Chorand Spheres

Sparking and Arousing

After I had posted to Yixue announcing the uploading of this material, Henri replied. His reply, and my response to his reply are interleaved below.

Hi Henri,

At 17:04 20/10/2005, Henri wrote:

H: Unfortunately, I really lack enough time to dwelve into it as much as I would like to.

A: It's a priority of mine to be able to organize my life to give this time. It's part of the practice.

H: I could not help posting about my own weird stuff

A: A few of my favourite things :-)

H: when I noticed others were doing more or less similar things. To me, when I built them, the most interesting thing was that it allowed to separate the 64 hexagrams into two distinct (unrelated) sets.

A: Yes, two domains. One set of hexagrams in each. Bohm (David Bohm - physicist, worth a google) names them the implicate order and the explicate order; what the Changes call heaven and earth.

H: The last clue (intuition) I'd like to share is that of axes. I see each of these two spheres as having an axis (like planispheres).

A: Absolutely.

H: It seems to me that the axis made up by hexagrams 1 and 2 can be seen as a vertical (orientated and stable) axis, with a clear "top" and "bottom",

A: Yes, this corresponds to their role in the Boolean lattice too. I think of it as an energetically quantitative polarization. However,

H: whereas the axis made up by hexagrams 63 and 64 can be seen as a horizontal (non-orientated, oscillating) axis.

A: Yes, definitely horizontal; an energetically qualitative polarization. When you say non-oriented, do you mean that it could be oriented at any point around the equatorial band? If so, then yes, too.

And oscillating relative to Receptive/Creative when you think about cycle waves too. Receptive and Creative are each invariant as cyclic waves, whilst the Resonating Pair transform directly into each other as cyclic waves.

H: So one would have an illustration of the two types of equilibriums - static and dynamic.

A: Neat, huh! experimental mathematical philosophy.

H: It would be a polarity, like firm and yielding, and at the same time, obviously, it's not based on firm and yielding lines.

A: Yes, this is a division into a pair of polarized domains, spaces where firm and yielding manifest as polarities in different ways. In the implicate set, the patterns of change are simple and smooth, ideals and models. This is the idea of coherent cyclic waves. In the explicate set, the patterns of change are more varied. For example, whilst there is only one coherent cyclic wave with 3 yang lines, there are 2 dispersed cyclic waves with 3 yang lines. Similarly for cyclic waves with 2 yang lines, 1 wave when coherent, 2 distinct waves when dispersed. As the room for maneuver decreases, this pattern breaks, there is only 1 dispersed cyclic wave with 4 yang, likes for coherent. However, there are no dispersed waves with 1 yang line, but of course there is a coherent wave with 1 yang. Similary, there are no dispersed waves with 5 yang lines, but there is such a coherent wave. So the explicate order is also less varied in its patterns of change compared to the implicate.

I'm not sure how much of that will make sense without reading the web material...

For Sparking and Arousing , thank you!


After this email, I then went back and rewrote the material in the internal energy boundary section and the wave function section, emphasizing cyclic wave sequences, and adding in the discontinuous waves. Which is the version that you've just read.