The Luoshu, south at the top as the classical charts draw it. Every line of three totals fifteen.
Start with the sentence everybody quotes. The Great Treatise, the long commentary
appended to the Book of Changes, says that the Yellow River put out a chart and the
Luo put out a writing, and that the sages took them as their model. That is the whole
of it. There is no turtle in the sentence, no square, and not a single number.
The first people on record to say what the Writing was did not think it was a square.
The History of the Former Han, in its treatise on the five phases, reports the view of
Liu Xin, the scholar who catalogued the imperial library at the end of that dynasty:
the legendary Fu Xi received the River Chart and drew the eight trigrams from it, and
Yu, when he tamed the great flood, was given the Luo Writing and set it out as the
Great Plan. The Great Plan is a chapter of the Book of Documents, a list of nine
divisions for governing a realm, starting with the five phases. For the Han, then, the
Writing from the Luo was a text with nine headings. Nine was already the number that
mattered; the digits had not arrived.
They turn up somewhere else entirely: in a description of the Bright Hall, the ritual
building in which a Zhou king was supposed to move from room to room with the seasons.
The Record of Rites of the Elder Dai says the hall had nine rooms, and then prints a
bare row of digits, two, nine, four, seven, five, three, six, one, eight. Cut it into
threes and you have the square, every line totaling fifteen. The Record never says
why. Its commentator Lu Bian, writing in the sixth century, supplies the reason: the
nine rooms copied the pattern on a turtle. The turtle itself had reached the story by
another road. The traditional commentary to the Great Plan, credited to Kong Anguo,
says a divine turtle came out of the Luo with markings on its back numbering up to
nine, and that Yu put them in order as the nine divisions.
The square was also a way of counting. The Shushu Jiyi, a short handbook of
calculation attributed to the Han scholar Xu Yue, lists fourteen methods, and one of
them is the nine-palace method. Its commentary gives the layout as a body: two and four
for shoulders, six and eight for feet, three on the left and seven on the right, nine
on the head, one underfoot, five in the middle. That rhyme is still the standard way
the square is remembered, and it is why the counting rods are in the picture at the
top of this page.
And the square moved. When the astronomer Zhang Heng petitioned the throne in the
second century against the prophecy books then in fashion, he listed the nine palaces
among the methods that, unlike the prophecies, gave results that could be checked. The
Tang commentary on his biography explains the term with a line from an apocryphal
Changes text, the Qian Zao Du: the Taiyi spirit takes its numbers and
travels the nine palaces. Then it quotes Zheng Xuan's note, which gives the route. The
spirit sets out from the Kan palace, goes to Kun, then Zhen, then Xun, rests in the
center, and goes on through Qian, Dui and Gen to finish at Li. Put the Luoshu numbers
on those palaces and the route reads one, two, three, four, five, six, seven, eight,
nine. It is precisely the path the stars take on every annual flying-star chart,
including our feng shui 2027 chart. Whoever later
systematized the flying stars was walking a road laid out in a second-century
footnote. (This page checks that the route and the square agree every time it is
built.)
The picture most people carry, a turtle with neat dots on its shell, is the Song
dynasty's. Writing in the seventeenth century, Huang Zongxi observed that ever since
Zhu Xi printed the River Chart and the Luo Writing in his commentary on the Changes,
every household had recited them, and he recorded that the statesman Ouyang Xiu had
dismissed the diagrams as preposterous. Song scholars could not even agree which
diagram was which. One of them, Wei Liaoweng, held that the nine-square was not the
Luo Writing at all but the numbers of the Taiyi's nine palaces, which, given Zheng
Xuan's route, is not a bad argument.