What Is Khổng Minh Thần Toán?
Khổng Minh Thần Toán is a divination card book used to look up readings after casting a hexagram, widely circulated in Vietnam with 384 cards. The number 384 is not arbitrary: it equals 64 hexagrams multiplied by 6 moving lines, meaning each of the 64 hexagrams has six possible moving lines, and each hexagram-line combination gets its own card. The querent casts a combination, then looks up that exact card to read its verse, translation, commentary, and reading.
A card in current editions usually has four parts. The first is the card number and hexagram name with a rating such as Thượng Thượng, Trung Trung, or Hạ Hạ, plus the moving line. The second is the Chinese verse with Hán Việt romanization. The third is the Vietnamese translation of the verse. The fourth is the commentary by Thông Huyền Lão Nhân and a detailed reading for the querent. For example, card 336, matching the hexagram Sơn Trạch Tổn with the Sixth line moving, has a Hán Việt verse about a small boat that has crossed the waves and now docks safely, and the reading rates this card as good, saying all matters flow smoothly, lost items are found, plans should proceed, and business is profitable. By contrast, card 342, matching the hexagram Bát Thuần Khôn with the Sixth line moving, has a verse about bad fortune, disaster, and prayers unanswered, and the reading rates it unfavorable and advises the querent to stop all pursuits and wait out the adverse period.
Notably, the cards do not only describe general fortune but tie to specific matters. For the same card, the book may give separate notes for seeking wealth, travel, lawsuits, and marriage. This presentation makes Khổng Minh Thần Toán closer to an applied lookup table than a purely philosophical work.
How Do You Cast a Khổng Minh Thần Toán Hexagram Using Three Number Groups?
The casting method in Vietnamese editions uses three number groups chosen or thought up by the querent. The first group is divided by 8, and the remainder gives the upper trigram. The second group is divided by 8, and the remainder gives the lower trigram. The third group is divided by 6, and the remainder gives the moving line. Remainders are matched to the Tiên Thiên Bát Quái sequence, where Càn is 1, Đoài is 2, Ly is 3, Chấn is 4, Tốn is 5, Khảm is 6, Cấn is 7, and Khôn is 8. For the moving line, dividing by 6 gives remainders from 1 to 6, and when the division is exact, 6 is taken.
The book gives an example with the three number groups 75, 47, and 58. The first group 75 divided by 8 leaves 3, matching Ly as the upper trigram. The second group 47 divided by 8 leaves 7, matching Cấn as the lower trigram. The third group 58 divided by 6 leaves 4, matching the fourth moving line. Combining upper Ly with lower Cấn gives the hexagram Hỏa Sơn Lữ, moving line 4, then the table is consulted for the matching card. Note that some printed editions show moving line 6 in the description but the calculation gives line 4; this is a printing or editing error in circulated editions, and users should trust the calculation.
This mechanism is similar to Mai Hoa Dịch Số in that both use division remainders to derive trigrams and lines, both based on Tiên Thiên Bát Quái numbers. So a Mai Hoa casting core, such as LapQueMaiHoa, can compute the upper trigram, lower trigram, and moving line for Khổng Minh Thần Toán, then only the 384-card table lookup remains. The difference is that Mai Hoa also uses external signs, time, and objects for deeper reasoning, while Khổng Minh Thần Toán mainly stops at the card lookup.
| Step | Action | Calculation | Example Result |
|---|---|---|---|
| 1 | Take the first number group | Divide by 8, take remainder, match Tiên Thiên number | 75 ÷ 8 leaves 3, matching Ly |
| 2 | Take the second number group | Divide by 8, take remainder, match Tiên Thiên number | 47 ÷ 8 leaves 7, matching Cấn |
| 3 | Take the third number group | Divide by 6, take remainder, remainder 0 counts as 6 | 58 ÷ 6 leaves 4, moving line 4 |
| 4 | Combine upper and lower trigrams | Ly above, Cấn below | Hexagram Hỏa Sơn Lữ |
| 5 | Look up the 384-card table | Find the exact hexagram and moving line | Card Hỏa Sơn Lữ moving line 4 |
| 6 | Read the card | Verse, translation, commentary, reading | Reading based on card content |
Why Is the Book Named After Gia Cát Lượng?
Official histories of Gia Cát Lượng mention no divination book. The main historical source about him is his biography in Tam Quốc Chí by Trần Thọ in the third century, later annotated by Bùi Tùng Chi in the fifth century with many additional sources. These sources record his service as chancellor of Shu Han, helping Liu Bei found the state, serving as regent for Liu Shan, pacifying the southwest, and leading several northern campaigns, dying in 234 at Wuzhang Plains. No passage says he composed a divination book or established a hexagram system for posterity.
Gia Cát Lượng's image as an all-knowing strategist comes largely from the 14th-century novel Tam Quốc diễn nghĩa, more than a thousand years after his death. The novel builds the character Khổng Minh into almost a saint who predicts wind and fate, arranges battle formations, and performs rituals to summon wind. From that literary figure, folk tradition gradually attributed many books and methods to him, including Khổng Minh Thần Toán.
In Vietnam, some libraries and book collections introducing Khổng Minh Thần Toán state that the book was created by Gia Cát Lượng, for example the introduction by Cao Thắng Library. This must be understood as legendary tradition, not a historical conclusion. No original text from the Three Kingdoms period confirms him as author, and the book's content itself reflects presentation, casting methods, and fortune classification that took shape much later.
This does not reduce the book's usefulness for querents. It only places the name correctly: Khổng Minh Thần Toán is a naming by the prestige of a historical figure, not evidence of authorship.
Three Often Confused Things: Chu Dịch Line Texts, Khổng Minh Thần Toán Cards, and Tiểu Lục Nhâm
These three systems all use hexagrams and lines but differ in lookup unit and casting method, so beginners easily confuse them.
Chu Dịch line texts are ancient wording tied directly to each line of the 64 hexagrams in the Kinh Dịch, predating Khổng Tử and passed down through generations. A Chu Dịch querent reads the hexagram text and moving line text, then interprets by hexagram image, line correspondence, and line position. This is the root layer; all later hexagram systems take the 64 hexagrams from here.
Khổng Minh Thần Toán cards are a layer over those 64 hexagrams. Each hexagram has six cards for six moving lines, totaling 384 cards. Each card has its own verse, translation, and commentary, not using Chu Dịch line texts as main content. The querent only needs the exact hexagram and line to find a card with a ready reading, without self-interpretation.
Tiểu Lục Nhâm is a completely different finger-counting method. It uses six palaces in order: Đại An, Lưu Niên, Tốc Hỷ, Xích Khẩu, Tiểu Cát, Không Vong, and casts by counting month, day, and hour on finger joints. The Tiểu Lục Nhâm book is often attributed to Lý Thuần Phong of the Tang dynasty, and some theories say a later author drew from Khổng Minh Thần Toán to simplify into the six-palace finger method. This is a simplified branch, not using 64 hexagrams and not having 384 cards.
| Criterion | Chu Dịch Line Texts | Khổng Minh Thần Toán | Tiểu Lục Nhâm |
|---|---|---|---|
| Lookup unit | 64 hexagrams, 384 lines, read hexagram and line texts | 384 cards, each matching one hexagram with one moving line | 6 fixed palaces |
| Casting method | Coin toss, yarrow stalks, or number methods | Three number groups divided by 8, 8, 6 | Count month, day, hour on finger joints |
| Source of readings | Ancient wording in Kinh Dịch | Ready verse, translation, commentary, reading | Meanings of six palaces and oral interpretation |
| Traditionally linked to | Văn Vương, Chu Công, Khổng Tử | Gia Cát Lượng by legend | Lý Thuần Phong of Tang by legend |
| Detail level | Short, needs interpretation | Long, with ready readings | Short, depends on the practitioner |
How Should You Read Khổng Minh Thần Toán Cards Correctly?
Vietnamese editions of Khổng Minh Thần Toán classify cards by levels such as Thượng Thượng, Trung Trung, and Hạ Hạ. This classification helps beginners get a quick view of the card's general trend, but it is also the most misleading part. A card rated Hạ Hạ does not mean everything fails; it usually advises slowing down, holding steady, and waiting for the right time. A card rated Thượng Thượng does not mean things succeed automatically; conditions are more favorable and the querent still must do their part.
Editions also differ somewhat in classification and commentary content. Some emphasize the Hán Việt verse, some expand readings by matter type, some add Thông Huyền Lão Nhân's commentary with its own interpretation. Users should know which edition they use, because the same hexagram with the same moving line may get different commentary on favorable level from two editions.
One note on the name Thông Huyền Lão Nhân. This is a title commonly seen in Vietnamese Khổng Minh Thần Toán editions, referring to the writer of the commentary section. Available documents do not give a specific identity for this figure, so it should not be assigned to any historical person. It is a compiling pen name, not a figure with a defined biography.
The most reasonable use is to treat the card as a suggestive framework for self-reflection, not a fixed verdict. If the card says avoid petty people, the action is to review current relationships and see where misunderstanding or unhealthy competition exists. If the card says travel far, the action is to see if you are stuck in the old place and what options exist to change environment. The book's value lies in forcing people to pause and look at what they are doing from another angle.
Should You Trust the Hexagram Result Absolutely?
No. The books in this line do not place themselves as deciding for humans. Sách Tử Vi ghi chép số 01 repeats the sayings "Nhân định thắng thiên" and "Đức năng thắng số", meaning human determination can overcome heaven and virtue can overcome fate, using Gia Cát Lượng himself as an example: he knew the realm would split in three yet still went to Kỳ Sơn six times and ultimately failed. This is a view many authors in the Eastern line repeat: the hexagram shows trends and conditions, not a certain outcome.
For matters involving finance, health, or law, the hexagram cannot replace professional advice. The querent still needs a doctor, lawyer, or financial expert as appropriate. Placing the hexagram in its proper role, as a self-inquiry tool, avoids both extremes: complete dismissal and absolute belief.
Practical Summary
For beginners, mastering Khổng Minh Thần Toán boils down to three tasks. Know the Tiên Thiên Bát Quái number sequence and the remainder division by 8 and 6. Know how to combine upper and lower trigrams to get the hexagram name. And know how to look up the exact card by hexagram with moving line in the 384-card table of your edition. These three are enough to cast and look up cards; deeper interpretation depends on affinity and familiarity with Kinh Dịch.
