Portland Juggling Festival
Nathan Hoover
people and watching the shows. Here's an article about it, mainly on Boppo's
siteswap workshop which was fun:
from http://www2.nando.net/newsroom/ntn/info/041696/info9_4870.html
Jugglers now juggle numbers to compute new tricks for ancient art
Copyright 1996 Nando.net
Copyright 1996 N.Y. Times News Service
PORTLAND, Ore. (Apr 16, 1996 01:01 a.m. EDT) -- Strung together, the numb ers
sound like a numerologist's incantation. "Six, six, six, seven, one," Bruce
Tiemann intones as he rhythmically tosses juggling balls toward the ceiling
of a Portland squash court. "Seven, seven, seven, one, six, one."
Each of Tiemann's five balls arcs through varying orbits, now going low, now
going sky-high. The whole flying array looks as orderly as a swarm of
mosquitoes, but still Tiemann, a shy bespectacled graduate student, keeps
catching the balls and calling out numbers. He is tranquil and in control;
he seems like the god of a small thrumming universe.
And in a way, he is. Tiemann, 30, is arguably the world's foremost expert
on "site swap," a complex system of juggling that codifies motion by
assigning each throw a number. He invented site-swap notation in 1985,
although two other jugglers independently invented other, almost identical
site-swap notations. Tiemann can now stare at a computer-generated string
of 11 numbers, and then repeatedly execute that 11-throw, five-ball pattern
gracefully, with the sort of aplomb that a classically trained pianist might
bring to a musical score.
The trick's charm is subtle. Tiemann, who is pursuing a doctorate in chemistry
at the University of Colorado, hardly delivers the thrills and chills you get
when you watch a street busker juggle machetes. No, what he offers instead is
a precision that is new to his ancient sport.
For 4,000 years, jugglers have been evolving routines through fumbling
experimentation. Now, thanks largely to Boppo, as Tiemann is known to his
fans, juggling has gone digital. Computer enthusiasts everywhere are ecstatic.
Recreational juggling has long appealed to brainy iconoclasts -- to tie-dye
clad mathematicians and Birkenstock-wearing engineers. And over the weekend,
as 450 such souls gathered at Reed College for the fifth annual Portland
Juggling Festival, 40 people packed into the doubles squash court to seek
Boppo's guidance.
Pacing before the crowd in a crisp T-shirt and jeans, Tiemann related the
basics of site swap. The hands, he said, always move in a constant rhythm,
and there are two kinds of throws -- odd-numbered throws, which pass from one
hand to the other, and even-numbered throws, which are both tossed and caught
by the same hand.
Time is measured in beats, which are the periods that elapse between throws,
and the number assigned to a given throw equals the number of beats that
transpire before that ball is thrown again. For a typical juggler, this means
that a three throw is about chest height. A five rises a couple feet higher
than that. And a seven -- well, wouldn't that be a couple feet higher than a
five?
No, said Tiemann, it is not that simple. "High throws," he informed his s
quash court assemblage, "are higher than you think." Tiemann explained that
gravity exerts its pull, and that high balls fall faster.
"So what," one juggler asked, "is a site swap?"
A swap, Tiemann said, is what happens when you stop throwing every ball to the
same height. If you are holding three balls, for instance, you can swap by
switching from incessant threes to a mixture of fours and ones. You "swap"
trajectories -- and you get away with it only if you counterbalance each low
throw with one that is equally high.
"The numbers," Tiemann exclaimed with a sort of evangelical zeal, "have to
add up."
Dr. Joe Buhler, a mathematics professor at Reed College who can juggle
seven balls, lurked in the corner, murmuring assent. "Once you get this,"
he said, "you can't understand why, at one time, nobody got it."
"And," he added, flipping a juggling ball through his hand, "it's remarkably
robust."
Mathematically robust, he meant. Recently, Buhler and three other scholars
wrote an article in American Mathematics Monthly that notes the primary
virtue of site swaps: the system allows jugglers to conceptualize an infinite
number of patterns.
There is an infinite array of number sequences that describe juggling routines
a person can do, the paper asserts. Jugglers are constrained only by the
shortcomings of t heir muscles and their memories. To do all possible tricks,
Buhler and his co-authors expl ain, a juggler would need to be able to juggle
an infinite number of balls, and to be able to remember an infinite
string of numbers -- that is, a series of digits describing an infinitely
long pattern. No one, not even Tiemann, can do either of these things, so
the paper asks how many juggling patterns can be done given real-life
constraints. It presents a formula for determining the number of patterns a
person could do if he or she were only able to juggle "b" balls, and only
able to remember a string of numbers "n" digits long.
What the paper does not quantify is the agony a neophyte endures in learning
site swap. And this agony can at times seem almost infinite. On the squash
court, Bob Hearn, an author of Clarisworks, the computer program, grimaced
as he tried to yank his way through a basic site-swap pattern, the 4-4-1.
"Your hands want to do the same thing over and over," he lamented. "You have
to change gears."
Rhys Thomas, a professional juggler, concurred. "When you first do these
tricks," he said, "you feel you're doing motions invented by a computer.
It's a struggle to take something digital and make it analog, graceful."
Site-swap tricks, Thomas added, are often lost on nonjuggling audiences:
they are just too complex.
So why then do people even bother with site swaps? Steve Mills, the ringleader
of The Dazzling Mills Family, a juggling troupe, says it is an enjoyable
diversion.
"You do it sometimes on stage," he says, "and it's just so neat. It's like
you're telling a joke to yourself."
Tim Furst, another professional juggler, gives a more common answer. He says
site swap is a useful learning tool that "helps you to think about each throw
independent of the next one."
But the real allure of site swap is probably this: you can generate new
patterns and observe them on a computer. Since 1989, there have been computer
programs that show small figures enacting site-swap patterns. Jugglers develop
new routines by studying the "balls" as they bound all over the screen -- and
they also tap into rec.juggling, an Internet newsgroup frequented by Tiemann.
The terse language of site swap lends itself well to electronic discussion,
but it is also limited in scope: it can only describe the timing of throws.
It is dumb to the more human aspects of juggling -- to, say, the spirited way
a performer flails his arms after a catch.
Tiemann does not mind, though. For him, the mere numbers have a poetic
resonance. He remembers "9-5-5-5-1," for instance, as a trick he learned
after much effort on the lawn at his alma mater, the California Institute of
Technology. "It was dusk when I got it and I was in the shadow of the
building," he said before poking at his glasses and adding: "I have red hair.
I try to stay out of the sun."
Tiemann is doing his dissertation on what he calls "ferro-electric liquid
crystals for nonlinear optics" and listening to him, you might guess as much.
He takes an intellectually pure approach to throwing balls in the air. "People
come up to me in parks," he said, "and they ask, 'Dude, can you like juggle
chain saws?' It's ridiculous. That's like going up to an enlightened tai chi
master and asking him how many blocks of concrete he can chop.
"For me, this is about beauty. When the whole pattern is good, it's a thing of
beauty. It's like you're under this dynamic work of art, and barely touching
the bottom of it."
Tiemann throws again. Six balls this time -- six balls floating skyward,
snapping sideways, dancing about Tiemann's labor-flushed cheeks. When the
balls stop, someone remarks that it is miracle such a pattern can even be
executed.
"I'm glad you said that," says Tiemann said, "because when I'm juggling, I'm
not following every ball. I'm just kind of aware of merging traffic, but
somehow it all works out. And I feel that miracle."
--
Nathan Hoover nat...@hal.com 408-379-7000x1331 Campbell, CA, USA
<A href="http://www.hal.com/~nathan/">Click here to see my home page.</A>
Ice Princess
hope will help me finally completely understand this site-swap thing.
The article quotes Boppo saying something like, 'the numbers just have
to add up.' Well, my question is, to what do they have to add?
Did I just open an entire can of worms here?
Donna (:
Alan Morgan
Ice Princess <koc...@polaris.me.jhu.edu> wrote:
>Hey, great article about site-swap. I have but one question, which I
>hope will help me finally completely understand this site-swap thing.
>
>The article quotes Boppo saying something like, 'the numbers just have
>to add up.' Well, my question is, to what do they have to add?
42 of course.
The numbers don't have to add up into anything particular. It is
necessary (but not sufficient) that the average of the numbers be
an integer (and that integer will be the number of balls in the
pattern). The actual rule is slightly more complicated (A throw
of height x+n can't be n throws before a throw of height x for
all n > 0 and all x >= 0).
>Donna (:
Alan
----
I was told there wouldn't be any math in this newsgroup
tm...@lehigh.edu
writes:
>Hey, great article about site-swap. I have but one question, which I
>hope will help me finally completely understand this site-swap thing.
>
>The article quotes Boppo saying something like, 'the numbers just have
>to add up.' Well, my question is, to what do they have to add?
>
>
>Donna (:
there are two basic rules to valid siteswaps; I leave the proofs to those more
versed than I:
1. The sum of the numbers in the siteswap, divided by the number of beats in
the siteswap, must be an integer.
AND
2. A number n, cannot be followed k positions later by the number (n-k), as
this will result in a collision.
It is interesting to note that the integer resulting from step 1 will be the
nubmer of balls in the pattern, i.e. the siteswap '618' mentioned a few
messages back is a 5-ball pattern ([6+1+8]/3=5).
* -------------------------------------------------------------------
* * | -Terry M. Auspitz, tm...@lehigh.edu, http://www.lehigh.edu/~tma2/
* O * |
\_/|\_/ | If you are a computer or music lover, check out the CD clocks
| | at http://www.lehigh.edu/~tma2/clocks/ - These make excellent
/ \ | gifts as well! Perfect for the music/computer buff in your
| | | life!
tm...@lehigh.edu
siteswap notation, and not to the special rules that have evolved for
representing patterns with multiplexes and/or other than two hands.
TIEMANN BRUCE
involved in doing it. Thus, an eleven-throw-long five-ball trick, in order
to average to five, well, all the individual throws _have_to_add_up to fifty
five, in this case. 6 6 6 7 1 7 7 7 1 6 1 serves in the article, actually in
the first paragraph, as an example of such a trick, which by the way I can do.
There are stricter requirements than this, but at this particular workshop I
wanted to have the least to do with math, and the most to do with juggling,
so I didn't dwell on math stuff; instead, I dwelt on just what, exactly, 1 4
1 4 0 is, and now could we all get out two beanbags and try it together.
Hence, I _seriously_ glossed over a lot of math stuff, even elementary stuff.
I am hoping to dispel the notion that an understanding of mathematics is
_necessary_ to understand siteswaps. I got lots of negative feedback from
jugglers early on in the exposition of siteswapping, for making it "so
complicated, so technical, so mathematical."
Please see JW, Summer '85, p. 30 for what describing tricks was like in the
world before siteswaps, and how confidently Juggler's World took on the
challenge of conveying new tricks to its readers.
FWIW, I tried to refer readers of my Summer, '91 JW article to the one cited
above in an attempt to compel them to learn a better system - the language of
siteswaps, but that reference was edited out and did not appear in JW.
I am still not entirely sure what prompted this editorial decision.
Now the siteswap puzzle:
What siteswap is on p.30 of the Summer, '85 JW? Hint: If you need more than,
oh, say, ten characters to convey it, you've got it wrong. If you need a
disclaimer, a hundred words, and seven photographs... But if you merely need
a few hours to wade through the contorted descriptions, well, that's about
par for the course. Good luck!
-boppo
Try new Organic Water... like turbinado sugar, and natural paper, its amber
color tells you just how pure it is, and that no harsh chemicals were used in
its processing. Just the natural goodness of rain water and peat bogs.
Organic Water. The natural choice.
C Wright
> I am hoping to dispel the notion that an
> understanding of mathematics is _necessary_
> to understand siteswaps.
When I give my exposition on SiteSwaps either
to a general audience or to jugglers I never
mention any math at all. It always happens
that the people in the audience notice for
themselves the simple rules and ask.
I got a nice comment from Ken Zetie in his
review about my SiteSwap presentation. Is
there anyone else who was at one of my talks
for BJC who wants to make any comments, good
or bad, about the material? I only ask that
you be truthful, I don't even ask that you
be tactful 8-)
Dr C.D. Wright,
personal opinions only.
Matt Brubeck
>The article quotes Boppo saying something like, 'the numbers just have
>to add up.' Well, my question is, to what do they have to add?
>
They have to add up to a multiple of the number of balls. The numbers in
a three-ball site swap must add up to 0, 3, 6, 9, 12... Actually, 0 isn't
a very exciting site-swap pattern, as it is just standing there with the
balls in your hand. :)
,--------------.--------------------.
| Matt Brubeck I bru...@eskimo.com |
`--------------^--------------------'
Andrew John Conway
bru...@eskimo.com (Matt Brubeck) wrote:
:[...] Actually, 0 isn't
:a very exciting site-swap pattern, as it is just standing there with the
:balls in your hand.
No, no, no, no, no. 2 is standing there with the balls in your hands. Also
club swinging and kinky sex.
0 is spitting ping pong balls and mime.
Andrew con...@bdt.com http://www.bdt.com/home/conway/
When you can't say 'fuck', you can't say 'fuck the government' - Lenny Bruce
Congress shall make no law [...] abridging the freedom of speech,
or of the press; [...] - First Amendment to the US Constitution
Rob Prior
]
] They have to add up to a multiple of the number of balls. The numbers in
] a three-ball site swap must add up to 0, 3, 6, 9, 12... Actually, 0
] isn't
] a very exciting site-swap pattern, as it is just standing there with the
Actually, if I understand siteswaps as well as I think I do, 0 is just
standing there with _nothing_ in your hands. Not an easy siteswap to do
with three balls (although I have been getting a lot of practice while
trying to learn mills mess... the time between me dropping three balls on
the floor and me bending over to pick them up could be characterized as a
'0' in siteswap).
Just standing there with the balls in your hand would be '2'. But that
isn't really right either, because you're really throwing two balls
multiplexed from one hand and one ball from the other... so maybe [22]2
would be a more appropriate siteswap... 8-)
Rob Prior
ro...@vcn.bc.ca
--
--------------------------------------------------------------------------
Rob Prior, B.A.Sc. Mech. Eng. (Aeronautical) Rob_...@mindlink.bc.ca
snail(if you must): #607-105 West Keith Road, North Vancouver, B.C. V7M1L1
--------------------------------------------------------------------------
Travis Nelson
chanting about Portland Juggling Festival:
>In article <4l2vav$e...@news.jhu.edu>, koc...@polaris.me.jhu.edu (Ice
>Princess) wrote:
>
>>The article quotes Boppo saying something like, 'the numbers just have
>>to add up.' Well, my question is, to what do they have to add?
>>
>a three-ball site swap must add up to 0, 3, 6, 9, 12... Actually, 0 isn't
>a very exciting site-swap pattern, as it is just standing there with the
>balls in your hand. :)
No, a 2 is just standing there with the balls in your hands. A 0 is even
less exciting; you are just standing there with no balls. (eek!)
As I understand it, (I was at the aformentioned workshop) the numbers in
a siteswap _will tend to average_ to the number of balls in the
siteswap. 3 can be juggled with any number of balls, but is most common
with, say, 3 or 5 balls. I believe that the rule strengthens in accordance
with the complexity of the siteswap.
------------------------------------------------------------------------------
Travis Nelson <tr...@clark.edu> Vancouver, Washington | One hundred miles
Will code perl for food. Juggle, juggle. | an hour seven
"But now I refuse to obey." -- EMACS "?" -- ed | days a week
C Wright
> As I understand it, the numbers in a siteswap
> _will tend to average_ to the number of balls
> in the siteswap.
Well, this now has me confused. If you take any
repeating SiteSwap, the average of the numbers
will exactly equal the number of balls. It you
take the average over less than the entire period
of the SiteSwap then you're not playing fair.
The only interpretation I can find to put on this
comment is this ...
Take any segment of a _very_ long SiteSwap
whose "length" you may not know. If you
average over a piece of it then you may get
a strange number.
( Example, pretend that 531451415520 is
_really_ long, and pick a bit in the
middle, say, 141. The average is 2 )
If you average over a longer piece then you
get another strange number. However, as you
average over longer and longer pieces, the
numbers you get will converge to the number
of balls.
Now this isn't actually true, but it's nearly
true, so maybe it's what you meant.
> 3 can be juggled with any number of balls,
Except 0, otherwise true when looking at any
single throw.
> but is most common with, say, 3 or 5 balls.
Well, I don't know what this means. We're
talking infinities here, and you need to be
a bit careful when talking about "common"
things.
> I believe that the rule strengthens in accordance
> with the complexity of the siteswap.
I don't know what this means either. A rule
is a rule. How does it strengthen?
Perhaps Boppo could enlighten us as to what
he actually said about this "rule".
Keith Sharp
I was at your workshop on the Saturday afternoon (the only workshop I go to
at the convention, and it's got a computer at it :-). I do not have much
of a maths background and I did not understand siteswap before the
workshop. I would say that the talk was pitched at just the correct level
and that your ability to actually do the patterns generated was the thing
that was most impressive.
What I'm interested in now is the extensions to siteswap you use in your
program, and how to extend it for passing patterns. Or maybe we need to
invent another notation for passing?
Keith.
--
Keith Sharp Telephone: (+44) 141 330 6297
Dept of Computing Science Fax: (+44) 141 330 4913
University of Glasgow Email: sha...@dcs.gla.ac.uk
Glasgow, G12 8QQ HREF: http://www.dcs.gla.ac.uk/~sharpkm/
C Wright
> I did not understand siteswap before the workshop.
> I would say that the talk was pitched at just the
> correct level and that your ability to actually do
> the patterns generated was the thing that was most
> impressive.
Many thanks. It's useful to have the specifics, as
well as general comments on whether it was good or
bad. I hope to be putting up a text version of a
similar "workshop" on the JIS soon(ish). It's in
the process of being checked by a few people now.
> ... extensions to siteswap you use in your program,
The extensions used in the program basically allow
you to specify a physical location and a time warp
for each throw and catch. These combine to give
enough flexibility in the SiteSwap to do more than
you might expect, although some things are much
easier or even only possible with the ladder diagram.
> passing patterns.
There are (at least) two notations that cover
passing patterns. There is Ed Carsten's
tremendously flexible Multi-Hand Notation,
which is as powerful as a full space-time
diagram for hands and balls. This is what
JugglePro uses and it can do almost anything.
On the other hand there's the angle-bracket
notation that Jack Boyce's J2 program uses.
The idea of that is to describe what two people
are doing in SiteSwaps, glue them together, and
say which throws are passes. For example,
<4p|3> <4|3p> <1|3>
This has one person doing 441 with crossing
doubles on the first 4, the other person doing
3 in 3-count, and it works. ( I may have got
this slightly wrong, but no doubt someone will
tell me 8-)
Neither of these methods helps the average
juggler much in inventing patterns, or even
in understanding them, but _a_ notation does
exist, and refinements are in the pipeline.
Thanks for the comments and questions.
l. thomas
In article <DqFxC...@cix.compulink.co.uk>,
C Wright <cd...@cix.compulink.co.uk> wrote:
>There are (at least) two notations that cover
>passing patterns. There is Ed Carsten's
>tremendously flexible Multi-Hand Notation,
>On the other hand there's the angle-bracket
>notation that Jack Boyce's J2 program uses.
i don't think (tho i may be miss taken) either of these are the
notation i just heard about, which, to my limited knowledge, is not
yet used in a simulator. enough qualifications in that sentence?
you didn't sit in an irish pub in bath and see charlie dancy's
eyes get all bright and misty as he waxed rapsodic about the
causal notation for passing patterns, which actually does help
sort out new patterns, and where to put the tricks. i did (but
it was hard to concentrate on what he was saying because he looked
lovely in eyeliner, having just done a show w/haggis).
martin frost is apparantly a proponant (if not progenitor) of this
notation. but i'll let them talk about this properly, shall? as i said,
it was hard to concentrate on the details.
Travis Nelson
While summoning Cthulu I overheard cd...@cix.compulink.co.uk
>
>> As I understand it, the numbers in a siteswap
>> _will tend to average_ to the number of balls
>> in the siteswap.
>
>Well, this now has me confused. If you take any
>repeating SiteSwap, the average of the numbers
>will exactly equal the number of balls. It you
>take the average over less than the entire period
>of the SiteSwap then you're not playing fair.
Mind you, I'm fairly confused when it comes to siteswaps myself, this is
merely my interpretation.
I now see where my misunderstanding stems. I thought that you could
juggle a 5 with 3 balls, mistaking that for 522. It was the time frame
that got me. I thought the numbers represented the throw for each hand
when a ball was ready, as opposed to when the beat came around, so to speak.
>
>> 3 can be juggled with any number of balls,
>
>Except 0, otherwise true when looking at any
>single throw.
>
Again, this is based on my misconception of taking the next siteswap
number when a ball was at hand.
Furthermore, I thought that you could juggle a 3 (that is, at the heighth
of a 3) with 5 balls, if you just juggled really fast. But then you are
speeding up the beat and changing the siteswap (to a 5).
Almost everything else I said was based on these two misunderstandings.
>
>Perhaps Boppo could enlighten us as to what
>he actually said about this "rule".
>
I think I've got it right now. It is impossible to juggle the same
siteswap with a different number of balls.
>
>Dr C.D. Wright,
>personal opinions only.
Previously confused,
C Wright
Hello Trav,
> I now see where my misunderstanding stems. I thought ...
_Now_ I see what you meant, and where things
went wrong. Now I'm no longer confused.
Thanks.
C Wright
thomasl entered the fray with ...
> C Wright <cd...@cix.compulink.co.uk> wrote:
> > There are (at least) two notations that cover
> > passing patterns. There is Ed Carsten's
> > tremendously flexible Multi-Hand Notation,
>
> > On the other hand there's the angle-bracket
> > notation that Jack Boyce's J2 program uses.
>
> i don't think (tho i may be miss taken) either
> of these are the notation i just heard about,
> which, to my limited knowledge, is not yet used
> in a simulator. enough qualifications in that
> sentence?
Brilliant !!! With so many disclaimers you can't
possibly be wrong.
Anyway, notations. The "Causal Diagrams" that Charlie
talks about are superb, but currently are used mostly
in their diagrammatic form, not as a notation. Well,
the difference is minimal, but I hope you see what I
mean.
In fact, if you take the ordinary ladder diagram and
make the dwell time zero, the time each object spends
in the air is equal to the SiteSwap value. If you
then make the dwell time 100% so that the hands are
full all the time, then you get the causal diagram.
The problem then is that "balls" apparently have to
move backwards in time. If you then stop thinking
in terms of objects and start thinking in terms of
"events" and "causes" then you get a reasonable
interpretation of the diagram.
We were using this sort of diagram back in 1984 and 85
when we were inventing SiteSwaps. We found it a lot
easier to use this sort of diagram because, as Charlie
says, there are fewer lines in the diagram, making it
less cluttered. However, in trying to describe juggling
to others, people found in hard to understand. After
all, we hadn't found the explanation of talking about
Causes and Events. People found it too hard to follow,
so we resorted to the more representational version.
We also didn't play much with passing, which is, after
all, when these diagrams _really_ come into their own.
When Charlie first showed me the state transition diagram
I pointed out that it was a known and common construction
for me, a research mathematician, and it's the same with
the causal diagram. It just shows how stupid I am not to
have seen how useful these things can be if explained
clearly to someone who wants to use them "in anger"
rather than simply as a theoretical tool.