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Hexagram as a Cycle(2)

breakmov

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continuing from topic Hexagram as a Cycle(1)

So, we have from the calculations 10 hexagrams that will be included in the construction of this tool:

- main hexagram= hex63
- derived hexagram= hex48
- main opposite hexagram= hex64
- Opposite derived hexagram= hex21
- XOR=yang pattern= lines that change= hex19=(hex24 + hex7)
- XNOR=yin pattern=lines that do not change= hex33=(hex39 + hex35)
- hexagram corresponding to the lines --o--= hex24
- hexagram corresponding to the lines --x--= hex7
- hexagram corresponding to the lines -----= hex39
- hexagram corresponding to the lines -- --= hex35

This tool has everything to do with the mathematical relationship XOR and XNOR expressed in the yin/yang pattern of change but also, especially in its use, with a correlated thinking posture, so the fact that there is a number of ten hexagrams immediately brings me back to the special meaning attributed to this number in antiquity, such as Pythagoras' tetractys, the 10-day week in ancient China or its 10 celestial stems still used today, for example in wuxing.


The Steps in the construction of the tool:




The first link between the number 10 and something ancient, and basic in its simplicity, is connected to the simplest figure to represent a three-dimensional volume, the Tetrahedron , used for example in 2600 BC in ancient Sumeria,today Iraq, through the Royal game of Ur or much later spoken of in the philosophy of Plato.

The interesting property of the Tetrahedron is connected to the number 10 by its 4 vertices and 6 edges.



geometrical relation between the 10 hexagrams.png


Further research led to the association of the Tetrahedron with its 4-dimensional version, the pentatope... the step to associate it with the cycle of the 4 seasons was inevitable.



pentatop_earth four season cycle.png


As you can see in the image, the planet earth is the basic, primordial factor, that unites everything else and allows its manifestation.
At any given moment on planet earth there are the four seasons occurring simultaneously, between the north and south pole. On a daily level, too, the planet is globally and dynamically with parts in a state of day, night, with dawn, with sun at maximum peak e.t.c...it is a globally continuous successive state where all possible states are present at any given moment.





4-season cycle.png


Passing now this concept for application using the hexagrams deduced with the help of Boolean algebra.
As you can see, there is an association between the four possible types of lines in a hexagram with the correlated position of the solstices and equinoxes... these are key points of change within the cycle and are also links between two consecutive seasons.


Hexagram_cycle.png


here is a small example, just to give you an idea, how the cycle would be arranged
As you can see it is very easy to associate directly, visually and without calculation, any reading (in this example 63.1.2>48) to the appropriate place in the cycle.


Hexagram cycle with correlative thinking_hex 63.png




The existing hexagram relations through this tool:



The 10 hexagrams and their relationship to each other in the cycle.png



That all for now,

In the next topic, I will talk about the correlated thinking of the various steps of the cycle and its importance. I will leave practical examples.


breakmov
 

hilary

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Thanks, breakmov. I've managed to follow along so far - well, not so much the tetrahedron and its four-dimensional friend, but I can see how you're deriving the other hexagrams. I hope you're just about to explain what all these hexagrams represent in a reading!
 

breakmov

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Thanks for the feedback Hilary and Remod. Yes, as soon as I can I will move on to the conclusion with examples. I will come back to this topic later to write about your feedback.

breakmov
 

dfreed

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I will come back to this topic later to write about your feedback.
I am glad you will be answering some of the questions that have been raised here. I hope you can answer a few of mine as well - and add them to your list of feedback to be addressed:

1) In your first thread you said, 'this "cycle tool" tries to answer a problem that we all have and want to solve in our relationship with the Yijing.' Based on this, my question is, what is the problem you (or we) want to solve in our relationship to the Yi?

For example, is the problem that we're too subjective, and you are instead trying to make our thinking more objective, or math- or binary-based (i.e. so our egos don't enter into our interpretations)? Since this problem is key to what you're doing here, it would be good to know what the problem is (that we're trying to solve).

2) Is this cycle tool something you came up with? I assume so, but it would be great if you can confirm that.

3) I can understand how you derived some of your hexagrams you use in your tool, but I cannot figure out how you arrive at Hexagrams 24, 7, 39, 35, which you describe as:
- hexagram corresponding to the lines --o--= hex24
- hexagram corresponding to the lines --x--= hex7
- hexagram corresponding to the lines -----= hex39
- hexagram corresponding to the lines -- --= hex35

I don't see any connections with the original hexagrams 63 and 48, and I just don't understand how you get to these?

****************

And ... a few observations: you mention that this tool is related to the idea of correlative thinking - or 'a correlated thinking posture'. I have my own ideas of what 'correlative thinking' is, but that's more an educated, intuitive guess on my part; so I did a bit of digging, and here is some of what I found:
The concept or idea of 'correlative thinking' was developed by sinologists and philosophers in the field of Chinese and comparative studies, including Marcel Granet, Joseph Needham, A. C. Graham, David Hall and Roger Ames. There is no common view among these scholars when they use the term “correlative thinking” to describe the Ancient Chinese mode of thinking. But they all recognize, more or less, that it includes being “non‐logical”, “pre‐logical”, “non‐rational”, “irrational”, “intuitive‐associative”? or “beyond analytic thinking”.​

As I understand it, you are describing a type of 'correlative thinking' that is math or numbers-based: e.g. there are five elements, five directions; there are ten things (4 vertices and 6 edges) associated with a Tetrahedron and therefore your tool uses ten hexagrams, and so forth ....

Two points come to mind:

First, using numeric-based 'correlative thinking' (as I understand your description of it), I can see making use of many different numbers: There is 1: one Dao, one universe, so therefore our answer - or our tool for getting to an answer - will have only one hexagram; there is 2: yin/yang, light/dark, etc. and based on this, our answer will be found within only two hexagrams, or maybe the two trigrams that make up the primary hexagram; or ...

.... there is 6: six lines in a hexagram, the six points of an octahedron, six points on the Star of David; the four directions plus above and below, etc.; so our answer will be found in a tool based on '6': that uses the six trigrams that make up the Yi's response: two for the primary hexagram; the two core or nuclear trigrams; and the two trigrams from the resulting hexagram, .... or we might use another "tool based on six": the primary hexagram and it's nuclear (2), it's pair (1 more), the shadow and ideal (as described by Karcher) hexagrams (2 more), and the resulting hexagram (1 more hexagram, adding up to 6).

My point being, that your base-10 tool is but one of many number-based tools that might lead us to - or offer us - 'a correlated thinking posture'.

Second, 'correlative thinking' does not necessarily have to be based on math or binaries, or numbers of any kind. Instead it can be about finding patterns, analogies, similarities, associations; or, seeing what a word, or phrase, or image seems like, or when it reminds us of something. Or it can be about associations and correspondences: where trigram Mountain is associated with late winter, a time to conserve, a time to look back at what has worked (or not) during the past year; it's a mountain gateway and a gatekeeper, who decides what from the past should be brought over (or into) the new year (associated with Thunder), and so forth.

As related to the Yi, one definition of 'correlative thinking' I found is that it means to have or be in relationship(s) with, - or to find relationships, connections, correspondences, patterns, imagery .... Based on that, I don't think all 'correlative thinking' is or needs to be math- or binary-based, though it certainly can be.

Regards, D
 
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breakmov

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Hi Dfreed,


from the first topic:
I will be glad to answer your questions after I expose the tool and also with practical examples that can be put by you. :)

I think in terms of images, and it is exceedingly more difficult for me to communicate in words. Please understand this. :) When I finish topic 3 I will be happy to answer you.

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dfreed

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When I finish topic 3 I will be happy to answer you.

I think in terms of images ....
That's what I was hoping for, and I can wait.

And to emphasize, my first two questions are very basic: what is the problem we all have that this tool can help with? And is this a tool you came up with? My third question is basic too: how do you arrive at - or come up with - these four hexagrams in particular - it's not at all clear to me.

And yes, I think the Yi also speaks to us via images.

D.
 
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