64 black+white beads contain all 64 hexagrams

morphyijing · Dec 27, 2007

To all,

I have in my possession a loop (necklace?) of 64 apparently randomly arranged black and white beads.
Supposedly they were brought back from China by a great-uncle.
Supposedly they are able to tell the future when you pick any group of six beads at a time anywhere around the loop :brickwall:

.
As you move around the loop, advancing the group 1 bead at a time, each new group of 6 beads shows a different hexagram using a combination of black and white beads.
The order of the hexagrams is like nothing I've seen before. At one point along the loop, 6 black beads, then 6 white beads are arranged adjacent to each other, but otherwise there is no recognizable (to me) pattern as you move around the loop.
Each hexagram is represented once and only once, all 64 hexagrams are represented, there are a total of 32 black beads and 32 white beads = 64 beads!

Has anyone heard of such a thing?

Sparhawk · Dec 27, 2007

Hi there,

Can you post a picture of the necklace?

bradford · Dec 28, 2007

I'd like to see that photo too, please?

martin · Dec 28, 2007

Would like to see it too.
It surprises me that it is at all possible to get all 64 hexagrams in this way. And if it's possible the next question would be: in how many ways can it be done?
Interesting mathematical puzzle. But I'm too sleepy for that now, tomorrow perhaps, if I'm not too lazy ..

rosada · Dec 28, 2007

If you're not able to post a picture could you just type out the order of the beads?
Like BWBWBBWW etc.?

charly · Dec 28, 2007

ichinguru said:
To all,

I have in my possession a loop (necklace?) of 64 apparently randomly arranged black and white beads. ... Each hexagram is represented once and only once, all 64 hexagrams are represented, there are a total of 32 black beads and 32 white beads = 64 beads!

Hy Guru:

You are describing an «I Ching Wheel», «Fortune Wheel» or «Magick Wheel», generally made with two disks one of them carved with entire or breaken lines, also like a fair fortune wheel. The yours is like a rosary, the principle is the same.

The order of the lines is of great importance, corresponds to a mathematical problem that was solved, if I remember well, by Tartaglia but I don get the precise treatment for to documentate.

I think that the problem has many solutions, I long ago get a solution by tryal and error, but there are mathematical solutions not only for binary number but for higher order too.

I find a sample I believe correct, I post it.

Yours,

Charly

morphyijing · Dec 29, 2007

Thanks Charly!!!

To all,

The bead sequence I have is very similar to the wonderfully done diagram you (Charly) provided, though parts of the sequence are different, and parts of the sequence in my set are missing.

The beads I have are held together by (silk?) thread of uncertain age. The thread has disintegrated in certain areas, causing many beads to fall off and roll around separately in the container where they were stored.

This is exciting to me because it seems that there might be a few sequences like this, just as (who?) suggested in an earlier post. How many could there be?

Charly, my question to you is what caused you to begin doing work like this, and have you let people know about this before, or has it been R/D you have been doing in private?

Considering the ancient history of the yijing, why are there no easy to find references to this type of thing in archives of antiques, art, etc? It's so cool!

Allan

rosada · Dec 30, 2007

Charly and Allan,
Wonderful! Thank you so much!
Rosada

charly · Jan 2, 2008

ichinguru said:
... Charly, my question to you is what caused you to begin doing work like this, and have you let people know about this before, or has it been R/D you have been doing in private? Considering the ancient history of the yijing, why are there no easy to find references to this type of thing in archives of antiques, art, etc? ...

Allan:
Years ago I was interested in the sequence problem, I reminded my studies in the economics school but I only get an empirical solution. I believe that ancient (included chinese) mathematicians had yet solved the problem. I had read about disk tools for divination applied in Han time, maybe Needham had something about it.

I post you some binary wheels from a mathematical document:

$bwheel.gif$

From: http://www.geocities.com/abcmcfarren/math/bwheel.htm

As you can see the outer circle from the left is the I Ching Wheel or hexagrams wheel, the inner circle is de Ba Gua Wheel, the eight trigrams wheel. Chinese mathematicians used whithe beads to represent odd(yang) numbers and black to represent even (yin) numbers, thus, we can take white beads for entire lines and black beads for broken lines.

Maybe also gambling wheels or roulettes had mantic origins. Maybwe Sparhawk could have some prints of binary wheels in the chinese books he owned.

Yours,

Charly

Sparhawk · Jan 4, 2008

Here some circular arrangement to browse

There are more pictures here

charly · Jan 11, 2008

sparhawk said:
Here some circular arrangement to browse

There are more pictures here

Luis:

I have looked once more your pictures and hadn't found the binary wheel. I don't remember any source describing it. I wonder if chinese really solved the sequences for bilding an I Ching wheel or necklace. Did chinese work in combinatory mathematics?

What do you know about it?

Had Ichinguru disappeared from the thread?

Un abrazo,

Charly

morphyijing · Jan 22, 2008

Still in the thread & "Divining Table"

Hello all!

I'm definitely still in this thread. Thanks everyone for all the links, backround info and especially opinions, which are for me a very valuable distillation of all your experiences and readings, especially to other language sites.

It does seem that there might be quite a few solutions to this binary arrangement ... maybe they are "lost" arrangements ... maybe some "crop circles" contain these sequences.

Does anyone out there use a special table for consultig the Yijing?
I've been looking at Feng Shui compasses (luo pan) and am thinking of cutting 64 wedges from wood, engraving hexagrams and earliest characters I can find for their names and making the wedges available either separately or bonded together in a circular arrangement matching the binary sequences contributed in this thread, for use as a divining table ...

Any opinions?

~Allan

charly · Jun 28, 2010

Please, see:
http://www.onlineclarity.co.uk/friends/showthread.php?t=10608

Charly

dawglass · Jun 18, 2013

I browsed into the site and ran into this discussion of bead rosaries that produce all 64 hexagrams. I recently was passing thru Beijing airport and saw in a shop (Beijing Gifts) just such a bead set with a manual describing how to use it. It was called Zhou-yi Long-zhu (Dragon Beads for the Changes). There was a bracelet for the 8 trigrams and a necklace for 64 hexagrams, all in BW beads. I think the bracelet was WWWBBBWB. Don't recall necklace except for WWWWWWBBBBBB section.

charly · Jan 13, 2019

The page about Memory Wheels moved here:

http://www.geocities.ws/abcmcfarren/math/bwheel.htm

Ch.

tacrab · Jan 13, 2019

Sparhawk, Thanks for posting Ming dynasty charts! Maybe we should crowd-source interpreting some.

...life can be translucent

64 black+white beads contain all 64 hexagrams

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