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The oldest divination system still in daily use is also, read as a diagram, a flawless piece of mathematics. That was almost certainly not the intention.

Sixty-Four Corners, Six Steps Apart

A hexagram is six lines, each either broken or unbroken. Change one line and you have a different hexagram, so every one of the sixty-four has exactly six neighbours, one for each line that could turn. That is the whole structure, and it has a name in mathematics: a six-dimensional cube, where every corner touches six others and no corner is more than six steps from any other.

So a reading that moves from one hexagram to another is a walk on the corners of that cube, and the longest walk anyone could ever need is six. The system has no far side. Whatever you are asked and whatever you are answered, the answer is at most six changes from where you started.

And One Monk

What makes this worth a page is a second thing, and it is a fact about the atlas rather than about the world. Transformation is recorded here as a relationship between one thing and another, and almost every such relationship the atlas holds belongs to the I Ching: the sixty-four hexagrams and their six changes apiece account for all but one of them.

The one that is left is not a hexagram. It is Dharmakara, the monk who made forty-eight vows and became Amitabha, the Buddha of Infinite Light. Across tens of thousands of records, the atlas records exactly two kinds of thing that turn into something else: a dynamical system, and an enlightenment.

That is a statement about what has been written down so far, not a claim that nothing else in religion transforms. Other metamorphoses are recorded in other ways, and more will be added. It is offered as a nice accident of the filing, which is what it is.

Where To Read More

• I Ching (Book of Changes)Astrological and Divinatory TextsThe book itself, and the sixty-four figures it is built from
• The CreativeQianOne corner of the cube: six unbroken lines, and six ways out of it
• DharmakaraBodhisattvasThe monk whose vows are the other transformation
• AmitabhaBuddhist DeitiesWhat he became: the Buddha of Infinite Light