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Complementary hexagrams in the sequence

bradford_h

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tatami is the traditional woven floor mat in a Japanese house.
Because the size is fairly standard, room sizes are denoted by the number of mats in a rectangular layout, a fact which might relate your dream to one of the Yijing grids.
Why didn't you Google the word?
 

bradford_h

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oops-
could also refer to more general processes like tesselation or the nesting of sets.
 

yly2pg1

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tesselation?



BTW, Why didn't I Google the word?
Coz I Ching is about connectedness. Aren't we are connected via 'negative-entropies' in one of a thread here?
 

yly2pg1

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Hi Bradford,

I go through your document G-YiFigs.
It could be your call to solve a riddle here?
 

bradford_h

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Si- tesselaton, with Yijing hypercubes no less!
Sixty four mat, big room.
Sorry - must ignore this call. You be puzzlemaster.
Am up to eyeballs researching next book.
 
S

simple_complexities

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A pattern can be found if you use a 384 degree circle, rather than a 360 degree. Impossible you might say, its not. You just have to think a little differently, without rules. There are 384 aspects in the I Ching, and it puzzled me for so long, how this number could be significantly incorporated into a time cycle. A spiral galaxy was the image that inspired me, and it fitted perfectly with the data I had - strange that the shape of a galaxy or pine cone can be so similar in essence, but not strange at all.

What you call entropy, I call harmony.
What you call the disorder of a system, I call the natural order.
What you call a time cycle, I call the expression of mystery, it is not chaotic, neither is it unchaotic.
To try and divine events according to a model of time only gets you so far, then amazingly, one thing becomes overwhelmingly apparent - look within and without shall become clear.

Divination is the practice of triggering intuition using an outside model, coins, yarrow.
Intuition is the practice of letting go of the outside, knowing it is the reflection of the innner.
The I Ching/YiJing/Tao Ching, are all gently whispering the same message - look to the inner, not the outer. The whole system is like the web of a spider, but what makes the web of a spider useful? The space around it.

We cannot plan for future events, in doing so you exert a force on the space around you.
We can prepare for future events events, simply by letting go and living in the moment, then "time" has a dynamic that is beyond dynamics.

The oracle was not meant for acquiring knowledge through the use of "structures", it is meant as letting go of knowledge in favour of "non-structure". Then the true pattern will birth.
 

yly2pg1

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384 degree?

The diagram is already in 384-scale, rather than 360-scale.

But it is not complete.
Any explicit ideas to input?
 

yly2pg1

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I notice that I have reversed the arrangement of 'entropy value' with respect to the Fu Hsi Circle Dynamic. It should look like this:

 

yly2pg1

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Map the binary_tree into the Chart to validate the entropy-value of the chart!

IOW, this chart is valid only for the Recursion of a Dichotomy due to the indeterminate value of '1-2' Pair in Shannon_Entropy. In the context of a Binary_Tree, this 'indeterminate' is 'filtered'.

Any comments?
 

freemanc

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That's the most astonishing gosh-damn thing I ever saw. I think ya got you a capital-A Achievement on your hands, Yly.

Yly, Can you tell me about the ancient circle diagram? What's its name, source, etc? Can you help me find a really good big graphic file of it?

I'm like Bradford, I just don't feel up to geeking out very hard on this right at this point, but I'd like to get set up to do so when I feel like it.

On the other side of Yly's mystery, does anyone have anything semi-solid on the history of the tai chi symbol?

FC
 

yly2pg1

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Freemanc,

Achievement on my hand?
If there is really any, it should belongs to this forum - 'Onlineclarity'. I learn a lot from this forum.

Ancient Circle (name, source)?
Honestly, i do not know much.
My sense of history is slightly 'distorted'.


I would like to x'plore a new thread "Symmetricity and Order in I Ching" and some of the diagram of King Wen's Order (by Van Den Bergh) will be used as reference.
 

freemanc

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Well, that's *apparently* two different inquiries, because they're two different sequences.

One, the matter of the ancient circle and the entropy formula and the alarmingly perfect tai chi symbol that the entropy formula+ancient circle yields.

My guess is that there's actually an underlying characteristic of order that's causing this, like my idea of "greyness", that can be described terms that a brilliant premodern shaman might have come up with.

Two, the King Wen order's neighborhoods and the operations linking pairs or webs of hexagrams.

I'm thinking about Steve Marshalls website's stuff about sequences. I think that there are "finding sequences" in all these.

I'm thinking of the simple and obvious case of the Mawangdui order. You memorize a certain order of the trigram, and then you look up the top trigram and then the bottom.

I hypothesize that there's a finding order rule in the King Wen order, but it's tricky and involves memorizing five or ten rules, like learning subtraction on an abacus. (Which I did when I was in college! Only subtraction; I could do my checkbook.
)

Harmen Mesker is a real Sinologist (as opposed to me; I'm a monoglot lit crit guy who likes puzzles) and has written a paper on the eight houses sequence. I'm going to read it really well sooner or later. It's on Marshall's web site. I hypothesize that Eight Houses is, *among other things* a finding order also. You learn a series of operations that involve turning one bar at a time.

Here is Steve Marshall's sequence page that discusses various sequences and has a link to Harmen's paper.

best,
FC
 

lightofdarkness

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Deriving sequences:

(1) Recursion of yin/yang leads inevitably to the binary sequence. This sequence can represent (a) symmetric dichotomies (guassian distributions) and (b) asymmetric dichotomies (spectrums, power law stuff - and so such dichotomies as far-from-equilibrium/equilibrium - aka negentropy/entropy).

(2) ROTATE the hexagrams in the binary sequence and you get the 'changing line' sequence 'up' hexagrams 01/02 (depending on which end you start - this is in the form of a sequence of 64 hexagrams mapping to the set of 2^6 states in each hexagram's line patterns))

(3) given (2) we can work in reverse. For ANY hexagram derive its changing line sequence of 64 hexagrams and then rotate that sequence to give the derived 'natural' sequence for that or some other hexagram.

(4) from (3) comes a world focused on a logic of relationships (A is to B as X is to Y etc)

See summary on logic of relationships in:

http://www.iimetro.com.au/~lofting/myweb/icstruct.html

see lots of sequences in:

http://www.iimetro.com.au/~lofting/myweb/icmatrix.html

Then note that each of these hexagrams in the binary sequence express all of the others. And so we move into the XOR dynamic of extracting the '27-ness' etc of each hexagram. (also covered in the icstruct.html pages)

Working with the binary sequence is a rich source of discovery re meaning generation and how it is all linked together and the IC metaphor is a reflection of what is in between our ears ;-)

Chris.
 

jte

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Yly -

Can you give some commentary to explain your diagram above. It's been a *long* time since I've tried analyzing anything geometrical such as a sine wave or algebraic expression.

I understand that you've put 384 degrees to the circle instead of the standard 360, what else did you do to map the lines and why is this of significance?

Thanks much!

- Jeff
 

yly2pg1

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Freemanc,
Thanks for the link.
There are 'orders' in the sequence but need to match with the right theorems. Same applies to the Eight House. Good luck!


Jte,

What else to map?
Anything that could be categorized/grouped under the Recursion of Dichotomy (or Recursion of ying/yang) - the binary sequence/order.

Significance?
I am still looking into it, the 'tatami' puzzle etc. Off hand, the chart may be a good indicator of 'time arrow'. Exactly how to use it, is still under investigation. You got any ideas?
 

jte

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Yly -

Actually, I was hoping you would explain what your diagram is showing - I don't quite understand what it shows/how you constructed it.

If I understood what the diagram is showing better, I might have some ideas how to use it (although I don't want to make any promises :) ).

- Jeff
 

yly2pg1

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Jeff,

How to construct?

(1) Use Excel spreadsheet
(2) Key in the data (1~64) using the method i posted above i.e 2^0, 2^1 ... 2^5, and calculate the n value.
(3) Then use Shannon's Entropy. You will notice that you need to convert n to p and q of simplified Shannon's Entropy formula.
(4) In Excel, you will get a table of entropy value for 1~64. (For Hex 1 and 2, equate them to zero)
(5) Construct using Chart type - 'Radar'

(6) You can rearrange the entropy value in ascending sequence. That gives you a graph "Hexagram Pairs vs Entropy Value" in spiral form

(7) From this graph, you can further expand the graph (in 64-scale) using the method of 'binary-tree mapping' as explained above (also confirmed by Chris -(2)). Notice that it is like a 'mirror effect'.

(8) With that you get a graph of 'Tai Chi Profile'.
 

jte

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Um. You lost me at step 2. What is step 2 "doing" - IOW, what is the data? What is the signficance of the method (what is the method showing us by taking 2 and squaring, cubing, etc up to the 5th power? How does that relate in anyway to a Hexagram?)? What does the n value mean?

Similar questions for 3 and 4 above, too.

If someone who's good at explaining math verbally (not the easiest thing in the world to do, I know) would like to step in, that is fine...

Thanks,

- Jeff
 

yly2pg1

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The basic idea is to convert the binary number to decimal number.

e.g. 100001<font size="-2">2</font>=2<sup>5</sup>+2<sup>0</sup>=33<font size="-2">10</font>
 

yly2pg1

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In simpler way:
If a system can be 'mapped/grouped' according to the binary order, and you are able to identify the binary level for each and every component of the system to the binary system (e.g. brain dynamics in IDM), then we are at a good position to 'see' its implication, with respect to this Entropy Graph/Profile.
 

yly2pg1

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Probably, the ancient people do know something about logarithmic calculation and the Shannon's Entropy?
 

freemanc

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Information Entropy, no.

Logarithms, yes, or anyway the idea of weighting the different yao "numbers" differently and adding 'em up, yes absolutely.

OOOOhhhhhhh... gosh damn! Cursory web search shows that place value number system came from guess where and co-occured wih the origin of guess what.

http://aleph0.clarku.edu/~djoyce/mathhist/china.html

So get rid of my inverted commas around "numbers."

Good stuff, Yly!

Hypothesis: Divination = Origin of place value numbers.

And the Tai Chi symbol literally a logarithmic spiral.

FC
 

lightofdarkness

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you need to go deeper - all this here is expression not what is trying to be expressed - LOCAL expressions will be selective and so hide the full spectrum of what is being delt with - the universals.

In the TWO forms of dichotomy coming out of the neurology we have:

symmetric - from where guassian distributions and the sense of 'opposites' comes from. These types of dichotomies show DIFFERENCE from SAMENESS (e.g. individual IQ/EQ from all members of the species)

asymmetric - from where spectrums and so power laws and log scales etc come from. These sorts of dichotomies show SAMENESS ACROSS DIFFERENCES (core common patterns despite different energy expressions)

You can rotate one to get the other if you like. (and so the traditional binary sequence is derived from XOR and so recursion. Rotate it and you get the 'changing' line sequence 'up/down' 01/02 etc etc etc - see patterns in the icmatrix pages)

For background re the IC and Mathematics etc see

http://members.iimetro.com.au/~lofting/myweb/icmaths.html

- IC and Maths are BOTH metaphors for the underlying patterns of meaning derived from the neurology (blend, bond, bound, bind)

the integers were formally derived by Peano from recursion of the empty set (Dedekind brough that to attention of mathematics)

The IC hexagrams reflect derivation from the binomial theorem (A + B)^n and IT is manifest in Pascal's Triangle and IT is a particularisation of the Sierpinski gasket.

The Sierpinski gasket is what emerges in sensory systems where a bounded space lets in 'noise' that will 'bounce' around and in that bouncing a pattern forms in 'meaning space'.

The derivation of integers etc etc from the sierpinski gasket, and the derivation of hexagrams etc from the same form shows isomorphism.

There is a 'translation' table for basic qualities from differentiate/integrate through emotions and into the IC and on into socioeconomic categories at:

http://members.iimetro.com.au/~lofting/myweb/translation.html

if you dig deep enough through the specialist perspectives you will start to hit the underlying universals but that does not mean that the specialists perspectives were precisely aware of those universals, their properties and methods. Specialist work is ad hoc, piecemeal, 'small world network' etc. that aims to reveal universals but only in THEIR language and in that revelation the local context customises perspectives and so 'the whole truth' is not shown.

Chris.
 

martin

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There is no end to going deeper.
Neurology is again only an expression. It reveals something and hides something else.
Our reality is bottomless.
 

lightofdarkness

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there is an end to going deeper - the method used to derive meaning determines all meaning.

Communication of meaning thus has a 'bottom' for us. Anything outside of that will be interpreted from inside and so appear as if paradox - see my page on paradox where the focus is on it coming out of the XOR realm.

http://members.iimetro.com.au/~lofting/myweb/paradox.html

This XOR realm aims to maximise bandwidth to identify something "NOW". If it cannot do that it will present through oscillation all of the aspects it is trying to deal with - IOW it will recruit TIME (past/future) to aid in resolving the 'paradox'. (and so my comments on this dynamic being the 'root' of our drive for argument)

The bandwidth/time dichotomy is a specialist dichotomy reflecting differentiating/integrating and as such an asymmetric dichotomy - a focus on a spectrum, power laws etc... all meanings derivable from differentiating/integrating dynamics are meanings derived from the METHOD where in our species the core method is in the neurology and it then gets relabelled as we specialise, ground universals in local contexts.

Since, using this method we can map the seed of consciousness back to the beginnings of the universe, as well as clearly differentiate basic particle physics dynamics (fermions/bosons) or basic molecular biology dynamics (mRNA/DNA) so the method covers a lot. ANYTHING outside will not be detectable other than as paradox and paradox is derived from a couple of issues (See the above page).

Now, if you need to IMAGINE there is more, if you NEED your reality to be bottomless, that is another matter and not necessarily representing 'what is'.

As a neuron-dependent species, in the communication meaning, it is objects/relationships, differentiating/integrating, yang/yin, all of the way. The richness is in the seemingly infinite ways those patterns can be expressed.

Chris.
 

yly2pg1

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(A) Quote:
<font size="-2">Neurology is again only an expression. It reveals something and hides something else.</font>

I find this statement interesting which may shed some light on the meaning and implication of why the "Tai Chi" curve is right in the "middle" of the "Feng Shui Compass".

The "expressed" part and the "hidden" part are both happens in parallel, giving a kind of "equilibrium".

(B) Quote:
<font size="-2">you need to go deeper - all this here is expression not what is trying to be expressed - LOCAL expressions will be selective and so hide the full spectrum of what is being delt with - the universals.</font>

That explains why the Tai Chi curve is a dynamic mechanism that flesh out the LOCALs (at a level) when the "small world network" at that particular level is achieved!
 

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