the definition of the unit circle with poi, as best I can understand it, is that is is the circle traced in an isolation by both the poi head and handle, with a diameter equal to the length of the poi.

Thought about this some more; Poi spin is a two dimensional circle even though it is within three dimensional space. I see no way to get beyond that. Since that is the case maybe what we are looking for is a base model of how that two dimensional circle can move within the larger three (or higher) dimensional space. To find that I would say we should look at the methods we have of moving around and between planes.
Before I begin that I want to mention that I think of planes as intersecting axis that the poi spin to either side of and that the location of those axis are determined by the cross points of the poi.

So then the components of three dimensional spinning I can think of off the top of my head are: crossing from one side of a axis to the other, and changing between two intersecting planes.
What am I missing?

"The more I play with it the more I am becoming convinced that the basic law of poi is gonna turn out to be that no movement can exist in more then two dimensions at any given time because the hand has to guide the movement of poi and thus the poi always has to be in the same plane as the source of it's momentum." - Drex
www.youtube.com/watch

So I'm on the same track as Drex now. Which is to say that the search for a unit sphere as a model for three dimensional spinning is probably a dead-end, but we did learn some interesting things in the process of trying to prove it. I believe that as a model is wrong mainly because of the realization, as Drex pointed out, that from the geometric perspective the poi is a two dimensional line and so the spinning circle it traces is also a two dimensional shape at any given instance in time. What that leaves us with now, if we are still interested in finding a base model that explains poi in terms of three dimensional space, I still think is to determine the methods we have for moving our two dimensional circle within the larger dimensions across time (which I consider to be the fourth dimension).

To do that I want to first distinguish between what many of us have been calling plane bending and the notion of changing planes with a stall. The difference I've found is in how soon along the duration of a stall we move our hand. The entire spectrum is about moving the hand to lead the momentum of the poi. In order to explain that statement I am going to talk a bit about what a stall actually is, or rather the shape it makes. picasaweb.google.com/lh/phot...qI8bjrog A stall is essentially a tangent line from the two dimensional circle traced by the poi head. If you look at the diagram in that link, the orange line in the first image is a sort of two dimensional J curve which the stall path traces. From the apex/height/middle of that stall the poi can be brought back out along any of the infinite possible J-curve paths around that three dimensional cone illustrated by the second and third diagrams. It is because the stall makes this shape that we can do things like change direction, change to intersecting planes or even continue on in the original direction (linear hand isolations).
Going back to the spectrum mentioned previously. In a full stall, the hand follows the poi head all the way along its tangent line and then leads the poi back out along some path on the J-cone. The other possibility is to move the hand to a new plane as soon as the stall begins, essentially making the same cone shape but one that is much shorter. Those are ends I've found of the plane changing spectrum.
Here are some interesting related examples. While it is comparatively short, pendulums make the same J-cone shape that full stalls do and so can be used for many of the same purposes. Since isolations and cat-eyes are movements in which the hand is already in motion, they can be used to plane bend in a less dramatically visible way from a static spin (center of rotation at the hand).

Let's back up another step and establish what exactly we mean by planes (disclaimer: we're approaching infinity here, stop now if you don't want to know the full extent of the rabbit hole). In my early growth as a poi artist people seemed to refer to the planes as a thing created by the spacial position of the poi themselves. For example I would often hear, work on maintaining straight planes, or look at how clean your planes are. I think this way of referring to planes works, for the most part, but for me it was misleading. Nick Woolsey uses tracks on the ground as a visual representative guide of the "planes" his poi spin on, which is the simple version of a very useful idea. If for now we only consider 90 degree angles, there are three primary panes; two vertical ones and the one horizontal one. We can think of each of these three planes as intersecting at the center of our body and when put in term of a poi crossing from one side of a plane to another then these three axis become the cross points. en.wikipedia.org/wiki/File...planes.svg After seeing Sensei Nick's track idea I one day set up a grid around my practice space with lines to represented the axis of the two vertical planes and also two sets of track to either side of the axis lines. It was revolutionary for me and I'll touch on it more latter.

Now back on the topic of spheres as they relate to poi. A large part of the mathematics of shapes (geometry and trigonometry) involves finding the size of the space within a regular object. For example the area of a square (a four sided polygon) is it's units of width, multiplied by it's length. The volume of a regular cube (a six sided polyhedron) is it's units of width, multiplied by it's length, multiplied by it's height. The area of a circle can be found by treating it as an infinitely sided polygon and in the same way, the volume of a sphere can be found by treating it like an infinitely sided polyhedron.

Now back to poi. While thinking of Mahatma Woolsey's visual track idea (and the whole cube grid) imagine yourself within another polyhedron aside from the cube based on three 90 degree intersecting planes. For example let's put the planes on 60 degree angles instead and see what sort of polyhedron grids that makes. If any of you have taken Arishi's 3d spinning workshops, this may feel familiar. Or going back, let's take one of the three vertical planes and offset it by 45 degrees. Let's take all of them and off set them by 45 degrees. Ultimately, we can think about an infinite number of different intersecting and parallel two dimensional planes all at infinitely different degrees with in the full three dimensional space. That is where we find a sphere.

There is a thing called body isolation in dance (the term has a somewhat different meaning and effect in in poi) which means moving only one part or muscle of the body independently of the rest. This brings up a very important and theoretically simple concept, which is the understanding that each poi are independent components of a whole. Poi is fundamentally comprised of a few basic variations which includes things like planes, direction, timing, center of rotation, crossing (from one side of a plane to another over an axis), winding-unwinding (weaves), and stalling (a change in momentum). Each poi can follow any of these variations completely separately from what the other is doing. This concept of individual parts is what gives us families of movements where the poi are doing different things such as polyrhythmics, atomics, and hybrids.

* personal note: This is a part of the reason it is so important to me to determine the elements that make up the whole proverbial interwoven multiple dimensional tapestry that is the art of poi. If we find the elemental components we can then arrange them how ever we want. *

Poi is two dimensional at any given instance in time, but over the duration of time it always exists within our three dimensional space. So If there is such a thing as a unit sphere then I think it will have something to do with the negative space of the J-cone created by plane bending the two dimensional circle that is poi around three dimensional space across fourth dimensional time. Or rather the sphere as it relates to poi is not a singe move that can actually be done but rather a matrix way of thinking which the poi (and ourselves) exists and moves within.

imitate, integrate, innovate,
- dyami -