A Small Summary on the Bagua

What We Know So Far...

• The eight Bagua trigrams appear to form the group Z8
• The 64 hexgrams appear to form the group Z2 x Z4 x Z8
• In ancient fortune telling, trigrams were generally not used, but hexgrams were formed by random tossings of yallow sticks, with particular lines marked as special (i.e. those with the numbers 6 and 9) -- or in motion (動)
• The I-Ching consists of fortunes for each line in motion for a particular hexgram formed

What We Still Do Not Know...

• Under what kind of procedure are the line patterns of the Bagua trigrams and hexgrams manipulated that can reflect their group theoretical properties -- this particular form of representation (i.e. solid and broken lines) must serve some kind of purposes...
• Formal relationship between trigrams and hexgrams, if any
• Why Jing Fang divide the 64 hexgrams into his particular arrangement of eight houses -- in particular, why the seven generation patterns are chosen

Moving Forward...

Fortune telling based on the I-Ching took the ancient form at least until around 50BC, when the scholar Jing Fang revolutionized the field by merging it with another concept -- the Five Elements, in particular that of the Gan/Zhi (i.e. trunk and branch) cycles, which form a calculus on the Five Elements.

Just as a reminder, the Bagua trigrams are mapped to the Five Elements in the following way:

The order of trigrams shown is the Binary Order -- an ordering invented only in the Sung dynasty (around 1000AD), or almost 1,000 years after Jing Fang merged the Bagua with the Five Elements and revolutionized fortune-telling techniques.