left palm: A
Right palm: C
Left inside elbow stall: J
Left outside elbow stall: K
Right inside elbow stall: L
Right outside elbow stall: M
Left palm overhead: Y
Right palm overhead: Z
Chestbone: !

So a LH butterfly is an AB or a BA. Circles/around-the-world are DCBA or ABCD. Left-to right folding line goes AJKBDMLC. Turn the same into a folding bridge with AJKYZMLC. Left-to-right chestroll would go BK!MD. We could even parentheses to imply a continuous loop, like (AB) implying that you're just going ABABABABABAB until you're bored.

So where would this system go with outlining some ridiculous bodyrolling sequences?

Knowing that "JK" is a left elbow line folding inward and that "YZ" means that we're bridging left to right, we can guess that AJKYZM!KB would start in the left hand, fold inward (JK), pop into a bridge (YZ), drop into a chestroll (!) and wind up coming down the left elbow into a LH cradle (KB). AJ(KYZM!) would be a folding bridge from the left palm that goes into a continuous bridge/chestroll loop.

It translates, but would anyone go to the effort to do so instead of saying "Just make a damn video?" And are there really only twenty-six stall points on the human body (hint: "no")?

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 Posted: 24 Apr 2010, 10:09

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Richard, you only need half of those, because every "left" stall point is the same as a "right" stall point =] So we just need a character to represent "reverse" or "other side." (l.A or r.A being left palm or right palm), so that gives you 13 more points to work with!

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 Posted: 24 Apr 2010, 10:35

Joined: 22 Oct 2007, 09:05
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Look!_This_ChÃ¥nges! wrote:
I'd love to be able to explain my theory in text, but unfortunately it's really hard to put into words.

A basic form is this: every action has an equal and opposite reaction. Chaos theory says that if we take the smallest information possible, and repeat it ad infinitum, ANYTHING can happen. that anything, is a fractal pattern. it looks random, but when viewed as a whole, it makes perfect sense. this to me is fractal thinking. two tiny bits of information I use: I have a ball, and I have a body.

Ball and body are opposite. but because they are opposite, my fractal theory says they are the same. EQUAL.... and.... Opposite. They Harmonise together to make something perfect, or fractal. and they can be interchanged at ANY point. Look at Nature. everything in Harmony together, (except humans) but still survival of the fittest.

in even simpler terms, I do something, and then try to contrast it as much as possible.say body still and ball isolated. the contrast is to move the whole lot. then the contrast of that is to stop again. but what about half stopped (the ball) and half moving (the body)? so many combinations.

But that's only step one.

After that everything goes crazy. we get into Quantum physics, and start seeing the world in a different light.

*sits back and waits the questions he can't answer yet* This is all VERY new to me, and I'm still trying to define it myself. I should also say that this theory has imprinted a firm belief in Zen Buddhism in my head as well

Yesterday, I put this theory to use with a stick, something I don't often play with. I blew my own mind.

I would have thought that a fractal contact juggling would involve a move that is reapeated ad infinitum on a smaller and smaller scale, im not sure how you would do this but its an idea.ad infinitum is rather difficult when your a fixed size so maybe not....
Like the branch of a tree is to the trunk then your fingers are to your arm, no?
that's pretty much waves then...
hmmm...
fractal isolations like flower patterns getting smaller and smaller maybe? or bigger and bigger.

So geometry is space and points or points existing within a space, whatever demensions that space has, this space is 3d so the pattern is 3 dimensional, can you repeat patterns like that?
creating a box like Drew has in his box and useing that as the basis of the fractal pattern. Im not sure how all this will work im lookign froward to when you ahve figured it out some more or at least how to explain it some more

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 Posted: 24 Apr 2010, 10:40

Joined: 22 Oct 2007, 09:05
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PS
richard the placing of the body has no bearing on juggling notations only where the ball is you would have to build some kind of model as a space for the ball to exist in and use taht as a frame.
Ie 441 does not mean that the hand throw the ball inside at a 4 twice and then cross in front for a one the hands can be anywhere as long as the balls create a 441 pattern. Either you map the entire body and limit yourslef to the ball only ever being on teh body or your create a frame but then its all rather pintless as in contact juggling the ball can be anywhere at any one time with very little restrictions it works for toss juggling because the balls are thrown in beats, if you can work out the beat notation for contact juggling i still dont see the point.
Dont mean to burst your bubble guys but i think your going in the wrong direction...

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 Posted: 24 Apr 2010, 16:08

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That is cool though, and it could give a rough idea of what someone means. good thoughts.

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 Posted: 24 Apr 2010, 20:05

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The Need.

I am searching for it.

I am not finding it.

But hell if it works for you then go for it.

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