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Thread: 64 black+white beads contain all 64 hexagrams

  1. #1

    Default 64 black+white beads contain all 64 hexagrams

    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 .
    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?
    Last edited by ichinguru; December 27th, 2007 at 10:10 PM.

  2. #2
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    Hi there,

    Can you post a picture of the necklace?

  3. #3
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    I'd like to see that photo too, please?

  4. #4
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    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 ..

  5. #5
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    If you're not able to post a picture could you just type out the order of the beads?
    Like BWBWBBWW etc.?

  6. #6
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    Quote Originally Posted by ichinguru View Post
    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

  7. #7

    Default 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

  8. #8
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    Charly and Allan,
    Wonderful! Thank you so much!
    Rosada

  9. #9
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    Quote Originally Posted by ichinguru View Post
    ... 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:

    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

  10. #10
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