body tricks theory
Denis Paumier
This is an essay about modelling trajectories of objects around the human
body.
I was inspired by topology and knots theory, especially "invariants" for
knots.
Advices and comments are welcome, it's easier for me by e-mail.
We begin the story with a juggler character after a cartoon crash (the back
stuck on a wall, his body being completely flat, so we can see the his eyes
and his palms); we have the shape of a star with five branches (two legs,
two arms and the head). Let's continue those directions by an infinite line,
so we have five distincts regions marked on the wall. In the wall we can dig
a hole in each of the regions.
Now let's simplify the situation: mathematically we can reduce it to a plan
divided in five regions each being punched by a hole; we also forget gravity
(balls can now move just by the will of the juggler).
The space is divided by the plan in two regions: forth and back. We allow
the balls only to be in contact with the palms of hands, so the balls can
only take off to the forth region and land from the same, and we also allow
it to change region (front or back) only by passing through a hole.
A ball can then take off and land while staying only in the front region,
or it can go through a hole to the back region and come back to the front
using a second hole before landing (it can be the same or a different one).
It can even pass through a hole four times, or six,...
Let's give a number to each hole: 0 for the one between both legs, and then
clockwise when we watch the juggler (anticlockwise for the juggler itself):
1 for the hole between right leg and right arm, 2 for the hole between right
arm and head, 3 for the one between head and left arm and 4 between left arm
and leg. Then we can write down every combination with two holes:
00 01 02 03 04
10 11 12 13 14
20 21 22 23 24
30 31 32 33 34
40 41 42 43 44
Call back the gravity and the human body. Of course you've got to move to
make the ball do the trajects. But I suppose you return to the basic
position between every traject, even if you don't really do it. I suggest to
practise every traject throwing with right hand back to right, from right to
left, from left back to left and from left to right. Some of the trajects
are common, some you wouldn't have thought of and for some others you need
to think about how to "translate" because of constraints of the body.
Here are some examples (R is right hand and L is left hand):
R10L: under the leg
R12L: shoulderthrow
R13L: backcross
R11R: shoulderthrow , catch in the same position
R00L: just bend and juggle between your legs
R40L: find it by yourself
...
You can find variations for each traject, based on the fact that a traject
has three parts (except the "null" traject which stays in the front zone):
two of them are taking place in the front zone (the beginning B and the
ending E) and the third is contained in the rear zone (the middle part M).
Then you throw in part B and catch in B, M or E; throw in M and catch in M
or E; throw and catch in E. By "throw" I mean that the ball can have an
aerial moment or not (you can sometimes just give it to another).
Notice that hole 1 is the ymmetric of hole 4 and 2 the symmetric of 3 (and
0 is symetric to itself), so to find the symmetric of a traject you only
need to replace each hole by its symmetric and its extremities by their
symetric (right hand or left hand). You can also find the reverse traject
just reading it backwards.
Let's play with extentions of these principles: you can try more
complicated trajects and different parts of the body.
Since then we limited ourselves to use only the plams of hands. But any
other spot on the body is worth using, you just have to know if it's on the
front side of the body or the rear side. If a ball goes from one side to
another, the traject will pass through an odd number of holes (mainly one or
three in real world), if not the traject will have an even length. You can
also use one of those three manners: throw, give or roll a ball on the body
to the next spot.
Example for a club going from right hand to right foot and passing under
the leg: RH 10 RF
For a ball going from right hand to "the cradle" on left: RH 3 LC or RH 143
LC...
Let's study trajects with four holes. Since there are many theoritical
possibilities and many of them are not really humanly possible (we'll talk
about simulators later), I'm just going to talk about certain families. You
have the one of double trajects, built by sticking a traject with itself:
R1414L, R1010L,... The family of trajects in which the first hole is the
same as the last one: R1431R, R0430R,...The one you can tell by words such
as "throw under X+catch under Y": "throw under the leg+catch behind the
back" is R0424, "throw under the arm+catch under the leg" is R4340R,...
You can even try six hole trajects: L012340R. Making a circle with an arm
(leg?) around a ball before catching it may add 21 (or symmetric or reverse)
to a traject. Making a pirouette could add 23...
Now we shall make a call to vanilla siteswap. The numbers tell us about
when a ball is going to be thrown again, and because we consider only two
hands constantly alternating, we can see in which hand the ball is going to
land. If we precise the first throwing hand of a sequence, then we know from
which hand any ball is thrown and to which hand it goes. So we don't need to
precise it on the traject any more.
I tried to find some less confusing way to speak about trajects, especially
while talking about siteswaps, numbers spring in every direction. So I tried
to give a name to each hole: the one between BOth Legs is called BOL, the
ones between Arms and Legs are called AL and the ones between Arms and head
(I tought Crane was more convenient for its initial) is called AC. You can
preceed by OP, which means OPposite relating to the throwing hand or to the
previous hole. Example: under the legs is ALBOL, under the arm is OPALAC,
behind the back is ALOPAC,....
This way we can add extensions to siteswap. I tried to write down for
example the family of "under the arm" tricks, using alac, acal, opalac,
opacal (I'll write that in small letters since I hope it's not confusing; I
don't think there are many other words that sound like that in english)
which are the opposites and reverses of 12, using different hand
combinations. We'll also use "in " and "out" for inside or outside throws
with this definition: throwing inside is throwing from one hand being on its
normal side to the opposite side of the next ball to be caught or throwing
from one hand being on the opposite side to the same side of the next ball;
throwing outside is throwing from one hand being on its normal side to the
same side of the next ball or throwing with one hand being on the opposite
side to the opposite side of the next ball. Sorry for the painful sentence.
Let's play with extending the standard cascade in HTML-style: "chops"
3<opalac>, "catch under the arms" 3<acal>, "shoulderthrows" 3<alac>,
"penguin catches" 3<opacal>. Then pattern with a period of two beats: kind
of shower 3<opalac>3<out>, Laurent Pareti's 3<opalac>3<alac>, juggling with
hands crossed 3<acal>3<opacal>,...Patterns of length three, which lead us to
messy patterns: 3<acal>33; 3<acal>3<opacal>3; 3<albol>3<bolopal>3;
boston mess: 3<out acal>3<out>3<in acal>3<out opalac>3<out>3<in>;
mills mess: 3<out acal>3<opalac>3;
half mess: 3<out acal>3<opalac>33...
You can also try: 4<acal>41; 441<alopal>; 441<alopac>; 53<acal>1;...In
general case when you have a 1 in a pattern you can do it behind the back
or under the leg, and when you have a 31 you can catch the 3 under the arm.
In the great finnish Peapot Videos I saw a surprising 1<opacal> and
1<opalopal>.
To the simulator makers: would it be possible to simulate bobytricks with
those ideas? I imagine possible tricks with more or less gravity, randomly
selected trajects on randomly selected siteswap patterns and virtually
extended body flexibility…Let me know about it! Have fun.
Denis Paumier
den...@mageos.com
Check Les Objets Volants' page http://mageos.ifrance.com/objvol
Jake Cooper
> or it can go through a hole to the back region and come back to the front
> using a second hole before landing (it can be the same or a different
one).
> It can even pass through a hole four times, or six,...
I have a little problem with this part. I'd argue that a ball can
either be thrown from the front plane or the back plane. If it's thrown
from the front plane, then it's just a normal siteswap. If, however, the
ball is thrown from the back plane, then it needs a description.
Each ball thrown from the back plane passes through 2 (and only two)
holes. It passes through one hole while in your hand (to get to the back
plane) and through another hole while in the air. So a behind the back
throw (from your right hand) would be 42 or ALOPAC. While this is exactly
how you described the behind the back throw, it indicates that the ball is
in your hand while you pass through the "Arm-Aeg" hole and is in the air
while it passes through the "OPposite Arm-Cranium" hole.
I like the notation.
Jake Cooper
Colin E.
I like the concept of the body having 5 holes which enable a ball to
travel between the two regions, back and forth.
I assume the division between the two regions is flexible?
For example to execute an under the leg throw, R10L the ball must pass
through two holes. You can carry the ball through the first hole and
throw it through the second. Alternatively you can lift your leg up so
that you can throw the ball through both holes.
I am slightly (very) unclear as to the meaning of the traject 'zones',
do these have any relationship with the 'regions'?
Also, you mention four hole trajects such as R1414L, presumabley this
describes a trick for the very flexible or very long armed jugglers?
Unfortunately the clarity of your notation seems to be lost towards
the end of your essay. I guess I just prefer numbers from letters!
If I am reading your notation correctly, in Mills Mess, "3<out
acal>3<opalac>3", is the second throw the "U"-ball?
As a simulator maker I cannot see any advantages in using your system
for the basis of a computer simulation. Virtual Juggler specifies
throw and catch positions as points in space (XYZ), the balls and
hands then move between these points using a systems of rules that I
hope is realistic. Although it must be said that the trick notation is
a bit long winded!
On another note, the reason why siteswap notation is so popular is not
simply because it is a concise notation system, more importantly
mathematical rules can be applied to it in order to validate patterns
and generate new ones. Does the topological basis of your notation
enable you to do the same?
Regards,
Colin E.
~~~~~~~~~~~~~~~~
Virtual Juggler:
http://www.fishsoft.co.uk/
Alessandro Scotti
>As a simulator maker I cannot see any advantages in using your system
>for the basis of a computer simulation. Virtual Juggler specifies
>throw and catch positions as points in space (XYZ), the balls and
>hands then move between these points using a systems of rules that I
>hope is realistic. Although it must be said that the trick notation is
>a bit long winded!
>
>On another note, the reason why siteswap notation is so popular is not
>simply because it is a concise notation system, more importantly
>mathematical rules can be applied to it in order to validate patterns
>and generate new ones. Does the topological basis of your notation
>enable you to do the same?
IMHO it is also very important that the notation can be used by us humans! For
many (simple?) siteswaps we can make an idea of the pattern without running it
thru a simulator, and that seems the case with the proposed system too. But
anyway I'd rather try to sort out a long siteswap than a sequence of 3D
points... :-)
Denis Paumier
Colin E. a écrit dans le message <3aa77616....@nntp.leeds.ac.uk>...
>I like the concept of the body having 5 holes which enable a ball to
>travel between the two regions, back and forth.
>
>I assume the division between the two regions is flexible?
>
>For example to execute an under the leg throw, R10L the ball must pass
>through two holes. You can carry the ball through the first hole and
>throw it through the second. Alternatively you can lift your leg up so
>that you can throw the ball through both holes.
Yes of course, it can be deformed if it stays the same in
topological sense. So the body can move while staying inside that division.
And two trajects can be notated the same way but have different points in
space.
>I am slightly (very) unclear as to the meaning of the traject 'zones',
>do these have any relationship with the 'regions'?
I employed those two words in the same sense, i.e. the two parts of the
space divided by the body plan. Sorry if it wasn't clear.
>Also, you mention four hole trajects such as R1414L, presumabley this
>describes a trick for the very flexible or very long armed jugglers?
Yes, I especially thought of a certain Dadadeus, a juggler I saw many
years ago on TV after he performed in Cirque de Demain in Paris, who does
each throw this way and keeping his arms behind the back.
>Unfortunately the clarity of your notation seems to be lost towards
>the end of your essay. I guess I just prefer numbers from letters!
I already know that some people prefer the numbers. Can you tell me why?
With the letters I tried to simplify the question of simmetry. Anyway I keep
searching on that.
>If I am reading your notation correctly, in Mills Mess, "3<out
>acal>3<opalac>3", is the second throw the "U"-ball?
Yes.
>As a simulator maker I cannot see any advantages in using your system
>for the basis of a computer simulation. Virtual Juggler specifies
>throw and catch positions as points in space (XYZ), the balls and
>hands then move between these points using a systems of rules that I
>hope is realistic. Although it must be said that the trick notation is
>a bit long winded!
I downloaded your simulator but I have problems to run it (I lack some
.dll file maybe) so I only saw the presentation image.
My argument is to find a notation related to human body, not dependent
on which one (most of them, sorry) and leaving some space for
interpretation. I tried to make it speakable also, and based on a
combination of simple elements (i.e. holes). Let me know more about your
rules (and how to run your program?)
>On another note, the reason why siteswap notation is so popular is not
>simply because it is a concise notation system, more importantly
>mathematical rules can be applied to it in order to validate patterns
>and generate new ones. Does the topological basis of your notation
>enable you to do the same?
It would be great, but I don't really know. For me it was more to
explore every possibility, so I know more about the descriptive aspect. I'm
still finding many tricks only by combining siteswaps, trajects and
inside-outside. Anybody finding some rules is welcome, I also keep on
searching about that.
Denis P
Nathan Peterson
> >the end of your essay. I guess I just prefer numbers from letters!
>
> I already know that some people prefer the numbers. Can you tell me why?
> With the letters I tried to simplify the question of simmetry. Anyway I keep
> searching on that.
The letters are kind of confusing to me too. Mostly because there are
too many letters in the notation and not all of the names are of the
same length. Having BOL as three letters and AL and AC as two letters
seems kind of confusing when you start mixing them together. Personally
I would prefer something like A, B, and C to represent the different
"holes." They are not as meaningful, but they would be so much easier
to read. You could signify which side the throw is made on by making
the letter capital or lowercase, or by preceding it with another
(single) letter. I think "x" would probably be appropriate since it
usually stands for crossing in siteswap.
-Nathan