Here are some more thoughts on my training paradigm and I would appreciate all input.
Erick, thank you for posting that information in the other thread. I will study it more. I must confess that like all skills my math is one that I have not used often and honestly didn't develop as much as I would now like and has thus waned over the years. I have been interested in architecture for a long time though and drafting and structural engineering was a class I took in high school which I greatly enjoyed and researched further in my own time.
Then we are not so far apart -- It is much more correct structural and dynamic models that allow intuition to function and seek practical insights. The closer they come to visualization or describing qualities of sensation -- the more useful. However, I struggle with the maths and geometries to make sure I am not simply making a "just-so" story to replace the "just-so" story I started with. YMMV.
Since the loaded images are not yet vetted by Jun, I uploaded them:
You can apply the spheres in looking at the action of the body acting as a whole -- or to two bodies acting as a whole -- or to each segment of your body acting in isolation. Essentially, the poles of the spheres are at any discontinuity in the the frame, creases in the "suit", or what have you, and they can be considered as a chain of such spherical actions (formed of these shear "windings"), and connected at the poles like a beaded chain.
Wind them and these discontinuities begin to reduce -- the spheres get larger, and fewer, as they fold into one another and double and double again, like twisting links in a chain, causes its links (spheres) to fold up with one another. The chain gets fatter, and shortens at the same time -- approaching a sphere in the limit, and becoming stiffer and less flexible. The larger the sphere of action the more cohesive the structural response and less overt motion.
The smaller and more multiple the spheres of action the more mobile and dynamic -- like the beaded chain. That gets you the multiple pendulum action of the Lissajous curve -- and I think the relationship is clear visually, but is just as robust mathematically and mechanically:
One thing I have been thinking about was your assertion of technique practice frequency. I have been pondering the different effects of varying frequencies, measuring intervals, and observing uke response. Unfortunately I don't have a training partner at the moment as I cannot afford to pay for a dojo. I think by the appearance of some of the training techniques in aikido that many would benefit from learning silk reeling and push hands as there is much overlap.
very much so. I did some of my most helpful work in just solo shadowboxing and weapons work while on several naval deployments. I treated it like solo chess. It forced me to move while thinking imaginatively or think while moving imaginatively -- and that began to form the rudiments of what I have been working out since.
"Liminality" has interesting resonance with the aikido concept of takemusu
the spontaneous birth of martial techniques in the moment of entry into connection with the attacker.