Ba Zuo: the star that mirrors San Tai

The You Bi palace as day 1, counted backward to the birth day

Ba Zuo (八座) is San Tai (三台) in reverse. San Tai counts the days forward from the Zuo Fu (左辅) palace, and Ba Zuo counts them backward from the You Bi palace.

Juan 2 puts the two stars in one verse. Its Ba Zuo half also puts the first day on the palace where You Bi sits and only changes the direction; its last words are "counting backward to the birth day, place it there".

Open the full-size diagram

Comparison sketch: how each star is counted and the formulas for where it lands; the landings match iztro 2.6.0.

You Bi (右弼) itself stands on the Dog palace for the first lunar month and steps back one palace per month, so the starting point of Ba Zuo is set by the month too; see You Bi. Put the two steps together: You Bi is the Dog palace counted back (month minus one) places, and Ba Zuo goes back a further (day minus one) places. The Dog palace is two ahead of the Rat palace, so the total is the Rat palace counted back (month plus day) places.

A fold: San Tai and Ba Zuo face each other across the Ox-Goat line

One goes forward and the other backward, so for each step the month-plus-day sum goes up, San Tai advances one palace and Ba Zuo retreats one. On the ring of branches the two always sit symmetrically, with the line through the Ox and Goat palaces as the axis. On a chart for month 5, day 15, San Tai is on Dog and Ba Zuo on Dragon, a pair; for month 4, day 5 the sum is 9, San Tai is on Pig and Ba Zuo on Rabbit, another pair.

The whole correspondence follows, each row labeled by what is left when month plus day is divided by 12:

When they share a palace, and when they face each other

The number of palaces between the two stars is twice the sum plus two, and every six more in the sum brings a full lap, so it runs in cycles of six by the remainder of the sum divided by 6: remainder 0 gives a gap of 2 palaces, 1 gives 4, 2 gives 6 (directly across), 3 gives 8, 4 gives 10 and 5 gives 12, which is the same palace.

The shared palace can only be Ox or Goat: a remainder of 5 mod 12 gives the Goat palace and 11 gives the Ox palace, which are exactly the two points of the axis.

"Ba Zuo" in the book: five places

Body, Life, Travel, Wealth, Career and Wellbeing: these six palaces are named the Eight Seats.

1. 1

   Find the You Bi palace first

   It is on the Dog palace for the first lunar month and steps back one palace each month.

2. 2

   Then count the days backward

   The first day sits on You Bi, and the birth day is (day minus one) palaces back; twelve palaces back return to the start.

3. 3

   Last, compare with San Tai

   Number the branches from Rat as 0: the two stars' numbers always add up to 2 after dividing by 12, and they can coincide only on Ox or Goat.

The other star counted from Zuo Fu is San Tai; once both stars are back on a whole chart, the palaces opposite and trine to them matter too, and the three sides and four directions explains how.