I Ching Algorithm: Further review of hybridization


In the article Hybridization, we have given two individuals to crossbreed to reproduce, but have not assessed the quality of the offspring. Now let's see which of the 64 hexagrams the child is born corresponds to.

To make it easier to remember, we copy the 64 hexagrams in order with their summary meanings below

Thuần càn, Thuần khôn, Thủy lôi truân, Sơn thủy mông, Thủy thiên nhu, Thiên thủy tụng, Địa thủy sư, Thủy địa tỉ, Phong thiên tiểu súc, Thiên trạch lý, Địa thiên thái, Thiên địa bĩ, Thiên hỏa đồng nhân, Hỏa thiên đại hữu, Địa sơn khiêm, Lôi địa dự, Trạch lôi tùy, Sơn phong cổ, Địa trạch lâm, Phong địa quan, Hỏa lôi phệ hạp, Sơn hỏa bí, Sơn địa bác, Địa lôi phục, Thiên lôi vô vọng, Sơn thiên đại súc, Sơn lôi di, Trạch phong đại quá, Thuần khảm, Thuần ly; Trạch sơn hàm, Lôi phong hằng, Thiên sơn độn, Lôi thiên đại tráng, Hỏa địa tấn, Địa hỏa minh di, Phong hỏa gia nhân, Hỏa trạch khuê, Thủy sơn kiển, Lôi thủy giải, Sơn trạch tổn, Phong lôi ích, Trạch thiên quải, Thiên phong cấu, Trạch địa tụy, Địa phong thăng, Trạch thủy khốn, Thủy phong tỉnh, Trạch hỏa cách, Hỏa phong đỉnh, Thuần chấn, Thuần cấn, Phong sơn tiệm, Lôi trạch quy muội, Lôi hỏa phong, Hỏa sơn lữ, Thuần tốn, Thuần đoài, Phong thủy hoán, Thủy trạch tiết, Phong trạch trung phu, Lôi sơn tiểu quá, Thủy hỏa kí tế, Hỏa thủy vị tế.

The arrangement of 64 hexagrams starts from the two hexagrams  Càn and Khôn. Càn is heaven, Khôn is earth, there is heaven and earth before there are all things. The book "Hexagram words story" divides 64 hexagrams into "Upper sutra" and "Lower sutra". The Upper sutra consists of the first 30 hexagrams meaning the Tao of heaven. The Lower sutra includes the last 34 hexagrams that talk about human relationships in the lower world:

  1. "Upper sutra" says: the Càn hexagram represents heaven,
  2. the Khôn hexagram represents the earth.
  3. In the middle of heaven and earth are all things, so the next is the "Truân" hexagram.
  4. Truân is enough for all things to begin. At the beginning, everything was still sinking, so the next hexagram "Mông". The Mông is still in the dark, is fragile.
  5. Everything is fragile, it is impossible not to nurture, so next is the hexagram "Nhu". Nhu means to be eaten.
  6. Eating and drinking will cause a fight, so the next is the "Tụng" hexagram.
  7. The fight ends in groups, so the next hexagram is the "Sư" hexagram. Sư means follow each other.
  8. The crowd will rely on each other, so the next is "Tỉ" hexagram.
  9. Tỉ means being close to each other, then gather, so the next hexagram is "Tiểu súc".
  10. If there is accumulation, it must be courtesy and moderation, so the next is the hexagram "Lý". Lý means ceremony and music.
  11. If there is courtesy, then there will be peace, so next is the hexagram "Thái", means trade.
  12. But everything cannot be traded from beginning to end, so the next hexagram "Bĩ" means failure, trouble.
  13. Difficulties can't last forever, so next is the hexagram "Đồng nhân".
  14. Being able to live in harmony with people, so all things must submit, so the next is the hexagram “Đại hữu”.
  15. People with a great career should not be complacent, so the next is the hexagram “Khiêm”.
  16. If you have a great career but still be humble, everything will be done, so it's very happy, so the next hexagram is the hexagram "Dự".
  17. The person who can make people happy, of course everyone comes to him, so the next hexagram is the hexagram “Tùy”.
  18. Being too happy is easy to sink and split, so the next hexagram is a hexagram "Cổ". Cổ means corruption, division.
  19. Divided to become independent, only then can create a new career, so the next hexagram is "Lâm". Lâm means taking big to rule small, meaning big.
  20. After growing up, there are enough conditions to compare and exchange with each other, so the next hexagram is "Quan", which means observation.
  21. Seeing and doing is still a distance, so you have to try to be, so next is the hexagram "Phệ hạp". Hạp means fit.
  22. Things that have been gathered together cannot be rushed, there must be a ritual, so the next hexagram is "Bí". Bí means literary, elaborate.
  23. But the literary style is too refined, it will lose its authenticity, causing damage to the common good, that is, the happiness has come to an end, so the next is the hexagram "Bác". Bác means peeling off each piece.
  24. Falling to the end becomes from top to bottom, so next is the hexagram “Phục”,
  25. again returning to reality, which means it is no longer a perishing thing, so next is the hexagram “Vô vọng”. It means hopeless.
  26. But things can't stay hopeless forever, hopeless to have a large capacity, so the next hexagram is "Đại súc", which is a large capacity, gets a crop.
  27. After accumulating matter, it can be nourished, so the next hexagram is "Di". Di means to feed.
  28. If you don't nurture, you can't grow up, but on the contrary, you can be over-nourished, so the next hexagram is "Đại quá".
  29. If it is too full, it must be empty, so the next hexagram is "Khảm". Khảm means sunken.
  30. The sunken thing must of course be compensated, so the next hexagram is the "Ly" hexagram. Ly means beautiful, is a complement to beauty to rise up.

  31. "Lower sutra" says: After heaven and earth exist, there are all things, and all things are divided into male and female. There are men and women, then there is a husband and wife. Hexagram "Hàm" represents husband and wife. Married, then father and son. There is father-son the society has a father-son relationship, building a institution. There is the institution the social divides the upper and lower castes. There are upper and lower castes, then build and execute rituals.

  32. The relationship between husband and wife cannot be not long-term, so after the hexagram Hàm is the hexagram "Hằng".
  33. Hằng means long, but things cannot remain the same without changing, so the hexagram "Độn" is followed. Độn means retreat.
  34. But things can't always retreat, so next is the hexagram "Đại tráng". Tráng means flourishing and growing.
  35. Next Đại tráng is hexagram "Tấn". Tấn means going forward.
  36. Going forward sometimes hurts, so next is the hexagram "Minh di", which means injury.
  37. If you get injured on the road, you have to return home, so then the hexagram "Gia nhân".
  38. When you have reached the end of the road, the behavior will of course have the opposite phenomenon, so the next is the hexagram “Khuê”. Khuê means opposite.
  39. Rebellion, of course, has an accident, so the next is the hexagram "Kiển". Kiển means accident.
  40. Things can't always have an accident, so next is the "Giải" hexagram. Giải is to resolve, to postpone.
  41. Postponing of course has losses, so next is the "Tổn" hexagram.
  42. But it can't be damaged forever, so next is the hexagram "Ích", which means benefit.
  43. Knowing that it is useful, then it must be decided or the opportunity ends, so the next is the hexagram "Quải", which means decisively.
  44. After that is the meeting, so the next is the hexagram "Cấu", which means meeting without an appointment.
  45. Everything after meeting will gather, so the next is the hexagram "Tụy". Tụy is the grouping, gathering.
  46. Gathering will gradually go up, so next is the hexagram "Thăng".
  47. Constantly going up will fall into a difficult situation of recession, so the next card is "Khốn".
  48. If you have difficulty going up, you will definitely go down, so the next hexagram is "Tỉnh". Tỉnh is a well.
  49. The principle of using a well is that if the basin is not always clean, the water will be cloudy, so it needs to be renewed, so the next hexagram is "Cách".
  50. To make things innovative, there is nothing like the Đỉnh (cauldron), the cauldron is used to cook food, it can change the taste of the food, so the next is the hexagram “Đỉnh”.
  51. The cauldron is the sacrifice, the ancestor sacrifice is the responsibility of the eldest son, so the next is the hexagram “Chấn”. The Chấn hexagram represents the eldest son, and the Chan means dynamic.
  52. Things can't always be in motion, must make it stop, so the next hexagram "Cấn". Cấn means stop.
  53. But things can't stop forever, so next is the "Tiệm" hexagram. Tiệm is the progressive.
  54. Going forward must be collected, so next is the hexagram "Quy muội".
  55. A good harvest will strengthen, so next is the hexagram "Phong", Phong is strong.
  56. Growing up to the extreme, of course, it will not stay in the same position, so the next hexagram is "Lữ" (Traveler).
  57. Travelers can't find a place to stay, they have to find a way to get in somewhere, so the next hexagram is "Tốn". Tốn is to go in.
  58. After entering will be happy, so next is the hexagram "Đoài".
  59. But every fun has its end, so the next is the hexagram “Hoán”. Hoán means to disperse.
  60. Dispersing and then meeting again because they know how to temper and control, so the next hexagram is "Tiết".
  61. With moderation, there is a measure of trust, so the next is the hexagram "Trung phu", which means trust.
  62. Being united will overcome obstacles, so the next hexagram is “Tiểu quá”. Tiểu quá is to pass.
  63. The work that has been passed will be completed, so the next is the "Ký tế" hexagram, which means that the work is done.
  64. But things in heaven and earth cannot end, so next is the hexagram “Vị tế”, which means it is not finished yet. This is the last hexagram in the 64 hexagrams with the meaning of endless I Ching, so it must end with the Vị tế, which is the work is not done, today's work is finished but tomorrow's work is not finished.

The child born is a binary sequence
Applying The hexagram space theorem, we transform it into a 6-bit sequence consisting of two 3-bit subsequences
1101111 1001001 1001001 1001010 1010110 0110110
100 011
We have the upper hexagram Chấn, the lower hexagram Ly. The double hexagram is Lôi hỏa phong (Thunderfire)

Thus, two parental chromosomes have produced a strong "Thunderfire" child. While Genetic Algorithms randomly breed and leave learning to machine learning, will not converge if the learning does not progress, then I Ching Algorithm has knowledge that evolves according to natural laws to ensure that the algorithm definitely converges.

Phong also means rich, full of all aspects. From a very natural example, we get a hexagram with many meanings. That tells us about the richness of I Ching transfromation through the 64 hexagrams. Not a simple linear process, the transformation embraces the laws of growth of all things, and of course it solves all the most complex nonlinear problems which are just human problems, small problems in the vast universe.
The machine learning does not need to point out the global optimal as it failed in the Genetic Algorithm. Its duty is to "order" a request by defining an objective function for each specific problem. It will learn a combination of hexagrams that make up the Tao or the way to the optimal solution.

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