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Chinese calculation bug - "xian-tian" method

peter

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Hello all!

Just a few days ago here was a topic on this method: "xian-tian", or Pre-Heaven method is used mostly in Plum Blossom, but may be used with other methods of interpretation as well.

It uses the date of event: year, month, day and hour. In traditional Chinese system one must take Earth branch of the year, Earth branch of the lunar month, day number in this month and also Earth branch of Chinese "hour" (two hours really). Master Jou Tsung-hwa transferred this method on Western calendar in the following way: take the remainder from dividing year number by 12, then take number of current month, current day of the month and current hour (0-23). Let's mark these four numbers as "Y", "M", "D" and "H". Then we sum "Y", "M" and "D", divide by 8 and the remainder will give us the upper trigram. Add here also "H", divide by 8 and receive the lower trigram (remainder also). then the same sum divide by 6 and the remainder will show the only moving line.

EG, for "Y" = 10, "M" = 5, "D" = 28 and "H" = 12 we have:
"Y"+"M"+"D" = 10+5+28 = 43, divide by 8, have 5 and 3 in the remainder, "3" is Li trigram, and it is the upper one;
"Y"+"M"+"D"+"H" = 10+5+28+12 = 55, divide by 8, have 6 and 7 in the remainder, "7" is Gen trigram, so the whole hexagram is "Traveller", #56.

Then the same sum - 55 - divide by 6, have 9 and 1 in the remainder, so moving line is initial, and we have "Traveller" moving to "Clarity" (#56 -> #30).

Now look carefully. We use the same sum for 2 calculations. And 6 and 8 are not mutually simple, their greatest common divider is 2. (Correct me if I use not proper English arithmetical terms.) So - if we have an even final sum, then the lower trigram will be 2, 4, 6 or 8 (Dui, Zhen, Kan or Kun respecitvely), but the moving line may only be 2, 4 or 6, while our sum is even. 4 and 6 belong to the upper trigram (which can be any in the whole set of 8), and 2 - to the lower trigram. Do you see? If we have a moving lower trigram, it may only be 2->4, 4->2, 6->8 and 8->6. Only 4 variants instead of 12 (any one moving line in these 4 trigrams).

I can't believe that this is the way the time works in Yi Jing. On the other hand, I never saw that explanation before, I found it by myself (through some logic). How could people use this method for 10 centuries and not see such a trivial "bug"?!

Maybe somebody still doesn't believe it, then please, pick your notes with hexagrams made using this method and try to find EG lower trigram "Li" with moving 2nd line; or lower trigram "Kun" with moving 3rd line. If you'll find, wouldn't you post it here with all calculations made?

With best regards.
 

peter

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Ouch, must add one more note (but couldn't find where I can edit my latest post). With this method we can't receive all 384 variants (64 hexagrams with any one line moving), but only half of them - 192. For hexagrams with even lower trigrams only 2nd, 4th or top lines can be moving, and with odd trigrams - only 1st, 3rd or 5th.
 

peter

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Ouch, must add one more note (but couldn't find where I can edit my latest post). With this method we can't receive all 384 variants (64 hexagrams with any one line moving), but only half of them - 192. For hexagrams with even lower trigrams only 2nd, 4th or top lines can be moving, and with odd lower trigrams - only 1st, 3rd or 5th.
 

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