The Five Elements Are the Only Minimum Complete Set That Expresses the Relations
This text was published on Zhihu. The bold text below is an editorial note for clarity.
Those who have studied the I Ching know that the Five Elements focus on describing the relationships between things, rather than discussing five separate elements. This is entirely different from the Western theory of basic elements. If you do not understand this, your reasoning will be wrong, and naturally, you will find it difficult to understand what the Five Elements are about.
There are generating and overcoming relationships among the Five Elements. However, these generating and overcoming relationships also depend on the subject, which distinguishes between the subject and the object.
Other answerers on Zhihu have reversed a relationship. It is not that the Five Elements exist first and then the relationships are discussed; rather, the relationships exist first, and then the Five Elements are discussed. This is why explanations can be unclear.
Here, we deduce how the relationships of the Five Elements arise:
First, things must be compared in pairs. Then, how many categories are needed in total to completely describe all relationships in these pairwise comparisons?
The relationships between things can be simplified and summarized as:
A generates B B generates A
A is identical to B
A overcomes B B overcomes A
To ensure a cycle, we need to construct a connected graph to express it. What conditions must be met?
When A is identical to B, it connects to itself, so it can be disregarded. Each node must satisfy generating, overcoming, being generated, and being overcome. Therefore, there are four connecting lines for each node, making it an even node. Thus, as long as we can construct a node with four connecting lines to others, the task is complete.
So, this is simple. With 3 nodes, each node has only 2 lines; with 4 nodes, each graph has only 3 lines. However, with 5 nodes, it is clearly possible to express such relationships.
Since the maximum number of connecting lines a node can have is the total number of nodes minus one, this is the origin of the Five Elements. First, the relationships between things determine the need for five categories, and then these five categories are abstractly described.
Therefore, the minimum complete set for expressing the most basic relationships between things can only be 5 elements.
As for the so-called four elements (earth, fire, water, wind) mentioned by some, they cannot express the relationships between pairwise things. With four nodes, each node is an odd node, making it impossible to connect in one stroke, i.e., forming a cycle. Therefore, neither the so-called four elements nor six elements can complete a cycle.
And why are these five categories summarized into the five classifications of Metal, Wood, Water, Fire, and Earth, and why are their characteristics borrowed for expression?
You can name them A, B, C, D, E, or change them to Tag1, Tag2, Tag3, Tag4, Tag5, or any other name. This is fine. The five names are based on characteristic descriptions, not that the naming of the Five Elements came first, leading to the classification.
So, based on the functional relationships, it has been determined that five classifications are needed. How should these five classifications be divided?
This abstract classification of the Five Elements involves many considerations. After careful thought, I will not elaborate further for now. If there is an opportunity in the future, I will provide a detailed explanation.