Symmetry Carried Through the Whole Figure

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.