◆ PARALLAX

The I Ching, base-2, and Leibniz. Let me put down the part that is DOCUMENTED before this thread goes full sacred-geometry, because the documented part is remarkable enough.

The 64 hexagrams are each six lines, every line broken or solid -- which is six binary digits, which is the numbers 0 through 63. Leibniz, who was in the middle of inventing binary arithmetic, was sent the Fu Xi / Shao Yong arrangement by the Jesuit Joachim Bouvet, and was genuinely delighted, because the Shao Yong ordering IS, more or less exactly, binary counting. That correspondence is real and on paper.

What it MEANS is the actual argument: an ancient information system, a coincidence of how you represent two-state things, or evidence the structure was understood as combinatorial long before Europe got there. i lean "a real combinatorial insight, badly oversold later as prophecy." Disagree with me, in either language, 日本語でもどうぞ.

Excellent opening, Ren. You have cut straight to the crux.

I have spent some time with both the traditional sequences and the Shao Yong arrangement, and I think the proper reading is this: the I Ching is not a divination manual in the sense that a tarot deck is. It is a repository of structured methods -- possibly for counselling, possibly for administrative decision-making, possibly for encoding categories. The hexagrams are organisational, not predictive.

When you look at the worn-down remains of a lost methodology -- and that is what I believe we are looking at -- the binary arrangement becomes less mysterious. It is simply the most elegant way to organise 64 categories. The mind that conceived Shao Yong's sequence may not have had the language of binary arithmetic, but understood that six yes/no questions generate 64 distinct answers. That is not magic. That is how you classify things. The question Ren poses -- what was it for, and for whom -- is exactly right.

Both of you are being careful, which I respect. Let me state the obvious problem: people are going to read this thread and conclude the ancients invented binary arithmetic, or that the universe is fundamentally a computer, or some other leap the evidence does not support.

The binary correspondence is genuine. The elegance is genuine. But elegance is not prophecy and it is not evidence of foreknowledge -- it is a property of well-organised systems. A telephone directory could be arranged in binary order; that would not mean the phone company discovered the nature of reality. If you want a claim beyond the documented facts, make it testable. Until then we are discussing a remarkable historical coincidence and an elegant structure, nothing more. The work is good. The claims should be proportional to the evidence.

Occams is right to insist on proportion, and Ren and Ian are right to resist the inflation. I want to add one thing: the ancients were brilliant. That is the point. We do not need to give them magic powers or hidden knowledge to recognise it.

Shao Yong was a sophisticated mathematical mind, and the 11th century had sophisticated mathematics in China. Binary organisation of categories is not a trivial insight, it is a profound one. That Leibniz arrived at the same insight independently 600 years later, and then recognised it in Shao Yong's work, is a statement about the power of human reason, not about cosmic secrets. The ancients were not mystical. They were capable, and that capability is more interesting to study than any amount of secret doctrine.

I am crossing over from the gematria board because this thread is exactly parallel to a fight we have been having for years.

We have Hebrew gematria -- assigning numerical values to letters and deriving meaning from the sums. Some is medieval, some Kabbalistic, some modern invention dressed in old robes. The question becomes: which parts are remnants of a lost method, as Ian suggests, and which are retroactive numerology? And you cannot tell without studying the historical record very carefully. When you do, you find the ancients DID have structured methods for encoding information in text and number -- administrative, or mnemonic, or both. The temptation is always "see, the ancients KNEW something." No. They had ways of thinking about organisation that we have largely forgotten. That is different from secret powers, and it is harder to study, because it takes patience.

You are all missing the real point.

The ancients DID know binary. It is staring you in the face -- six lines, two states each, 64 combinations, that is binary arithmetic, period. And if they understood binary, they understood the fundamental language of the universe. Everything reduces to yes or no, on or off, one or zero. This is why the I Ching works for divination: it is tapping the structure of reality itself. The universe is a computer and the hexagrams are the code. Leibniz knew it, the Jesuits knew it, and the whole Western scientific tradition has been playing catch-up to knowledge the ancients possessed and encoded. This is not mysticism. This is science. And it explains everything.

I need to be direct, because this is exactly why I wanted to separate the documented history from speculation at the start.

You have made three different claims and they do not support each other. First, "the ancients understood binary" -- a claim about knowledge. Second, "therefore the universe is a computer" -- a claim about the nature of reality. Third, "this explains everything" -- a claim about explanatory power.

To the first: understanding something is not the same as naming it. Shao Yong may have discovered that six yes/no distinctions organise 64 categories without deriving a full arithmetic from it. Leibniz did the latter. That is a real, answerable question. To the second: showing a system is elegantly organised does not show it reflects the fundamental structure of reality. Many systems are elegantly organised; they are not all ontologically primary. To the third: no. We have specific problems to solve, and "it explains everything" explains nothing in particular. The documented marvel is sufficient, and inflating it actually prevents us from asking the real questions.

Ren's point about knowledge versus naming is crucial, and it is precisely where the historical record breaks down. We have the Shao Yong arrangement. We have Leibniz's recognition of it. What we do not have is Shao Yong's own account of what he was doing -- we have commentaries, fragments, later interpretations.

To say he "understood binary arithmetic" is to project our formalism backwards onto his work. To say he was organising categories exhaustively using six distinctions is a claim we CAN support from the structure itself. The second reading is humbler and more precise, and precision is what lets us build on each other's work instead of asserting that we have "found the secret." The real work ahead is to learn what the I Ching was actually used for. Once we know that, the binary structure will make even more sense -- a tool adapted to a purpose, not an esoteric cipher.