TL;DR: Counts in Thái Ất are the way of counting the numbers of host and guest to compare the strength of the two sides. The host count belongs to the host, the guest count belongs to the guest; harmony or disharmony is judged by whether that number is even or odd relative to the yin or yang seat of the palace, not by whether the two numbers are equal. A long count is a number of 11 or above, a short count is a number of 9 or below; the book says that when long one should delay and it favours advancing deep, when short one should hurry and it only favours advancing a short distance.
What is toán số in Thái Ất?
Toán số in Thái Ất is a counting system used to compare the strength of two sides within a single Thái Ất chart. Each side has its own number, called a toán. The number of the host side is called chủ toán, and the number of the guest side is called khách toán. The book also examines whether each toán is an odd number (yang) or an even number (yin) relative to the yin-yang position of the palace, in order to call it hòa or not hòa. The book Thái Ất kim kính thức kinh by Vương Hy Minh of the Tang dynasty[1] devotes an entire chapter to the calculation and interpretation of these toán.
It is necessary to distinguish toán from other factors within the same chart. Thái Ất also has the palace of Thái Ất, has mắt, has the thần, and has eight gates. Toán is only a number attached to the host or the guest, used for comparison, and does not replace the examination of palaces and thần. In practice, the person setting up the chart usually reads the toán first to know the situation of the two sides, and only then reads the remaining factors for details.
How are chủ toán and khách toán calculated?
Chủ toán is the count of the host side, and khách toán is the count of the guest side. The counting is based on the position of the host mắt and the guest mắt on the ring of sixteen thần, then added or subtracted according to the specific rules of each chart. The book Thái Ất kim kính thức kinh clearly records the steps for placing the host mắt and the guest mắt, and from there derives the toán[1].
From the chủ toán the book derives the palace of the chủ đại tướng and chủ tham tướng, and from the khách toán it derives the palace of the khách đại tướng and khách tham tướng. For example, in one chart in volume 6: with chủ toán 14, the đại tướng is in palace 4 and the tham tướng in palace 2; with khách toán 9, the đại tướng is in palace 9 and the tham tướng in palace 7. The section "suy nhiều ít để chiêm thắng phụ" records: when the guest brings a large toán to a place of small toán, the host is defeated; when the guest brings a small toán to a place of large toán, the host wins[1].
What is the difference between hòa and not hòa?
Hòa and not hòa in the book concern the yin-yang nature of the number, not whether the chủ toán equals or differs from the khách toán. The section "suy âm dương hòa bất hòa" in volume 2 cites the Trương Lương kinh: match the toán with the position of Thái Ất and the two mắt; at a yang position an odd toán is double yang, at a yin position an even toán is double yin, and both are not hòa; at a yang position an even toán, at a yin position an odd toán, that is yin-yang hòa, and "hòa thì cát". The book also lists the numbers: 14, 18, 33 are thượng hòa; 23, 29, 32 are thứ hòa; 12, 16, 27, 34, 38 are hạ hòa[1].
The book uses this pair of concepts as a condition for consideration. The section "suy chủ khách" in volume 4 records: when the three gates are sufficient, the five tướng arise, and yin-yang is hòa, then raising troops is favorable; when the three gates are insufficient, the five tướng do not arise, and yin-yang is not hòa, then raising troops is not beneficial, and one should hold fast on defense[1]. This is the word of a Tang dynasty military divination book, not a basis for judging matters today.
What are trường toán and đoản toán?
Trường toán is a long number, and đoản toán is a short number. The book Thái Ất kim kính thức kinh records: thiên mục sở toán, chủ dĩ trường toán nghi hoãn, đoản toán nghi cấp; thập nhất dĩ thượng vi trường, đơn cửu dĩ hạ vi đoản; trường đa lợi thâm nhập, đoản thiểu lợi thiển nhập; trường vi thắng, đoản vi phụ[1]. That is: a toán from 11 upward is called trường, and from 9 downward is called đoản. Trường means one should fight slowly, đoản means one should fight quickly. A large trường favors advancing deep, a small đoản favors only a shallow advance. The book regards trường as victory and đoản as defeat.
The number 10 does not fall into either group according to the above record. The book places it under a different rule in the immediately preceding section, the tam tài section: a toán of 10, 20, 30, 40 is called "vô nhân"; a toán from 1 to 9, that is with no tens digit, is called "vô thiên"; a toán whose units digit runs from 1 to 4 is called "vô địa"[1].
Comparison table of the main concepts
| Concept | Definition | Use in interpreting a chart |
|---|---|---|
| Chủ toán | The count of the host side | Compared with the khách toán to know the strong and weak situation |
| Khách toán | The count of the guest side | Compared with the chủ toán to know the strong and weak situation |
| Hòa | A yang position receiving an even toán, a yin position receiving an odd toán | The book records "hòa thì cát" |
| Not hòa | A yang position receiving an odd toán (double yang), a yin position receiving an even toán (double yin) | The book records that raising troops is not beneficial, and one should hold fast on defense |
| Trường toán | From 11 upward | One should fight slowly, it favors advancing deep, it is victory |
| Đoản toán | From 9 downward | One should fight quickly, it favors only a shallow advance, it is defeat |
Why must one examine both the toán and the palace and thần?
Toán is only one layer of information. To interpret fully, one must also examine the palace of Thái Ất, see where the host mắt and guest mắt are placed, examine the supporting thần, and examine the eight gates. The book Thái Ất kim kính thức kinh has a chapter on the eight gates and the five tướng, in which it states clearly: when the host and guest armies are evenly matched, the one that receives sinh khí wins, and the one that receives tử khí is defeated[1]. Thus a large toán is not necessarily a victory if it falls into tử khí, and a small toán is not necessarily a defeat if it falls into sinh khí.
The book also records how to examine the five tướng according to the season: in spring mộc is prosperous, in summer hỏa is prosperous, in autumn kim is prosperous, in winter thủy is prosperous, and in the four transitional seasons thổ is prosperous. Whichever tướng meets its own prosperous season receives sinh khí, and whichever meets a season that controls it falls into tử khí. This is the second layer for evaluation after the toán has been examined[1].
Specific cases in the book
The book Thái Ất kim kính thức kinh contains many concrete chart examples. Volume 6 has the 28th chart of the Giáp Tý nguyên, on the day Tân Mão: Thái Ất is in palace two, Lữ Thân is the thiên mục (host mắt), chủ toán 14, đại tướng 4, tham tướng 2; Hợi is the kế thần, Thủy Kích is at Đại Quýnh, khách toán 9, đại tướng 9, tham tướng 7. According to the sections above, chủ toán 14 is a trường toán and belongs to the thượng hòa group, while khách toán 9 is a đoản toán. But in this chart the book does not interpret by the number; it examines the palace of the khách đại tướng: palace 9 belongs to mộc and meets a thần belonging to kim, which the book calls the khách đại tướng "receiving tử khí"[1].
Comparison with the other systems in Tam Thức
Within Tam Thức, Thái Ất leans toward toán số and the situation of the battle line, Kỳ Môn leans toward gates and stars, and Lục Nhâm leans toward khóa and truyền. The method of counting toán in Thái Ất is not shared with the method of setting up khóa in Lục Nhâm or the method of placing gates in Kỳ Môn, but all three systems share the same foundational concepts such as yin-yang, ngũ hành, and can chi.
The main difference is that Thái Ất has its own toán số system, used to compare the two sides. Kỳ Môn has no equivalent toán số system, and instead uses gates and stars for evaluation. Lục Nhâm uses khóa and truyền for evaluation. Therefore, when reading a Thái Ất chart, one should not apply the reading method of Kỳ Môn or Lục Nhâm, but must follow the rules of Thái Ất exactly.
Points to keep in mind when reading toán số
First, toán số is a convention of the book, not an astronomical measurement. The summary note of the Tứ khố edition also records that the book contains portions added by later generations (in some places the accumulated years are calculated up to the Cảnh Hựu first year of the Song dynasty), and is no longer the original work of Vương Hy Minh. This is why this article states clearly that it follows the Tứ khố edition of Thái Ất kim kính thức kinh[1].
Second, toán số does not by itself assert victory or defeat. The book Thái Ất kim kính thức kinh repeatedly reminds the reader to also examine the palace, the thần, the season, and the gates. Toán alone is not enough to conclude.
Third, the numbers in the book are examples from the ancients, not statistical data. One should not use those examples to infer a fixed rule for every chart.
Nhật Nguyệt's suggestion:
If you read Thái Ất as a system of ancient knowledge, treat toán số as one layer of information among many. Do not use toán số to decide real matters in life, work or finance. The reasonable approach is to read the original book, compare the commentaries, and state clearly which edition you are following.
