kenny wrote:Thus, I have three simple questions.

1. Did those ancient Yijing authors know about those points you just mentioned?

2. It is obvious that those ancients did not associate hexagrams with the electromagnetic field as they did not invent TV and computers. What kind of associations (if any) had they done with the hexagrams?

3. I did follow your links of cellular automaton and alife. But, I am still not very clear about how the hexagrams to be an alife. Can you give a better description on this?

These are good questions. I will answer them one at a time.

For alife (artificial life), it must imitate the real biological life. Thus, we should list the basic traits and attributes of the real life first. The followings are the key attributes.

1. There is a set (in finite numbers) of amino acids (

http://en.wikipedia.org/wiki/Amino_acid ).

2. These amino acids produce a set (in finite numbers) of proteins (

http://en.wikipedia.org/wiki/Protein ).

3. There is a set (in finite numbers) of enzymes (

http://en.wikipedia.org/wiki/Enzyme ) which are special kind of proteins, and they act as traffic controller for the movements of amino acids and proteins.

4. The three above constitute the process of metabolism (

http://en.wikipedia.org/wiki/Metabolism ) which allows organisms to grow and reproduce, maintain their structures, and respond to their environments.

The above life attributes can be imitated with the followings.

1. The living space (the environment) is a space (1 to n dimensions) divided into grids (cells).

2. There is a set (in finite numbers) of life substances. Each substance can take up one grid. The simplest alife has only one life substance, a black stone, such as in the most famous alife, “Conway's Game of Life” (

http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life ). These substances imitate the amino acids.

3. There is a set (in finite numbers) of rules for those life substances to be either dead or alive after “a time step”. These rules mimic the enzymes.

4. There is a set (in finite numbers) of emerged “stable” patterns after a finite numbers of time steps. These patterns mimic the proteins.

By having proteins (the stable patterns), the metabolism of the system can be maintained, and it becomes an alife.

While the living space can be (and should be) infinitely big (open), the life substances (~ amino acids) and the life moving rules (~ enzymes) must be in finite numbers (closed). Thus, every alife is,

a. a moving (dynamic) system,

b. a closed system.

Note: there is no limitation on the numbers of the life products (the stable patterns), but in general it will be in finite numbers because that the interaction is limited. For example, every cell has only 8 neighbors in a two-dimension space.

The hexagram system meets the two criteria above. A hexagram can become a different hexagram after one of its six lines is changed to its opposite. This change can be done by a set of preset rules, the interaction of it with its neighbors (the environment). Yet, no amount of change can create something out side of those 64 hexagrams.

I will show a simplest hexagram alife by using Conway’s Game of Life which is described in details at the web page provided above. Here, I will only give a short summary of it.

1. It is a “zero-player” game, meaning that its evolution is determined by its “initial state”, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. Note: this is very important as our universe is a zero-player game. After its creation, it evolves by itself.

2. There is only one “live-substance”, such as a blackstone.

3. This live-substance lives on grids (cells) of infinite size.

4. This live-substance has only two possible states, dead or alive.

5. There is a set of rules to determine the fate of any life-substance. Every live-substance interacts with its eight neighbors, which are in the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:

a. Any live-substance (blackstone) with fewer than two live neighbors dies, as if caused by under-population.

b. Any blackstone with two or three live neighbors lives on to the next generation.

c. Any blackstone with more than three live neighbors dies, as if by overcrowding.

d. Any dead cell (without blackstone) with exactly three live neighbors becomes alive (with a blackstone), as if by reproduction.

The above constitutes the Conway’s Game of Life. After an initial seeding, such as randomly spread out a handful of blackstones to a clean grids, some stable patterns will evolve. And there are three types, the Still lifes, the Oscillators and Spaceships. In the Spaceships category, a stable pattern is called “glider” which is the one that I will use as the body (the carrier) for the hexagram alife. The life cycle of the glider is described below.

As you can see that after three generations, the glider “replicates” itself, and it becomes a genuine life, an alife to be exact. Yet, there is a problem for glider which was never discussed before. That is, it is an immortal. It will not die by itself if it is not perturbed externally. Thus, it cannot be a model for any earthly life which is always a mortal. However, this problem can be resolved by adding the hexagrams into the life of glider. I will show this with the following steps.

1. Those 64 hexagrams are inert and opaque blackstones. By using these 64 opaque blackstones in the glider, it is still a Conway’s glider.

2. Those 64 hexagrams are inert but transparent blackstones. By using these 64 transparent (but still inert) blackstones in the glider, two different gliders might consist of from different hexagrams.

3. Those 64 hexagrams are transparent but no longer inert. A hexagram will interact with its neighbors in addition to Conway’s blackstone rules. For example, we add the following “internal” rules.

a. If a hexagram (blackstone) has two live neighbors, the bottom line of that hexagram will change to its opposite, Ying to Yang, or Yang to Ying.

b. If a hexagram (blackstone) has a live neighbor which is identical to itself, it will die. In fact, both die.

With these two internal rules, an immortal glider can slowly reach to a state that two blackstones die because of these internal changes, and thus end the life of that glider.

These two internal rules are aging process. And, the hexagram-glider becomes a mortal life, an earthly-like life.

This simple example gives only a hint of how hexagram system works in an alife system.