Posted:

A forward - Parallels between music and poi:

I like to think of object manipulation as a form of "spatial music". I think there can be some good analogies drawn from it.

Music is the sonic expression of harmonic proportions sequenced over time. The human voice is the most intimate and natural way to make music but there is something wonderful about playing an instrument, interacting with an otherwise inanimate object to make music with qualities the voice can't.

The spatial analogue to the human voice is dance. One sequences proportionately interesting body movements in space. So it seems that dancing with an object and manipulating it in proportionately interesting patterns is roughly analogues to playing a spatial instrument.

With both musical and spatial instruments, to play well, we need to be aware of how oscillations (sounds or otherwise) can be structured proportionately, how the instrument functions, and how our body can work effectively to make it function. So when modeling how to think about poi spinning and communicate it clearly, I think it is useful to be clear about what aspect you are talking about :

Conceptual geometric principles

Actual physical properties of poi

Actual body mechanics and things in the anatomical realm

Qualities that arise from the combined interactions of the above mentioned aspects

As music has developed we see an evolution from purely intuitive to using theory and theoretical models to describe what is going on, ultimately to the extent of being informed by the physics of sound waves. In recent history we've seen not only the playing of instruments, but the recording, sampling, and remixing of sampled instruments. Ultimately understanding of the physics of sound has lead musicians to synthesize and manipulate the sounds they want from the ground up (or is it sine-wave on up).

I see poi (and general object manipulation) understanding following a similar path. Early on, a lot of people spun more intuitively, without a strong mental model for what they were doing. But we have been evolving our understanding of technique such that emphasis on techpoi is very prevalent. We are getting to the point of mentally modeling and understanding the physics of our body spinning objects around such that we can easily sample ideas from one prop and apply it to another prop. I would say that we are now well into collectively developing our understanding of "object manipulation synthesis".

A forward - Parallels between music and poi:

I like to think of object manipulation as a form of "spatial music". I think there can be some good analogies drawn from it.

Music is the sonic expression of harmonic proportions sequenced over time. The human voice is the most intimate and natural way to make music but there is something wonderful about playing an instrument, interacting with an otherwise inanimate object to make music with qualities the voice can't.

The spatial analogue to the human voice is dance. One sequences proportionately interesting body movements in space. So it seems that dancing with an object and manipulating it in proportionately interesting patterns is roughly analogues to playing a spatial instrument.

With both musical and spatial instruments, to play well, we need to be aware of how oscillations (sounds or otherwise) can be structured proportionately, how the instrument functions, and how our body can work effectively to make it function. So when modeling how to think about poi spinning and communicate it clearly, I think it is useful to be clear about what aspect you are talking about :

Conceptual geometric principles

Actual physical properties of poi

Actual body mechanics and things in the anatomical realm

Qualities that arise from the combined interactions of the above mentioned aspects

As music has developed we see an evolution from purely intuitive to using theory and theoretical models to describe what is going on, ultimately to the extent of being informed by the physics of sound waves. In recent history we've seen not only the playing of instruments, but the recording, sampling, and remixing of sampled instruments. Ultimately understanding of the physics of sound has lead musicians to synthesize and manipulate the sounds they want from the ground up (or is it sine-wave on up).

I see poi (and general object manipulation) understanding following a similar path. Early on, a lot of people spun more intuitively, without a strong mental model for what they were doing. But we have been evolving our understanding of technique such that emphasis on techpoi is very prevalent. We are getting to the point of mentally modeling and understanding the physics of our body spinning objects around such that we can easily sample ideas from one prop and apply it to another prop. I would say that we are now well into collectively developing our understanding of "object manipulation synthesis".

+Alien Jon

Posted:

My personal method:

So I've been drawn to explore and apply ideas that seem to show up a lot in various fields of synthesis (sound synthesis, image synthesis, physical modeling, etc)

My approach is to break down what my poi and body do in reality into different components and dimensions, in a hierarchy of subsystems. This is similar to how physicist in general have dissected and defined the properties of forces in our physical world, iteratively digging deeper to find the "true" forces that everything is a structural configuration of. Of course the deeper you dig, the more you are abstracted from actual direct human experience and the more you are dealing purely with a conceptual model.

Conceptual models are useful for removing distractions in order to make clear the properties underpinning the whole thing you are trying to model, and where the distinctions are. This is what I'm doing when I'm thinking about and simulating poi patterns on a computer. I can play with novel arrangements of said properties, without the distraction of assumptions about what is or isn't physically possible.

Of course from there I could just as easily put down poi forever and make spinny screen-savers. So it is important to reintegrate the conceptual with how the heck your poi and body can do that in the real world.

What I find myself coming back to over and over, when applying the conceptual, is the principles of oscillation and symmetry. These concepts show up everywhere in the arts, sciences, engineering, etc, because they are accurate models about relationships present in just about every aspect of the reality we experience. So, let's stand poi and object manipulation on the shoulders of the giants that have come before us, and make use of these principles.

My personal method:

So I've been drawn to explore and apply ideas that seem to show up a lot in various fields of synthesis (sound synthesis, image synthesis, physical modeling, etc)

My approach is to break down what my poi and body do in reality into different components and dimensions, in a hierarchy of subsystems. This is similar to how physicist in general have dissected and defined the properties of forces in our physical world, iteratively digging deeper to find the "true" forces that everything is a structural configuration of. Of course the deeper you dig, the more you are abstracted from actual direct human experience and the more you are dealing purely with a conceptual model.

Conceptual models are useful for removing distractions in order to make clear the properties underpinning the whole thing you are trying to model, and where the distinctions are. This is what I'm doing when I'm thinking about and simulating poi patterns on a computer. I can play with novel arrangements of said properties, without the distraction of assumptions about what is or isn't physically possible.

Of course from there I could just as easily put down poi forever and make spinny screen-savers. So it is important to reintegrate the conceptual with how the heck your poi and body can do that in the real world.

What I find myself coming back to over and over, when applying the conceptual, is the principles of oscillation and symmetry. These concepts show up everywhere in the arts, sciences, engineering, etc, because they are accurate models about relationships present in just about every aspect of the reality we experience. So, let's stand poi and object manipulation on the shoulders of the giants that have come before us, and make use of these principles.

+Alien Jon

Posted:

Breaking it down beyond planes and building it up again:

Years ago, most people didn't think of poi in terms of planar orientation. Of course planes are a useful mental tool to help with poi spinning, because rotational energy seems to want to stabilize its orientation along a plane perpendicular to the axis of rotation. Once the concept of planes propagated in the poi world, it help refine and clarify the patterns people where playing with, and open up all sorts of lovely geometric patterns like flowers.

It is, however important to remember that planar theory is only a model of only one aspect of spinning. We are after all spinning in 3D + T it is impossible to spin in 2D. We can certainly get good at generating almost all of our rotation energy into a spin that is aligned with a planar orientation, leaving only very small wobbles in the 3rd dimension. This means almost all of your energy is invested in making a nice pattern to be seen by observers viewing the spin plane face on, wile keeping the poi oscillating in clean lines from the side.

Unfortunately it seems some people have been so enamored with exploring the possibilities of making spirography poi patterns on a plane they have forgotten or at least neglected to hone their understanding of helical motion, ie the stuff that goes on in the volume in-between our imaginary spin planes. I like to think of spin planes as simply the flat boundaries that frame and contain the volume through which the poi pattern moves. The prevalence of planar conceptualization has dictated how we think about the timing of what we do with poi. Many people, myself included, tend to talk about poi in terms of the 4 basic modes of timing and direction. However this is only looking at the poi's space-time relationship from the planar point of view. There is another dimension to consider.

Let's break it down even further than 2D planar exploration of poi, to 1D components. Poi is by nature cyclical/periodic. When you watch someone spinning a circle in a clean vertical plane from the side or top, you don't see the circle, you see the poi head oscillating up/down or left/right. In fact, sometimes it can be hard to tell wether someone is spinning same or opposite directions, when seen side on. This is because you are only seeing the change in the poi caused by energy in 1 dimension.

Rotation can be conceptualized as being made up of the oscillations of sine waves in 2 perpendicular dimensions, a quarter cycle out of phase (Another way to think about graphing this is: position = sine of x cosine of y).

In order for something to oscillate, it needs to move back and forth between 2 boundaries, through a middle point.

When you start looking at 1D components of poi patterns you can no longer compare rotational timing & direction. You can only compare phase as the pattern cycles. So, in terms of cycle timing, the 4 major timings that show up are:

In-phase: thing R and thing L move together.

1/2 cycle out of phase: Thing R reaches one boundary, thing L reaches the other boundary, and they pass each other in the middle.

1/4 cycle out of phase: Thing R reaches a boundary as thing L reaches the middle, then as thing R reaches the middle again, thing L reaches the last boundary that thing R was at. this continues to the other boundary and back In effect L is chasing R a quarter cycle behind.

3/4 cycle out of phase: Thing R reaches the middle as thing L reaches a boundary, then thing R reaches the last boundary of thing L as thing L reaches the middle again. This continues to the other boundary and back. R is chase L.

If R & L oscillate at different rates, then they share "polyrhythmic" properties, and phase shift.

There are also the possibilities of timings such as 1/3 or 2/3 out of phase, etc, but these have been explored relatively little.

So why is this important to poi spinning? The properties of oscillation can be applied to both poi and body parts (and just about everything else in the universe) to make meaningful comparative observations about what is going on between specific attributes. For instants, thinking of the poi head path as 3 oscillatory components in 3D helps remove the in-plane biased of thinking only of rotational Timing & Direction, wile more accurately describing what is going on with rotational timing & direction relationships in-plane.

If we think of the parallel planes we move between as boundaries, it is easy to think of periodically crossing our poi between these boundaries as simply adding another dimension of oscillation to the spinning. What this inferrers is that there is a 3rd plane, bisecting the volume that is framed by the boundary planes in half. This is the plane on which evenly balanced cross-points cuts through.

Let's consider a figure 8 (2-beat cross over). If the rotation in-plane is comprised of 1 sine wave cycle in x for every cosine cycle in y, then in z (volume between planes), only half a cycle will happen in that time. In other words it takes 2 rotations of the poi to cross from right plane to left plane back to right. So we have cycle timing x:y:z = 2:2:1. If you adjust the phase of z, you adjust when the poi head passes through the cross-point plan. Therefore you adjust where around the proverbial clock the cross-point is pointing: front, up down, back, and all the angles in-between.

When spinning figure 8's many spinners associate specific cross-over timings with specific rotational modes of timing & direction. It should feel familiar to just about any one to do the following patterns, aiming your cross-points out at the horizon:

Start both hands on the right side of the body and spin a figure 8 in together-same rotation. Aside from the small offset you need to make to keep the poi heads from tangling, your poi pass through the cross point together, in other words their z cycles are in-phase.

Start on either side of your body and cross your 8s, you will likely also hit your cross-points at the same time, but going to opposite boundary planes so your z cycles are 1/2 cycle out of phase.

Start a right-handed 2-beat weave in split-time then you will your z cycles are 1/4 out of phase. If left handed, you are 3/4 out of phase. (in this example I've arbitrarily assigned 1/4 to right and 3/4 to left as a "right-hand rule" of sorts).

Start a split-opposite 2-beat and your z cycles will be in-phase.

Start a together-opposite 2-beat and your z cycles will likely be in-phase with each other, but something will be different. Your cross point will be pointing up (or maybe down). In order to maintain together-same rotation and hit the horizontal cross points your z will have to be 1/4 out of phase (if you start with right hand forward on the right side). Just like a right handed split-same 2-beat, your right will lead to the left by crossing the left wrist, and the left will follow through the cross=point a quarter cycle behind. Then the right will uncross the left wrist and head back a quarter cycle ahead of the left.

In reality cross-over timing is independent of rotational T&D, as long as your body is out of the way. As you change the cross-over phase, you also shift the angle of your cross-points.

An example of this is spinning split-same in wall-plane and crossing the poi to the back plane at the same time. The left poi hits a left cross-point and the right hits a right cross-point.

Cross-over timing is only one attribute that we can look at with oscillations.

Breaking it down beyond planes and building it up again:

Years ago, most people didn't think of poi in terms of planar orientation. Of course planes are a useful mental tool to help with poi spinning, because rotational energy seems to want to stabilize its orientation along a plane perpendicular to the axis of rotation. Once the concept of planes propagated in the poi world, it help refine and clarify the patterns people where playing with, and open up all sorts of lovely geometric patterns like flowers.

It is, however important to remember that planar theory is only a model of only one aspect of spinning. We are after all spinning in 3D + T it is impossible to spin in 2D. We can certainly get good at generating almost all of our rotation energy into a spin that is aligned with a planar orientation, leaving only very small wobbles in the 3rd dimension. This means almost all of your energy is invested in making a nice pattern to be seen by observers viewing the spin plane face on, wile keeping the poi oscillating in clean lines from the side.

Unfortunately it seems some people have been so enamored with exploring the possibilities of making spirography poi patterns on a plane they have forgotten or at least neglected to hone their understanding of helical motion, ie the stuff that goes on in the volume in-between our imaginary spin planes. I like to think of spin planes as simply the flat boundaries that frame and contain the volume through which the poi pattern moves. The prevalence of planar conceptualization has dictated how we think about the timing of what we do with poi. Many people, myself included, tend to talk about poi in terms of the 4 basic modes of timing and direction. However this is only looking at the poi's space-time relationship from the planar point of view. There is another dimension to consider.

Let's break it down even further than 2D planar exploration of poi, to 1D components. Poi is by nature cyclical/periodic. When you watch someone spinning a circle in a clean vertical plane from the side or top, you don't see the circle, you see the poi head oscillating up/down or left/right. In fact, sometimes it can be hard to tell wether someone is spinning same or opposite directions, when seen side on. This is because you are only seeing the change in the poi caused by energy in 1 dimension.

Rotation can be conceptualized as being made up of the oscillations of sine waves in 2 perpendicular dimensions, a quarter cycle out of phase (Another way to think about graphing this is: position = sine of x cosine of y).

In order for something to oscillate, it needs to move back and forth between 2 boundaries, through a middle point.

When you start looking at 1D components of poi patterns you can no longer compare rotational timing & direction. You can only compare phase as the pattern cycles. So, in terms of cycle timing, the 4 major timings that show up are:

In-phase: thing R and thing L move together.

1/2 cycle out of phase: Thing R reaches one boundary, thing L reaches the other boundary, and they pass each other in the middle.

1/4 cycle out of phase: Thing R reaches a boundary as thing L reaches the middle, then as thing R reaches the middle again, thing L reaches the last boundary that thing R was at. this continues to the other boundary and back In effect L is chasing R a quarter cycle behind.

3/4 cycle out of phase: Thing R reaches the middle as thing L reaches a boundary, then thing R reaches the last boundary of thing L as thing L reaches the middle again. This continues to the other boundary and back. R is chase L.

If R & L oscillate at different rates, then they share "polyrhythmic" properties, and phase shift.

There are also the possibilities of timings such as 1/3 or 2/3 out of phase, etc, but these have been explored relatively little.

So why is this important to poi spinning? The properties of oscillation can be applied to both poi and body parts (and just about everything else in the universe) to make meaningful comparative observations about what is going on between specific attributes. For instants, thinking of the poi head path as 3 oscillatory components in 3D helps remove the in-plane biased of thinking only of rotational Timing & Direction, wile more accurately describing what is going on with rotational timing & direction relationships in-plane.

If we think of the parallel planes we move between as boundaries, it is easy to think of periodically crossing our poi between these boundaries as simply adding another dimension of oscillation to the spinning. What this inferrers is that there is a 3rd plane, bisecting the volume that is framed by the boundary planes in half. This is the plane on which evenly balanced cross-points cuts through.

Let's consider a figure 8 (2-beat cross over). If the rotation in-plane is comprised of 1 sine wave cycle in x for every cosine cycle in y, then in z (volume between planes), only half a cycle will happen in that time. In other words it takes 2 rotations of the poi to cross from right plane to left plane back to right. So we have cycle timing x:y:z = 2:2:1. If you adjust the phase of z, you adjust when the poi head passes through the cross-point plan. Therefore you adjust where around the proverbial clock the cross-point is pointing: front, up down, back, and all the angles in-between.

When spinning figure 8's many spinners associate specific cross-over timings with specific rotational modes of timing & direction. It should feel familiar to just about any one to do the following patterns, aiming your cross-points out at the horizon:

Start both hands on the right side of the body and spin a figure 8 in together-same rotation. Aside from the small offset you need to make to keep the poi heads from tangling, your poi pass through the cross point together, in other words their z cycles are in-phase.

Start on either side of your body and cross your 8s, you will likely also hit your cross-points at the same time, but going to opposite boundary planes so your z cycles are 1/2 cycle out of phase.

Start a right-handed 2-beat weave in split-time then you will your z cycles are 1/4 out of phase. If left handed, you are 3/4 out of phase. (in this example I've arbitrarily assigned 1/4 to right and 3/4 to left as a "right-hand rule" of sorts).

Start a split-opposite 2-beat and your z cycles will be in-phase.

Start a together-opposite 2-beat and your z cycles will likely be in-phase with each other, but something will be different. Your cross point will be pointing up (or maybe down). In order to maintain together-same rotation and hit the horizontal cross points your z will have to be 1/4 out of phase (if you start with right hand forward on the right side). Just like a right handed split-same 2-beat, your right will lead to the left by crossing the left wrist, and the left will follow through the cross=point a quarter cycle behind. Then the right will uncross the left wrist and head back a quarter cycle ahead of the left.

In reality cross-over timing is independent of rotational T&D, as long as your body is out of the way. As you change the cross-over phase, you also shift the angle of your cross-points.

An example of this is spinning split-same in wall-plane and crossing the poi to the back plane at the same time. The left poi hits a left cross-point and the right hits a right cross-point.

Cross-over timing is only one attribute that we can look at with oscillations.

+Alien Jon

Posted:

So what I've been playing around with, that I alluded to in the Drex thread, is considering repeating patterns of motion as time-repeating frieze groups under the following operations:

reflection

rotation

reverse (essentially amounts to temporal reflection)

pause/advance (temporal translation)

advance reflection (glide reflections, except the translation is temporal)

advance rotation (rotation and temporal translation; equivalent to one of the symmetries that 3d helical patterns have)

I'm working under a few constraints for the sake of simplicity. First, I'm considering 2D motions through time, so atomics and plane-breaking CAPs are excluded under the model. Second, I'm ignoring the spatial arrangement of the poi, so that for all practical purposes we can consider their centers of rotation to be in the same place (the center of rotation may not be the "hand") and on the same plane, though it is relevant to distinguish which hand/poi is which, and where in their respective cycles they are.

(In my mental simulations I use red vs. blue like in Jon's simulations and I time-stamp the heads. This is important because a symmetry operation, or a composition of such operations, will equal E, the identity element, if it puts the same colors back on themselves with the same time stamp. If red is superimposed on blue, or blue is superimposed on blue but the timestamp reads differently, you've preserved symmetry but have not produced identity.)

It's important that this approach can only handle infinite repeating patterns (you could make it more concrete, but then you lose theoretic power). This repetition means that everything has at least an "advance" symmetry of one cycle (note that one cycle will not necessarily be in one beat, as in the case of polyrhythms). But it also means that in practice, what pattern someone is doing will be underdetermined by their performance. That's because it is not within the scope of this treatment to distinguish between long combinations that are repeatable, and smaller "moves" that they pass through as part of the combination. There is no unique breakdown of what someone is doing while they spin. But that's all right by me; in practice we usually know what the interesting level of analysis is, since we seem to be able to see the sweet spot between movements that are too short to even be cyclical, and movements that are too complex for symmetry to be hoped for.

I'm still working on the algebra I need to classify the patterns and find interesting relationships. Most of my advanced mathematics is self-taught, so it can be slow-going.

EDITED_BY: Sister Eleven (1278128656)

EDIT_REASON: realized a couple of symmetry operations were listed out of habit, and not strictly necessary under the constraints I listed

So what I've been playing around with, that I alluded to in the Drex thread, is considering repeating patterns of motion as time-repeating frieze groups under the following operations:

reflection

rotation

reverse (essentially amounts to temporal reflection)

pause/advance (temporal translation)

advance reflection (glide reflections, except the translation is temporal)

advance rotation (rotation and temporal translation; equivalent to one of the symmetries that 3d helical patterns have)

I'm working under a few constraints for the sake of simplicity. First, I'm considering 2D motions through time, so atomics and plane-breaking CAPs are excluded under the model. Second, I'm ignoring the spatial arrangement of the poi, so that for all practical purposes we can consider their centers of rotation to be in the same place (the center of rotation may not be the "hand") and on the same plane, though it is relevant to distinguish which hand/poi is which, and where in their respective cycles they are.

(In my mental simulations I use red vs. blue like in Jon's simulations and I time-stamp the heads. This is important because a symmetry operation, or a composition of such operations, will equal E, the identity element, if it puts the same colors back on themselves with the same time stamp. If red is superimposed on blue, or blue is superimposed on blue but the timestamp reads differently, you've preserved symmetry but have not produced identity.)

It's important that this approach can only handle infinite repeating patterns (you could make it more concrete, but then you lose theoretic power). This repetition means that everything has at least an "advance" symmetry of one cycle (note that one cycle will not necessarily be in one beat, as in the case of polyrhythms). But it also means that in practice, what pattern someone is doing will be underdetermined by their performance. That's because it is not within the scope of this treatment to distinguish between long combinations that are repeatable, and smaller "moves" that they pass through as part of the combination. There is no unique breakdown of what someone is doing while they spin. But that's all right by me; in practice we usually know what the interesting level of analysis is, since we seem to be able to see the sweet spot between movements that are too short to even be cyclical, and movements that are too complex for symmetry to be hoped for.

I'm still working on the algebra I need to classify the patterns and find interesting relationships. Most of my advanced mathematics is self-taught, so it can be slow-going.

EDITED_BY: Sister Eleven (1278128656)

EDIT_REASON: realized a couple of symmetry operations were listed out of habit, and not strictly necessary under the constraints I listed

p|.q|r:|::s|.s|s:|:.s|q.|:p|s.|.p|s

Posted:

Quote:..let's stand poi and object manipulation on the shoulders of the giants that have come before us, and make use of these principles...

Quote:..let's stand poi and object manipulation on the shoulders of the giants that have come before us, and make use of these principles...

Posted:

An aside:

(Oh, and Drex, if you see this, one of the consequences of the treatment I'm using above, if it's a criterion for "hybrid", is that hands-together, poi opposite C-CAPs are not hybrids. They have too many interesting symmetries over full cycles. It has reverse points, and advance reflection points [flip the pattern vertically and advance half a cycle].)

An aside:

(Oh, and Drex, if you see this, one of the consequences of the treatment I'm using above, if it's a criterion for "hybrid", is that hands-together, poi opposite C-CAPs are not hybrids. They have too many interesting symmetries over full cycles. It has reverse points, and advance reflection points [flip the pattern vertically and advance half a cycle].)

p|.q|r:|::s|.s|s:|:.s|q.|:p|s.|.p|s

Posted:

Sister Eleven: Interesting. This is promising! I was not specifically aware of frieze groups yet. It's late and I'm tired, but am I correct in understanding that for a repeating pattern graphed over time, you are looking at the time dimension as the infinitely wide dimension of the rectangle?

This is great, as I had been looking at symmetries mostly in focusing on how they relate to the rotational driving styles. I've only done it in software very briefly and now need to get around to reinstalling the software I was using. >_< So it has mostly been purely thinking about it. Basically the idea is graphing the planar projection over time to get a 3d shape (because it's hard to think in 4-space). Then performing various operations (rotation and reflection mostly) to test for symmetries. I had been wondering how translation and glide reflections fit in, and glimpsed that it was more useful in the time dimension, but the frieze groups over time is great! I need to go study the 7 types for a bit to really grok the implications. This looks like it will really refine how we can apply symmetry checks along both time and space axes to gain new insight!

Sister Eleven: Interesting. This is promising! I was not specifically aware of frieze groups yet. It's late and I'm tired, but am I correct in understanding that for a repeating pattern graphed over time, you are looking at the time dimension as the infinitely wide dimension of the rectangle?

This is great, as I had been looking at symmetries mostly in focusing on how they relate to the rotational driving styles. I've only done it in software very briefly and now need to get around to reinstalling the software I was using. >_< So it has mostly been purely thinking about it. Basically the idea is graphing the planar projection over time to get a 3d shape (because it's hard to think in 4-space). Then performing various operations (rotation and reflection mostly) to test for symmetries. I had been wondering how translation and glide reflections fit in, and glimpsed that it was more useful in the time dimension, but the frieze groups over time is great! I need to go study the 7 types for a bit to really grok the implications. This looks like it will really refine how we can apply symmetry checks along both time and space axes to gain new insight!

+Alien Jon

Posted:

Originally Posted By: AlienJonSister Eleven: Interesting. This is promising! I was not specifically aware of frieze groups yet. It's late and I'm tired, but am I correct in understanding that for a repeating pattern graphed over time, you are looking at the time dimension as the infinitely wide dimension of the rectangle?

Yeah, that's basically how I'm looking at it. Though an effective and compact way of looking at it also is as operations you could perform on a video loop. I don't know if software with the exact capacities to run such transformations in real time actually exists, but it wouldn't be the hardest thing to program by a long shot.

The differences between this and a standard frieze group is that the infinite dimension is orthogonal to the "cell", so things like advance rotations have no analogue in a 2d frieze (at least not without making things much more complicated). Also because of the constraints I'm using, (spatial) translations and glide reflections are irrelevant because we're ignoring spatial positioning of the poi for simplicity.

Oh, and I forgot to mention that your idea of extending the 2d motion along a third spatial axis would accomplish, I think, exactly the same things. That is, all of the same symmetry operations would translate over into 3d analogues.

EDITED_BY: Sister Eleven (1278147983)

Originally Posted By: AlienJonSister Eleven: Interesting. This is promising! I was not specifically aware of frieze groups yet. It's late and I'm tired, but am I correct in understanding that for a repeating pattern graphed over time, you are looking at the time dimension as the infinitely wide dimension of the rectangle?

Yeah, that's basically how I'm looking at it. Though an effective and compact way of looking at it also is as operations you could perform on a video loop. I don't know if software with the exact capacities to run such transformations in real time actually exists, but it wouldn't be the hardest thing to program by a long shot.

The differences between this and a standard frieze group is that the infinite dimension is orthogonal to the "cell", so things like advance rotations have no analogue in a 2d frieze (at least not without making things much more complicated). Also because of the constraints I'm using, (spatial) translations and glide reflections are irrelevant because we're ignoring spatial positioning of the poi for simplicity.

Oh, and I forgot to mention that your idea of extending the 2d motion along a third spatial axis would accomplish, I think, exactly the same things. That is, all of the same symmetry operations would translate over into 3d analogues.

EDITED_BY: Sister Eleven (1278147983)

p|.q|r:|::s|.s|s:|:.s|q.|:p|s.|.p|s

Posted:

well it is a bit off topic but a strange idea imagine if you could rig up a camera to a computer and have it watch you spin and use all of the ridiculously complex math that you get out of poi and make music with it like there is a program called fruity loops that has a graph that adjusts sounds and other things so you could have a complex graph adjuster that changed tempo beat make adjustments on the types of sound and many other things by using the math from geometry and physics thought it would be intresting concept

well it is a bit off topic but a strange idea imagine if you could rig up a camera to a computer and have it watch you spin and use all of the ridiculously complex math that you get out of poi and make music with it like there is a program called fruity loops that has a graph that adjusts sounds and other things so you could have a complex graph adjuster that changed tempo beat make adjustments on the types of sound and many other things by using the math from geometry and physics thought it would be intresting concept

"Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able, and willing? Then whence cometh evil? Is he neither able nor willing? Then why call him God?" - Epicurus

Posted:

Damn, Jon--excellent post with a lot of food for thought! I need to let this sink in further and go through the article on Frieze groups, but some initial thoughts:

In some respects this is a deconstructionalist approach in that we are seeing a given pattern as a function of its on-axis components of which each pattern must possess at least one phasing for any two-point relationship (can we have more than two? I haven't worked one out just yet--I'm assuming that in this equation we are temporarily ignoring the spirograph result on the audience plane given that it is the product of both graphs and therefore possesses both phase relationships). In other words, rather than the assembly of a 2D roulette pattern we're focusing instead on the individual functions of x and y that when combined yield our antispins, CAPs, and extensions.

I think there might also an additional phase relationship missing from the list given that if we look at this one hand at a time, static spin will yield a pattern wherein there will be no phase relationship at all. I'm thinking of this specifically when it comes to applying these relationships to linear extensions wherein if we are performing a vertical LE, from the side we can be said to have hand and poi in phase but from above we for all intents are performing a static spin. Even if the relationship is designed only to describe the relationship between poi heads, there are many movements in which a rotating head will be played against a static head, be it stacking moves or other moves that can be extrapolated from this relationship (pendulum vs antispin, for example, though we could just as easily perform a weave with a pendulum moving only along the Z axis to match the hand of a spinning side).

Interesting side note: I went ahead and got a copy of that book Thom had at Firedrums and I'm realizing some of the diagrams in it conform not just to the spirograph patterns we've long played with, but also cross-point arrangements for multiple Z-planes. One such figure was a 3:3:1 weave that one could visualize as a 3-plane weave with the first crosspoint set directly in front of the left shoulder and a second directly behind the right shoulder such that the poi pass a crosspoint above and slightly behind and above the right shoulder on their journey to that side.

Back with more soon--thanks for the brain food!

Damn, Jon--excellent post with a lot of food for thought! I need to let this sink in further and go through the article on Frieze groups, but some initial thoughts:

In some respects this is a deconstructionalist approach in that we are seeing a given pattern as a function of its on-axis components of which each pattern must possess at least one phasing for any two-point relationship (can we have more than two? I haven't worked one out just yet--I'm assuming that in this equation we are temporarily ignoring the spirograph result on the audience plane given that it is the product of both graphs and therefore possesses both phase relationships). In other words, rather than the assembly of a 2D roulette pattern we're focusing instead on the individual functions of x and y that when combined yield our antispins, CAPs, and extensions.

I think there might also an additional phase relationship missing from the list given that if we look at this one hand at a time, static spin will yield a pattern wherein there will be no phase relationship at all. I'm thinking of this specifically when it comes to applying these relationships to linear extensions wherein if we are performing a vertical LE, from the side we can be said to have hand and poi in phase but from above we for all intents are performing a static spin. Even if the relationship is designed only to describe the relationship between poi heads, there are many movements in which a rotating head will be played against a static head, be it stacking moves or other moves that can be extrapolated from this relationship (pendulum vs antispin, for example, though we could just as easily perform a weave with a pendulum moving only along the Z axis to match the hand of a spinning side).

Interesting side note: I went ahead and got a copy of that book Thom had at Firedrums and I'm realizing some of the diagrams in it conform not just to the spirograph patterns we've long played with, but also cross-point arrangements for multiple Z-planes. One such figure was a 3:3:1 weave that one could visualize as a 3-plane weave with the first crosspoint set directly in front of the left shoulder and a second directly behind the right shoulder such that the poi pass a crosspoint above and slightly behind and above the right shoulder on their journey to that side.

Back with more soon--thanks for the brain food!

Peace,

Drex

Posted:

Hard to read through...

My language skills limits my self a bit while reading this...

I think that I have to print it and get a second or third reading with a translation...

Could you may put up some images to virtualize about what are you talking?

Or make something like a vlog out of it?

Hard to read through...

My language skills limits my self a bit while reading this...

I think that I have to print it and get a second or third reading with a translation...

Could you may put up some images to virtualize about what are you talking?

Or make something like a vlog out of it?