Earlier Heaven Bagua

The defining property is that every trigram stands opposite the figure that inverts it line for line. Heaven faces earth, fire faces water, and the same holds for the remaining pairs, so the circle balances on every axis rather than only on one. A passage in the treatise on the trigrams states these relationships in prose, describing the pairs as acting on one another, and the circular arrangement is a way of showing that statement rather than a separate doctrine.

Because the trigrams are built from broken and unbroken lines, they can be read as three place numbers, and when the arrangement is extended to all sixty four hexagrams in the corresponding order the sequence corresponds exactly to counting in base two. That was noticed in Europe in the early eighteenth century by a correspondent of Leibniz, who had been developing binary arithmetic and found the ordering of considerable interest. The correspondence is genuine and is often overstated. It shows that the arrangement is generated by a consistent rule of line succession, which is a real property of the figure. It does not show that anyone in China was doing binary arithmetic, and the tradition's own accounts of the arrangement are not arithmetical.

The attribution to Fu Xi places the arrangement at the mythic beginning of Chinese civilisation, and that placement is itself a claim about authority rather than a historical record. What can be traced is the diagram, and the diagram is medieval. Circular and square charts of the trigrams and hexagrams became prominent in Song dynasty scholarship, associated particularly with one eleventh century thinker who built an elaborate numerological cosmology around them. Their establishment as standard came through the commentary tradition.

When the dominant Song synthesis of the classics incorporated the diagrams into the authoritative reading of the book of changes, they were printed at the front of editions and became for later readers a part of the classic rather than an addition to it. Most people meeting the arrangement today meet it in that position. Its practical use follows from what it depicts. Because it shows the trigrams in balance and not in motion, it is used for contemplation, for the theory of how the changes work, and in internal alchemy, where the pairing of opposites is the operative idea. Siting and directional practice use the other arrangement, and confusing the two produces a system that does not work on its own terms.