Binary count of the I Ching

[imagenerator]

Nowhere but here have I seen the binary valuation of the hexagrams made such that the topmost line is of the highest value (and thus changes the least when counting up or down) and the bottom line is of the least value so that it always changes when counting either up or down the binary scale. I made hint of this technicality in this other thread http://forums.abrahadabra.com/showthread.php?t=830, where I laid out a valuation of the trigrams to the hands which runs contrary to the binary interpretation of the hexagrams/bigrams/trigrams on this site. The status quo on the binary count of the I Ching seems to be opposite the "ABRAHADABRA count"; some examples are sources like wikipedia http://en.wikipedia.org/wiki/I_Ching and http://www.yijing.co.uk/. Have you folks any references of materials running with or contrary to the "ABRAHADABRA count" ?

Intuitively it makes sense to me that Heaven is less volatile than Earth and so it should change less when counting, but I think if the ABRAHADABRA system is to effectively challenge the status quo on the binary count, it will need to lay out a well grounded proof for this. How do you folks relate to the issue of the I Ching binary count? Since m1thr0s seems to be up to his apex in truths to prove already, maybe this is something we can all contribute to.

[m1thr0s]

I work with variations all the time imagenerator, so your question isn't making sense to me. You need to be a little clearer what context you are dealing in so people have some chance of following your logic I think. Are you talking about the arrangement of the bigrams as they would appear in the Lo Shu Square? Traditionally Heaven has always been said to "change the least" so it's hard to figure out what you are driving at here. I follow a standard inverse to the Liebniz standard of yin=0, yang =1 primarily because it is important to me that my numbers unfold as they would in the Tree itself which means that the Heaven bigram has a count of 00 while Earth has a count of 11...exactly opposite of what you have said. My binary count follows the same chronology as is found in the Tai Hsuan Ching where yang=0, jen=1 and yin=2. If you extrapolate the binaries from that system and number them so they fall out in the same order, you'll get yang=0, yin=1 (numerated from top to bottom as a rule) as I have said. Again, it is important to me in this system that the binary and ternary systems are always in sync and also important that the "0" numeration comes before the 1 or the 2 in chronological progression. It has to be remembered that Liebniz was neither a qabbalist nor a tantricist...he wasn't actually trying to "do" anything with his count so it didn't matter to him if it happened to fall out ass-backwards from the structures themselves (which it does).

Anyway...some additional explanation as to what you are looking for would help here. In general my attitude with numerations is that you should experiment with all available possibilities. I have simply settled upon what works the best for me in general, as also what seems to me to be the best coordination between traditional systems. You have to bear in mind that there is no iron-clad rule saying that yangs = 1 and yins = 0. That is an arbitrary assignment probably stemming from the fact that 0 is being treated as an "even". You can certainly go with that logic if it suits you but in my case there are a number of technical reasons it doesn't pan out as well as the reverse. In point of fact, traditional Chinese I Ching practitioners never used these numerations at all, so we are pretty much free to do whatever seems to suit us in that respect.

In my case, greater-or-lesser numerical values is not much of an issue. I am more concerned with before-and-after, or first-to-last kinds of chronologies. Hexagrams generally have more to do with time relationships than matter. We can draw parallels with matter, but the changes themselves are really more of a time-related clockwork, plotting motion "through time"...

m1thr0s

[imagenerator]

Apologies making false claims about your work m1thr0s. I see that my thoughts on this are muddled. The issue I was looking to clarify is how the levels of the bigrams/trigrams/hexagrams correspond to the binary number positions. I see now that the ABRAHADABRA arrangement as laid out here http://www.abrahadabra.com/eightkua001.htm runs contrary to the Wikipedia definition in two ways: the valuation of digit (1 or 0) to lines (broken or unbroken) AND the valuation of level to the numerical column of a binary number (i.e. in 100 the 1 is in the 8's column).

[m1thr0s]

yes, that's quite correct and there are some very important reasons for this as well. I have attempted in all of my introduction articles to prepare people for that but the whole site is a bit of a mess right now so it may have been missed.

I love Wiki in many ways but it also has its shortcomings. One of the problems with open-source publishing of articles (especially on more obscure subjects) is that we never get to know who is actually writing these articles. Since we can't know who is writing them, we also can't be sure what their motivations might be, nor their background, nor their bias...none of the things we might normally want to take a look at when trying to assess if an author might be someone whose presentations can be trusted or are otherwise worth considering.

The trigram chart you have referred us to in this case is incomplete in that it is not giving us the whole story and is also inserting a few things that are rather weird for a presentation of its kind. What we have here in this chart is a complete mish-mash of conflicting influences masquerading as a generic standard and it fails either as a theoretical or a traditional presentation because the author (apparently) doesn't know which is which.

This isn't your fault and I am not taking you to task for it...it just is what it is. If you look on the far right of that table you will see something that would set any I Ching scholars teeth on edge. These Elemental attributions that have been assigned to the eight Kua originate with Aleister Crowley and have nothing to do with traditional Chinese thinking at all. As a matter of fact, the "elemental" assignments of the Chinese Sages can be found in the column labeled "Nature" although I have never seen "swamp" applied to Tui...this would ordinarily be called The Lake.

Crowley can get away with assigning an entirely unknown system of elements to the eight Kua because he's crazy...basically..and everybody who studies the man had better know that going in. Crazy or not, he's a brilliant syncretist and has this uncanny habit of hitting the nail on the head as regarding futuristic applications of ancient metaphysical constructs. But the Chinese themselves would have absolutely no idea what that column was about or why it was there at all and we all need to be aware of that.

The "Names" column is also completely off the mark but I am going to skip the blow-by-blow critique of the entire chart and just let you know that it should not be regarded as conclusive or authentic in any way shape or form. What is occuring on the far left is what we are really talking about in the immediate...the column he has labeled "Trigram Figure". This arrangement of trigrams belongs to what is typically called the "Inner World", or "Early Heaven", sequence most often, normally assigned to Fu Hsi historically and distinguished by virtue of being mathematically chronological.

That is was mathematically chronological was always understood by the Chinese long before Gottfried Leibniz (http://en.wikipedia.org/wiki/Gottfried_Leibniz) came along and assigned a binary number system to it. There are 2 things that have to be determined in advance before you can do this though. You have to decide what values to give to yin and yang and you also have to decide which way your counts will run, because you will get completely different results counting from the top-down than you will counting from the bottom-up. Leibniz decided the way to assign numbers was to give Yins a standing value of 0 and Yangs a standing value of 1. He then went to the Early Heaven arrangement itself and examined the count possibilities both ascending and descending and discovered immediately that by assigning these values and counting from bottom-to-top you get an exactly chronological numerical sequence! The only trouble was...the numbers ran exactly backwards from the Hexagrams so that the first hexagram out carries a numerical value of 63 (translated back into base 10) whereas the last one out carries a value of 0, making it the first one out in the numbers.

Nevertheless...he was elated with his discovery and rushed right out and published his findings and everybody kissed his genius butt and told him how smart he was and all that crapola. And he was a genius...there's no doubt about it...he invented calculus for Xst sake and other things as well but he left a very important puzzle hanging in limbo with respect to the I Ching itself and never did bother to try to resolve that puzzle.

Now it happens that there are at least four ways of attaining chronological sequences in binary line structues such as the trigrams, hexagrams etc. What I am telling you is that it would ultimately be to your best advantage to play around with all four and decide for yourself which one best suits your needs. I can guarantee you the Chinese themselves really don't give a crap because they have no traditional use for any of binary number stuff anyway. From their perspective, it isn't necessary...any moron can tell just by looking at the lines when an arrangement is chronological or not!

But here in the West we do not believe our eyes unless they report back to us in numbers, and there are certain strengths in this alongside certain subtle limitations. We look to numbers as the final validation of just about anything of a "logical" nature. The Chinese Sages venerated numbers as well but had a slightly more flexible approach to their aesthetics.

m1thr0s

[imagenerator]

I will give your suggestion to "play around" with the configurations due consideration. Particularly, I'm curious to know how each configuration traces out in the Inner and Outer Heaven arrangements and also the symbolic progression in each count.

[Anibis]

Well, work it out, dude. Don't 'give it due consideration'. Sit down, map it out and ask yourself what it would achieve. Then come up with an interpretation of what it means, and share with us, if you will, that interpretation. I'd like to hear you give us a notion of what it is you think all this is about, what it does. Just how do you understand these operations? I have seen you play with lots of weapons, but I have not really heard you account for why you would be interested in them, or what your philosophy of their use actually is.
-Ibisis