Blog post: A Hidden Pattern in the Sequence of hexagrams

hilary · Sep 4, 2015

The King Wen Sequence of hexagrams (who knows who really created it or how old it might be?) is a source of endless fascination. People keep on finding patterns in it.
The first to catch my interest was Danny Van den Berghe’s discovery of a ‘landscape’ of trigrams (download the articles ‘King Wen’s Order’ and ‘The I Ching Landscape’ from here). There are 660 pages on Classical Chinese Combinatorics*by Richard Cook.*(I haven’t read that one; my maths isn’t remotely up to it.) Scott Davis has recently elucidated some beautiful patterns that combine text and structure in his The Classic of Changes in cultural context. (Huge, fascinating, and not light*reading.) I’ve been captivated by*sequence patterns*myself – and no doubt there’s a lot more good*work I’ve omitted to mention.
I’ve read claims that*the arrangement of the pairs through the Sequence is random – that if you want regularity and pattern, you need to turn to an alternative arrangement such as Shao Yong’s. This strikes me as bizarre, since the problem’s almost the opposite: there are so many interwoven patterns and connections that it seems impossible to find a single*pattern running through*the whole sequence.
Except… that it isn’t. The King Wen*Sequence makes a single, perfectly simple pattern that you can understand at a glance. You’ll find it in this unassuming little pdf by Gert Gritter,*The Hidden Pattern in the Classical Sequence of the I Ching. In the course of reading it I went from ‘Oh, pretty…’ (on page 7) to ‘Wow‘ (by page 10) – I expect you’ll do the same. How could we have failed to notice this?
…and now, how do we use this in readings?

Liselle · Sep 4, 2015

"Maybe you should not pooh-pooh the Sequence," says Lisa to herself.

"Maybe you should not have been doing that all along."

(I'm one of those who always thought - without any thought at all, mind you - "Harumph. The hexagrams or pairs could be put in any random order*, and stories could be concocted to tie one to the next. Bah humbug.")

As far as what to do with it - probably what you've been doing with it all along, Hilary - first, accept it as purposeful, and then things like, "Your situation/reading grew from here, and might lead there" (if I'm getting that even superficially correct?).

*obviously things like 1 and 2 (and 3) at the beginning and 63-64 at the end make sense

:bag:

diamanda · Sep 4, 2015

This is amazing, thanks so much Hilary!

how do we use this in readings?

I personally wouldn't.
There are countless factors to take into account with any reading.
If I tried to take everything into account every time I'd feel 'drowned'!

My lesson and conclusion after reading that article was:

The I Ching is a masterpiece of wisdom and harmony.
It is so perfectly constructed that it truly fills me with awe with its completeness.

Liselle · Sep 5, 2015

Here is the closed Grid diagram from page 9 of the pdf, with hexagram numbers added:

http://1drv.ms/1IPkVZl

(Please let me know if I've made mistakes.)

rosada · Sep 5, 2015

Especially fascinating how this pattern has been here all along but only now this lady just sort of noticed it. Maybe all sorts of heretofore unrecognized patterns will be seen in the year coming up as Saturn, the planet ruling organization enters into Sagittarius, the sign of wisdom and philosophy. Thanks for posting this.

Liselle · Sep 5, 2015

Question: is the closed Grid suppposed to be the end result of Gritter's analysis? (It seems to be, to me, but I've only read the document once plus a little skimming.)

Asking because if so - if the closed Grid is the new suggested arrangement, rather than the standard checkerboard - it seems to put the hexagrams in a whole new order. Reading top to bottom and left to right, the closed Grid order is: 31, 32, 33, 34, 35, 36, 1, 2, 37, 38, 39, 40, 3, 4, 5, 6, 41, 42, etc.

But that's not the King Wen order, and the whole point of this discovery (I think) is to "prove" the King Wen order, or at least show a very convincing explanation of its validity.

So a question might be, what does it mean (for example) that hexagram 31 is legitimately 31st, but in the closed Grid it comes first? Maybe "end result" isn't the way to think about it? Maybe the open Grid is more the end point?

(Actually - reading through it again - Gritter states on pg. 8, "The new pattern will be referred to as ‘the Grid’," referring to the open Grid. I think I was confused by the fact that the document begins on pg. 1 with the closed diagram - I thought it was leading with its conclusion; maybe not.)

hilary · Sep 5, 2015

diamanda said:
This is amazing, thanks so much Hilary!

How to use it in readings?

Click to expand...

I personally wouldn't.
There are countless factors to take into account with any reading.
If I tried to take everything into account every time I'd feel 'drowned'!

There's definitely wisdom in that. If we looked at every sequentially and structurally connected hexagram to the one we cast, we'd probably be looking at all 64. Sometimes more really is less.

I'm working on the Sequence for Change Circle - that's how I came back to studying this - and will be looking for manageable, non-counterproductive (and thoroughly optional) ways to take these larger structures into account.

lisa said:
Here is the closed Grid diagram from page 9 of the pdf, with hexagram numbers added:

http://1drv.ms/1IPkVZl

(Please let me know if I've made mistakes.)

Hooray, thank you!
(I've been writing it out on bits of paper and making a tremendous mess.)

rosada said:
Especially fascinating how this pattern has been here all along but only now this lady just sort of noticed it. Maybe all sorts of heretofore unrecognized patterns will be seen in the year coming up as Saturn, the planet ruling organization enters into Sagittarius, the sign of wisdom and philosophy. Thanks for posting this.

Gert's a he, not a she. And apart from that, yes, it is extraordinary that - as far as I know - there is no other mention of this in the literature at all.

What else are we not seeing??

lisa said:
Question: is the closed Grid suppposed to be the end result of Gritter's analysis? (It seems to be, to me, but I've only read the document once plus a little skimming.)

Asking because if so - if the closed Grid is the new suggested arrangement, rather than the standard checkerboard - it seems to put the hexagrams in a whole new order. Reading top to bottom and left to right, the closed Grid order is: 31, 32, 33, 34, 35, 36, 1, 2, 37, 38, 39, 40, 3, 4, 5, 6, 41, 42, etc.

But that's not the King Wen order, and the whole point of this discovery (I think) is to "prove" the King Wen order, or at least show a very convincing explanation of its validity.

So a question might be, what does it mean (for example) that hexagram 31 is legitimately 31st, but in the closed Grid it comes first? Maybe "end result" isn't the way to think about it? Maybe the open Grid is more the end point?

(Actually - reading through it again - Gritter states on pg. 8, "The new pattern will be referred to as ‘the Grid’," referring to the open Grid. I think I was confused by the fact that the document begins on pg. 1 with the closed diagram - I thought it was leading with its conclusion; maybe not.)

I don't think there is any 'end point' or 'end result' apart from Diamanda's. In fact, it all combines to suggest that thinking of the Sequence as a sequence - with start point and end point - is not necessarily the best way. He's finding symmetry and complementarity, so it's a bit like asking for the beginning and end of a roundabout, or of an object between two mirrors.

I did spend time looking at the closed grid to see if the hexagrams brought into proximity seemed to belong together in any way - themes or text or structure. Is there in any sense a 'gap' between 6 and 7 that's naturally filled by 41-42, for instance? Nothing obvious leaps to the eye so far.

Oh, except that you could say that the gap in experience between 46 and 47, which is considerable, is naturally bridged by 11-12, with emphasis on 12. Maybe I need to pay more attention*.

(*Possible title for autobiography of life with Yi.)

hilary · Sep 5, 2015

P.S. Lisa, is there a way to download that spreadsheet? I can't find one.

pocossin · Sep 5, 2015

lisa said:
Or (having nothing to do with spreadsheets in OneDrive) - could the original pdf be made editable, and the hexagram numbers typed directly on top of the colored blocks? Don't know if that's possible - and maybe it would be too small & wouldn't look nice? - and maybe you wouldn't want that anyway - ?

LiSe's version is clearer.

http://www.yijing.nl/structures/Gritter.html

Liselle · Sep 5, 2015

pocossin said:
LiSe's version is clearer.

Not sure how it's clearer...it's all there, certainly, but it's small, blurry, and not downloadable, which was Hilary's question. Am I missing something?

pocossin · Sep 5, 2015

diamanda said:
My lesson and conclusion after reading that article was:

The I Ching is a masterpiece of wisdom and harmony.
It is so perfectly constructed that it truly fills me with awe with its completeness.

Look closer.

pocossin · Sep 5, 2015

lisa said:
Not sure how it's clearer...it's all there, certainly, but it's small, blurry, and not downloadable, which was Hilary's question.

It is clearer to me because both hexagrams and their KWS numbers are there. It is blurry -- artistically blurry -- in places, but those of us who know the hexagrams, not the appended texts, are not inconvenienced. I mean, Do you want impressionism or the harsh glare of realism? Where is the artist in you?

Am I missing something?

Yes.

Liselle · Sep 5, 2015

Hilary - some downloading options (this may not be absolutely exhaustive - the internet is full of options):

The full working Excel spreadsheet as an .xlsx file. Do you have a recent version of Microsoft Excel (2007 or above, I think)? It will work there, and probably in some free knock-offs (LibreOffice, for example). And of course in the Excel web app, if you have a Microsoft account (OneDrive, Office Online, Outlook.com web email..).
PDF - unfortunately, Excel Online (OneDrive) does not have a direct option to save as a pdf. But Google Sheets does, and I could use that instead if you'd like a pdf.
HTML code for embedding. Via OneDrive, this will be an iframe, whatever that is. There are options for letting viewers sort, filter, and type into cells (which may not be useful for this). It comes out rather small and with scrollbars, but the height and width may be adjustable before you'd embed it.
JavaScript code for embedding (using a <div>, whatever that is).
A jpg screen clip. (This will be readable, but blurry.)
Open Document Format, whatever that is.
Google Docs also has an option to download as a zipped webpage (they say - have never tried it).

Liselle · Sep 5, 2015

pocossin said:
It is clearer to me because both hexagrams and their KWS numbers are there.

Yes, you're right, in that particular Gritter diagram. But that isn't the one we're talking about - we want the hexagram numbers on some of the folded or closed diagrams, like here:

http://1drv.ms/1IPkVZl

(Unfortunately, I buried this thread in a vast flurry of posts*, which makes it hard to unearth the point of anything

- sorry, Pocossin.)

*since deleted, after the downloading question was resolved

hilary · Sep 5, 2015

pocossin said:
LiSe's version is clearer.

http://www.yijing.nl/structures/Gritter.html

That's an earlier version - Gert said he'd prefer to have this newer version distributed, with the neater graphics. (I think it's a bit of a shame he's cut out the part about the Hetu diagram - it's not a perfect match, but there are enough points of correlation to be interesting.)

lisa said:
Hilary - some downloading options (this may not be absolutely exhaustive - the internet is full of options):

The full working Excel spreadsheet as an .xlsx file. Do you have a recent version of Microsoft Excel (2007 or above, I think)? It will work there, and probably in some free knock-offs (LibreOffice, for example). And of course in the Excel web app, if you have a Microsoft account (OneDrive, Office Online, Outlook.com web email..).

PDF - unfortunately, Excel Online (OneDrive) does not have a direct option to save as a pdf. But Google Sheets does, and I could use that instead if you'd like a pdf.

HTML code for embedding. Via OneDrive, this will be an iframe, whatever that is. There are options for letting viewers sort, filter, and type into cells (which may not be useful for this). It comes out rather small and with scrollbars, but the height and width may be adjustable before you'd embed it.

JavaScript code for embedding (using a <div>, whatever that is).

A jpg screen clip. (This will be readable, but blurry.)

Open Document Format, whatever that is.

Google Docs also has an option to download as a zipped webpage (they say - have never tried it).

Someone find me a smilie with a dunce's hat, please. I just clicked 'edit in browser' and found the 'save as' menu. All's well.

:duh:

:bag:

pocossin · Sep 6, 2015

This complementarity has a direct reference to the concepts of yin and yang, having a
prominent position in the Yijing. The Lower Canon (red, 17 hexagram pairs) is yang, the
Upper Canon (blue, 15 hexagram pairs) is yin.

This is the opposite of how I have always understood it.

pocossin · Sep 6, 2015

Gert has unconsciously arranged the hexagrams in the pattern of the kabbalistic Tree of Life with its left, right and middle pillars.

hilary · Sep 9, 2015

pocossin said:
This is the opposite of how I have always understood it.

Yes... it's a surprise, you'd think Canon #1 would be yang and #2 yin. But it's hard to argue with those groupings of 6, 8, 9 and 7 hexagrams.

pocossin · Sep 10, 2015

hilary said:
Yes... it's a surprise, you'd think Canon #1 would be yang and #2 yin. But it's hard to argue with those groupings of 6, 8, 9 and 7 hexagrams.

Not too hard for me

The leftover group is

29-30
31-32

It is left over on the assumption that the upper canon is yin (8 + 6 = 14) and the lower canon is yang (9 + 7 = 16). Split the leftover group, and the idea that line numbers can be summed to describe the canons works. I do not find this reasoning persuasive. With enough flexibility, anything can be harmonized. Still, it's ingenious.

pocossin · Sep 10, 2015

Having applied line numbers vertically, Gert then proceeds to apply line numbers horizontally (p.10). I think this is as reasonable as the vertical division, and congratulate Gert on consistency. After all, the number of blocks (hexagram pairs) is the same whether one counts them from top to bottom or from left to right. By this account, the upper left quadrant of the Grid is yin-yin, but how does this affect the blocks that occur in that area? That is, Is there some way to go from the Grid to the meaning of a hexagram?

pocossin · Sep 11, 2015

Below is an image of the closed Grid in which the yang blocks are white and the yin blocks
black (p.12).

How does Gert determine this? How can there be yang blocks in a yin canon?

pocossin · Sep 11, 2015

conclusion

At page 12, I no longer understand what Gert is doing. Perhaps the more understanding can enlighten me. Gert's initial observation that between any two consecutive blocks in the central column, there are either 0, 4, or 8 blocks is a valuable discovery. Gert's central column is composed of the 4 trigram-doubled pairs and the 4 trigram-opposite pairs. The importance of trigram-opposite pairs in that they occur at both the beginning and end of the second canon is a valuable observation. I had not noticed it.

Disclaimer: I have my own reconstruction, made decades ago, of the pattern underlying the King Wing Sequence, and so I am one of the few who has a standard based on ancient Chinese artifacts for criticizing the efforts of others.

Liselle · Sep 11, 2015

pocossin said:
Disclaimer: I have my own reconstruction, made decades ago, of the pattern underlying the King Wing Sequence, and so I am one of the few who has a standard based on ancient Chinese artifacts for criticizing the efforts of others.

Is that available anywhere?

(Am completely bewildered by all of this

uch:, so I'll just ask that really obvious question

.)

pocossin · Sep 11, 2015

lisa said:
Is that available anywhere?

(Am completely bewildered by all of this uch:, so I'll just ask that really obvious question .)

Yes, Lisa, for one with your computer competence, everything is available, including my medical record and x-rays. I had this information on the internet for ten years or longer, and when its server was infected with a virus, I deleted it. I have no interest in making it more accessible again because I remember how I was treated in the past. Some of this information is available in the Clarity Jewel Box, or whatever it is called. Basically, if you do not recognize the primacy of visual features of the hexagrams to King Wen and his son, the Duke of Zhou, all of this is as frivolous as a bit of glass. Really, I would like this thread to be devoted solely to Gert's contributions.

svenrus · Sep 18, 2015

... just one detail, not serious: On page 10 in THIS pdf-file about the symmetry he marked one wrong pair blue, namely the second lower pair which should had been white while the third lower center-pair instead had been blue to make the mirror-image. But: just a detail that surely wasn't intended....

svenrus · Sep 18, 2015

A remarkable point I found was that the eight dubble-lined trigrams * ie. hex. 1-2, 19-20, 33-34 and 61-62 is to be found, one pair in each category namely hex. 1-2 in the row of Old yin (6). hex. 19-20 in the row of Young yin (8). hex. 33-34 in the row of Old yang (9) and finally hex. 61-62 in the row of Young yang (7). See p. 11 HERE where You'll find those dubble-lined trigram-pairs situated each in the green, the blue, the yellow and the red section.

* What to call those eight "dubble-lined-trigrams" I don't know but to example take the trigram for Fire: stroke-broken stroke-stroke and dubble each line: stroke-stroke /broken stroke-broken stroke/stroke-stroke Youll get hex. 61..... and so on

svenrus · Sep 18, 2015

What about the tidal guas (the twelve Waxing and Waning hexagrams ILLUSTRATION) ? They are not to be found divided equally in those four sections (as mentioned in #26, this thread). You will find hex. 1-2-11-12 in the green section (see #26 page 11 link), hex. 19-20-23-24 in the blue section, and hex. 33-34-43-44 in the yellow section but none in the red section... Could have been fitting if those tidal guas had been found equally divided - three in each section.

pocossin · Sep 18, 2015

svenrus said:
What about the tidal guas (the twelve Waxing and Waning hexagrams ILLUSTRATION) ? They are not to be found divided equally in those four sections (as mentioned in #26, this thread). You will find hex. 1-2-11-12 in the green section (see #26 page 11 link), hex. 19-20-23-24 in the blue section, and hex. 33-34-43-44 in the yellow section but none in the red section... Could have been fitting if those tidal guas had been found equally divided - three in each section.

This is a good point. All the tidal gua except 33-34 and 43-44 occur in the first canon, and 33-34 and 43-44 occur together at the top of your diagram.

pocossin · Sep 18, 2015

svenrus said:
... just one detail, not serious: On page 10 in THIS pdf-file about the symmetry he marked one wrong pair blue, namely the second lower pair which should had been white while the third lower center-pair instead had been blue to make the mirror-image. But: just a detail that surely wasn't intended....

Hilary's version is dated 2015.
http://www.onlineclarity.co.uk/Gritter Hidden Pattern.pdf

LiSe's version is dated 2014.
http://www.yijing.nl/structures/grit/Gritter THE HIDDEN PATTERN.pdf

hilary · Sep 19, 2015

pocossin said:
How does Gert determine this? How can there be yang blocks in a yin canon?

By this stage he is showing both canons in one diagram. He has, as it were, taken his grid and folded it in half, mapping one canon onto the other. The blocks from the Upper Canon fit perfectly into the spaces in the Lower Canon.

lisa said:
Is that available anywhere?

(Am completely bewildered by all of this uch:, so I'll just ask that really obvious question .)

Lisa - Tom's work is available from this thread in the Change Circle archives (which has replaced the Jewelbox).

Tom - if you would rather this were removed, obviously please just ask and I'll do so at once.

svenrus said:
A remarkable point I found was that the eight dubble-lined trigrams * ie. hex. 1-2, 19-20, 33-34 and 61-62 is to be found, one pair in each category namely hex. 1-2 in the row of Old yin (6). hex. 19-20 in the row of Young yin (8). hex. 33-34 in the row of Old yang (9) and finally hex. 61-62 in the row of Young yang (7). See p. 11 HERE where You'll find those dubble-lined trigram-pairs situated each in the green, the blue, the yellow and the red section.

* What to call those eight "dubble-lined-trigrams" I don't know but to example take the trigram for Fire: stroke-broken stroke-stroke and dubble each line: stroke-stroke /broken stroke-broken stroke/stroke-stroke Youll get hex. 61..... and so on

That's very neat - I hadn't noticed that distribution. I wonder if Gert has?

As for what to call them: I learned from Brad Hatcher to call them da bagua - big trigrams. I think they're clearly part of the pattern-making that goes on with trigrams through the sequence. 19-20, for instance, immediately precede a series of 7 hexagrams with mountain or thunder.

Blog post: A Hidden Pattern in the Sequence of hexagrams

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