Superficially, there is a world's difference between Yijing and modern physics. However, this paper will demonstrate that not only is this ancient theory of Yijing and Wo-Hsing isomorphic to the modern quark theory but is much more advanced than it. Of course, we must first explain what the modern physics is.
Many people are terrified by physics, and the quark theory is one of the most advanced modern physics theory. However, if anyone can understand what atom is, he can understand the quark theory.
All matters are made of atoms, such as, water is composed of two hydrogen atoms and one oxygen atom. Then all atoms are made of three elementary particles -- proton, neutron and electron. Of course, there are other elementary particles, but we will not discuss them here.
Quark theory says that both proton and neutron (not electron) are made of two quarks -- up quark (u) and down quark (d). Why up and down? There is no particular reason. They are just fancy names for two different elementary particles which are the building blocks for both neutron and proton. The up quark carries +2/3 of electric charges; the down quark carries - 1/3 of electric charges.
There are two kinds of electric charges. So, we can easily distinguish them with two symbols (+, -), positive or negative. However, quark is different from electric charge in two ways. First, there are three varieties (not two, as electric charge) for each quark. Thus, a two symbol system (+, -) will not be enough to distinguish them. A three symbol system is needed.
Second, the difference among the varieties cannot be seen outside of proton or neutron, that is, they must cancel one another in some ways.
Physicists quickly discovered that there is a ready-made system which can meet the two requirements above. The color system of light consists of three prime colors: red, yellow, and blue. Then, the combination of all three colors becomes colorless (gray).
So, physicists borrowed the word "color" to describe the two characteristic of quark listed above. That is, the up quark has three varieties and are distinguished with three color labels -- red up quark, yellow up quark, and blue up quark. It is the same for the down quark.
Now, proton can be written as composite of quarks, such as: P = [ u(red), u(yellow), d(blue)]. Of course, proton has one positive electric charge because +2/3 +2/3 - 1/3 = 1. And, proton is colorless as required because red + yellow + blue = colorless.
The neutron can be written as n = [ u(red), d(yellow), d(blue)], and it has zero electric charge because +2/3 - 1/3 -1/3 = 0.
All ordinary matters (excluding the products of some very high energy processes) of our current universe are made of protons, neutron, electrons and electron neutrinos. That is, only up quark, down quark, electron, and electron neutrino are needed for building up the entire universe.
However, physicists found two other sets of quarks in the laboratories, and they said that those quarks did exist in the early stage of the universe and are still produced by some very high energy processes today. In short, there are three generations of elementary particles.
|1st generation||2nd generation||3rd generation|
|1st quark||up quark||Charm quark||Top quark|
|2nd quark||down quark||Strange quark||Bottom quark|
|neutrino||electron neutrino||muon neutrino||tau neutrino|
The figure 1a on the left is a topological representation for the quark theory. There are three generations of quark, represented by G1, G2, and G3, and each generation of quarks have three varieties (red, yellow, and blue).
Most of the western books translate Five Walk (Wo-Hsing) as five elements while in Chinese the term literally means Five Walk. Buddha talked about Four Great Elements -- earth, water, fire and air. The ancient Greek also talked about a similar idea the same as Buddha's. Those elements were supposed to be the building blocks of the universe in the eyes of Buddha and the Greeks. This conception of elements is quite primitive and has no valid meaning any more after the advancement of modern knowledge. On the contrary, the Five Walk are five bases of two processes. They are not building blocks laying upon each other to build up the universe.
As for the Chinese (ancient or modern), the Cosmos is a process. There is a Wu Ch'i. Wu means nothingness, imagelessness. Wu Ch'i beget Tai Ch'i. Tai literally means the greatest. Ch'i means pole, the monopole, the only One. Then Tai Ch'i gives birth to Yin and Yang. Yin and Yang are two forces. Yang is aggressive and is always moving forward. Yin is passive and yielding. In time of conflict, they are opposite forces. In constancy, they not only complement each other but are imbedded in each other. After reaching their full strength, they transform into the opposite, that is, Yang becomes Yin and Yin to Yang. Thus, Yin can conquer Yang by yielding and allowing Yang to reach its full strength. On the other hand, Yang can only conquer Yin temporarily. Being conquered, Yin transforms into Yang and leads the ultimate conversion of Yang to Yin at end. With Yin and Yang, they form eight kwas, then 64 hexagrams. Chinese claims that Yin-Yang theory plus the Five Walk theory forms a perfect cosmology.
For the Five Walk, there are only two sets of rules to control the interactions. Rule one is the Generation rule which is also called the Mother and Child rule. Earth generates (gives birth to) metal. Metal generates water. Water generates woods. Wood generates fire. Fire generates earth. Thus completes a cycle of generation and birth. See Figure 2a on the left.
Rule two is the rule of Conquest or Destruction which is also called the Man and Woman rule. Metal conquers wood. Wood conquers earth. Earth conquers water. Water conquers fire. Fire conquers metal. See Figure 2b on the right.
The rule of Generation forms a pentagon. The rule of conquest forms a pentagram. These rules seems to be very primitive and non-scientific. I was outraged by its apparent arbitrariness. Figure 2c on the left shows the combination of these two rules, and they rule the entire universe according to this Five Walk theory. In fact, they are the cornerstones of Chinese medicine, Chinese geomancy, etc., that is, everything.
Superficially, there is a world's difference between the ancient Five Walk theory which arose somewhat arbitrarily and the modern quark theory which is supported with very advanced scientific proofs. However, we are able to find at least two evidences to prove that these two systems are isomorphic or identical to each other.
I have showed that Figure 1a (on the left above) is a topological representation for quark theory which consists of three generations of quarks (G1, G2, G3) and three quark colors (RYB; varieties of quarks) for each generation of quark.
However, you can see, the G3 triangle (G3-RYB) in Figure 1b (on the right above) has identical physics and topological meanings to the Figure 1a on the left.
By following the same process as Figure 1b, it is very easy to see that Figure 1c on the left is topologically identical to the Figure 1a above. But, the most important of all is that Figure 1c on the left which is the topological representation of quark theory is identical to the Figure 2c above which is the Five Walk theory of ancient China. That is, the Chinese Five Walk (Wo-Hsing) theory invented more than 2,000 years ago is identical to modern elementary particle physics in terms of their topological representations.
In linear algebra, a vector space is defined by its base. For example, the ordinary space can be defined by a base which consists of three base vectors (x, y, z) or by a different base which uses three different base vectors (radius, angle 1, angle 2). Although these two bases are quite different superficially, they are defining the same vector space. Of course, the above space could be defined by a set of vectors which have more than three vectors, such as (a, b, x, y, z). However, this new set of vectors can always be reduced to three vectors because two equations can be found among these five vectors (such as, a = c1x + c2y + c3z). Only un-reducible set of vectors is called a base of a vector space. Our ordinary space needs at least three vectors to define it. The number of vectors in a base is the number of dimensions for that vector space. So, the dimension for the ordinary space is three because only three vectors (x, y, z) are needed for its base. If two different bases [such as, (x, y, z) and (radius, angle 1, angle 2)] have the same dimensions, their corresponding vector spaces are identical to each other.
By knowing the above definitions, it is very easy to see and to prove that the vector space defined by Five Walk theory is identical to the vector space defined by modern quark theory.
The quark theory is defined with the following three concepts. One, there are three generations of quarks (G1, G2, G3). Two, every quark has three varieties which are labeled with three colors (R, Y, B). Three, the combination of these three colors must cancel one another and becomes Colorless (C). That is, the vector space of quark theory must be defined with seven (7) vectors (G1, G2, G3, R, Y, B, C), and it has seven (7) dimensions.
The Five Walk theory is defined with two concepts. One, there are five (5) vectors (metal, water, wood, fire, earth). Two, there are two rules for those five vectors: rule 1 -- rule of generation; rule 2 -- rule of conquest. Thus, the vector space of Five Walk must be defined with seven (7) vectors (metal, water, wood, fire, earth, rule 1, rule 2).
It is very obvious that the two bases above cannot be reduced any further for their corresponding vector spaces. Because these two different bases has the same dimensions (both are 7), their corresponding vector spaces must be identical to each other.
Although the above two bases define the same vector space, the vectors in one base are significantly different from the vectors of the other base. The transformation between the two sets of vectors are not simple. We cannot say that wood equals to G1, nor metal equals to Red. The transformation equations are generally having the following formula.
In physics community, one issue has been argued for more than 20 years. Are laws of physics designed to created life (strong Anthropic principle)? Or, life is merely permitted by laws of physics (Weak Anthropic principle)?
Obviously, just by looking at the quark theory as it is, there is no sign of any kind that it can give rise to biological life. We cannot even find any direct connection between it and life although all lives must obey physics law after their births. That is, the laws of life could be different from the laws of physics. However, by looking at the topological representation of quark theory, there is a hint that laws of life is, in fact, the same as the laws of physics.
Leonardo Fibonacci invented a Fibonacci Series: 1, 1, 2, 3, 5, 8, ..., 34, 55, 89,.... This series is constructed by adding up the last two numbers in a sequence to give the next number; such as the next number after 55 is 89 (=34 + 55). Then, the Fibonacci Series is found in many lives and natural formations: the leaves on trees, the skins of onions, the shells of microscopic protozoa, the shape of rams' horns and of nautilus shells. Each section of the spiral, such as the rams' horns, relates to the next section in the sequence in the same progression as the Fibonacci Series. That is, there are some kind of connection and association between the Fibonacci Series and the laws of life.
At the first glance, there is seemingly no connection between the Five Walk theory, modern Quark theory and the Fibonacci Series, but there is one. As the numbers rise, the ratios between the two neighboring numbers in the series creep closer and closer to the Golden Section, which is 1.618014, for examples, 5/3 = 1.66, 8/5 = 1.6, 55/34 = 1.617, 89/55 = 1.6181, etc.. But, the Golden Section (the Divine Proportion) is the ratio between the side of the pentagon and the side of the pentagram. As I have showed in Fig. 2c on the left, the Five Walk theory constructs a pentagon with the birth rule and a pentagram with the destruction rule.
In China, the Five Walk theory is viewed as one of the cornerstone for Chinese medicine. It is the law of life. The above discussion does provide a hint that that claim is correct, and it is the Five Walk theory providing quark theory with new meanings. Will anyone be surprised that quark theory is, indeed, having some connection to the laws of biological life?
The original quark theory predicted only two quarks (up and down quarks). The physics community was very excited and thought that it was the final theory for elementary particle physics because two quarks formed a perfect theory. When the third quark was discovered, that beautiful dream of a final theory was broken because the quark theory became too complicated to be the most fundamental law of nature.
In theoretical physics, there is a theoretical reason that the most fundamental particles should not be more than two. The entire universe consists of two parts, computable and uncomputable. The computable part of universe should be expressed with a two code system, such as (0,1), according to mathematics. Because of this theoretical demand, I proposed a Prequark theory in 1979, and it was published in my book Super Unified Theory in 1984 with ISBN 0-916713-01-6 and Library of Congress Catalog Card Number 84-90325.
In quark theory, quark is the most fundamental and undivisible elementary particle, that is, it is not composed of subparticles. On the contrary, quarks are composed of prequarks [Angultron (carries 1/3 electric charge) and Vacutron (vacuum, carries 0 electric charge)] in Prequark theory.
In Prequark theory, quark is composed of three prequarks, that is, three seats are needed for each prequark to sit in. For each seat, it can be either empty (Vacutron) or occupied (Angultron). Thus, only four different kinds of particles can be formed:
|Generation||Particle name||Prequark Representation||Quark color||Electric Charge|
|1st||Electron||-(A, A, A1)||colorless||one (1)|
|1st||Neutrino||(V, V, V1)||colorless||0|
|2nd||Muon||-(A, A, A2)||colorless||one (1)|
|2nd||Muon neutrino||(V, V, V2)||colorless||0|
|3rd||Tau||-(A, A, A3)||colorless||one (1)|
|3rd||Tau neutrino||(V, V, V3)||colorless||0|
|Generation||Particle name||Red||Yellow||Blue||Electric Charge|
|1st||Up quark||(V, A, A1)||(A, V, A1)||(A, A, V1)||2/3|
|1st||Down quark||-(A, V, V1)||-(V, A, V1)||-(V, V, A1)||-1/3|
|2nd||Charm quark||(V, A, A2)||(A, V, A2)||(A, A, V2)||2/3|
|2nd||Strange quark||-(A, V, V2)||-(V, A, V2)||-(V, V, A2)||-1/3|
|3rd||Top quark||(V, A, A3)||(A, V, A3)||(A, A, V3)||2/3|
|3rd||Bottom quark||-(A, V, V3)||-(V, A, V3)||-(V, V, A3)||-1/3|
In Prequark theory, the quark generations are also colors (Genecolors). They obey the color complementary rules, such as 2 is the complement of (1,3) and 3 the complement of (1,2). In the 1st order, genecolor 2 can be represented as (1,3); in the 2nd order it can be represented as (1, (1,2)). Table III shows the genecolors representation in terms of complementary rules.
|Genecolor||1st order||2nd order||2nd order (simplified)|
|1||(2, 3)||(2, (1, 2))||(2, 1, 2)|
|2||(1, 3)||(1, (1, 2))||(1, 1, 2)|
|3||(1, 2)||(1, (1, 3))||(1, 1, 3)|
In physics, the validity of any theory must be verified at least by three laboratories. The prequarks reside in the quarks, and it is too small to be tested directly with today's technology. However, in February 1996, Fermi Lab. reported that they had some indirect data which support the concept of prequarks. Two years went by, there is no other laboratory second their finding. That is, we are still waiting for a traditional scientific proof about the prequark theory. However, the validity of the prequark theory can be supported by other means. One of them is that the prequark theory can explain many known physical processes and without any contradiction with any known knowledge. The followings are two such examples.
Muon decay is a well-known process. A Muon will decay into one electron, one electron neutrino and one muon neutrino. The Prequark Theory not only verifies the above process but gives much more detailed information of how exactly this process works. In Prequark Theory, a Muon -(A, A, A2) will decay into one electron -(A, A, A1), one electron neutrino (V, V, V1) and one muon neutrino (V, V, V2). Obviously, the total Angultrons are conserved. The seemingly nonconservation of Vacutrons are also conserved because Vacutron is just a vacuum (nothingness). The most important event in this reaction is the transformation of genecolor 2 to (1, 1, 2) according to the genecolor complementary rules listed in table III.
The diagram below consists four detailed steps for neutron [ u(blue), d(-red), d(-yellow)] decay.
The above diagram not only verifies the old theory that neutron decays into a proton, an electron, and an electron neutrino but gives much more detailed information of how exactly this process works.
In short, the two examples above do support the validity of Prequark Theory although the traditional laboratory proof of it is not yet here.
As I have mentioned before, the development of Prequark theory had nothing to do with Yijing in anyway but was a direct consequence of a mathematical demand that the computable universe must be expressed in a two code system, such as (0, 1) or (Angultron, Vacutron). However, it is not hard to see that the Yijing eight kwa system is a very good approximation to the Prequark Theory.
|Prequarks||(A, A, A)||(V, V, V)||(V, V, A)||(V, A, V)||(A, V, V)||(A, A, V)||(A, V, A)||(V, A, A)|
|Prequark name||Positron||Neutrino||Blue d-quark||Yellow d-quark||Red d-quark||Blue u-quark||Yellow u-quark||Red u-quark|
Of course, there are two major differences between the Yijing and the Prequark Theory.
Ancient Chinese always claimed that the laws of Yijing are the laws of life. This claim is now supported by a modern research. In the late 1940s, John Von Neumann came up an idea of automaton which is an imagined machine that processes information, proceeding logically, inexorably performing its next action after applying data received from outside itself in light of instructions programmed within itself. His idea became a new discipline -- the artificial life. In 1980, many Self-replicating Systems (SRS) were described with the concept of cellular automaton. In 1982, Dr. Stephen Wolfram used an one-dimensional cellular automaton with cells in only two possible states -- on or off, Yin or Yang. It started with an initial configuration, a row of cells turned on or off at random. This was the 1st line. A new row beneath, 2nd line, would represent the next generation.
The state of each cell in the 2nd line was determined by three neighbors of the first generation cell on the 1st line. These triplets in the 1st line have only eight possible combinations (111, 110, 101, 100, 011, 010, 001, 000) which are identical to the Yijing eight kwa system (see Table IV). The row of eight boxes on top of Figure 3 (on the left) shows the rule set: for each combination of three cells in generation 0, there is a determined result for the next-generation cell below the triplet. Beginning from a single seed, these rules are applied consistently, each generation represented by a horizontal row of cells. Figure 3 shows five generations of growth. With this, Wolfram showed that there are only two possible classes of outcome -- dead patterns (lifeless stable structures or random noise) or very complicated patterns with very complicated behavior and often long lived. Figure 4 (below) shows a comparison between the natural pattern on a mollush shell and the pattern of a simple one-dimensional cellular automaton.
Dr. Wolfram's work does support the ancient Chinese claim that the Yijing theory is a theory of life.
Biological life has many attributes: reproduction, metabolism, intelligence, etc.. Although it is very difficult to define exactly what life is, we can easily to tell what is not alive. Anything cannot process information cannot be alive. All life activities (physical, physiological or psychological) can be performed only if information can be processed. So, the ability to process information is the minimum requirement for life. It is a necessary condition, not a sufficient condition. Thus, a super computer is not yet alive.
In 1936, Alan Turing invented a Turing machine which is an ideal computer. No super computer of today can reach its capability.
In 1970, John Horton Conway wanted to find a set the simplest rules that could explode into the infinite power of a universal Turing computer. He invented a mathematical game, LIFE.
In the game of LIFE, there are many patterns appear. Most of them are stable patterns unless perturbed externally. Since every computer must have a counter, a clock, and a memory, all stable patterns will have no use in building a computer. In order to prove that the rules of LIFE (game) do support a universe in which a universal Turing computer could be embedded, it is necessary to show that LIFE (game) can generate some patterns which have a means of locomotion.
Such a walking pattern was, indeed, found in LIFE (game), and it was called glider. Glider not only walks but can reproduce itself. However, Conway must find a glider generator which can shoot out a stream of gliders in order to prove that LIFE is, indeed, a universal computer. The glider shooter was discovered by R. William Gosper at MIT in December 1970. Using glider streams to represents bits, all logic gates (And- Or-, Not-gates) can be produced. In the web site of Conway's game of Life (http://mindspring.com/~alanh/life/) by Alan Hensel, you can experience yourself how to seed a small universe to see the rise of activities of artificial life.
Life (game) occurs on a virtual Go (checker) board. The squares are called cells. They are in one of two states: alive or dead. Each cell has eight possible neighbors, the cells which touch its sides or its corners. There are only three rules.
With these three simple rules and a few randomly seeded live cells on the board, many patterns appeared. Most of them quickly settled into stable patterns. Figure 5 (below) shows such a pattern. The generation 0 consists of 4 live cells. Obviously, the two cells at each end must die of exposure in the next generation, and 4 dead cells will be born. So, generation 1 consists of 6 living cells which form a rectangular shape. Then, two middle cells in generation 1 must die of over crowding, and two dead cells will come alive to form a shape roughly resembling a beehive in the next generation. Since each live cell in beehive have exactly two live neighbors, beehive is stable unless perturbed externally.
Figure 6 (below) shows the life cycle of a glider. A glider consists of 5 live cells. From generation 0 to generation 1, it moves down one row. From generation 2 to 3, it moves to right one column. Then the most important of all, it recaptures its original form in the next generation. It is fun to work out the transformation of glider from one generation to the next by applying the rules of game of Life. Try yourself. You can also get on the Internet to visit the web sites listed above.
So, Conway, indeed, succeeded in accomplishing his original goal of trying to prove that the simple rules of Life (game) can, indeed, support a universe in which a universal Turing computer is embedded. furthermore, the glider meets the minimum requirements to be a life according to the outline listed in the previous section.
However, Life (game) is still only a game, a very complicated game perhaps, but a game nonetheless. It lacks the essence of any biological life, the mass. In fact, Life (game) does not even give the slightest hint of how the biological life arose.
But! But! But! If the glider is a graphic representation of some basic building blocks of matter (such as: proton or neutron), then Life (game) will give rise to biological life immediately. When glider captures mass, it turns into a wet stuff, the biological life.
Is this possible? In quark theory, proton can be written as Proton = [u(red), u(yellow), d(blue)]. Obviously, there is absolutely no resemblance of any kind between glider and quarks, or between glider and proton according to the quark theory which views quarks as the rock bottom building blocks of our universe.
I did not know anything about Life (game) until 1992. As soon as I saw glider, I recognized immediately that glider is, indeed, a graphic representation of proton according to Prequark theory.
In Prequark Theory, proton can be represented as follow: (see Table I and Table II)
|up (red)||(V, A, A)|
|up (yellow)||(A, V, A)|
|down||-(V, V, A)|
This is, indeed, a proton. First, it is colorless as it is required -- red + yellow + blue becomes colorless. Second, it has one electric charge (4A - a = 3A = e).
But, the most important of all is that this proton is, in fact, a glider. It is identical to the glider of generation 0 when you view V as blank spot in the Game of Life.
Although Prequark theory still lacks laboratory proofs, its validity is greatly strengthened because it can provide a perfect theory for how biological life arise.
For many years, I strongly dislike those claims which proclaim that many ancient Chinese philosophies are as good as Western science, if not better. One example claims that the relativism of Laotse is the same as the Relativity theory of Einstein while the difference between the two is about the same difference between Moon and Sun.
Against my old belief and my old emotion, I am writing this paper to proclaim that Five Walk theory is identical to the quark theory and that Yijing is much more advanced than the modern quark theory because Yijing is a very good approximation to the Prequark theory. I tried to support my claim not with slogans or declarations but with detailed facts and reasoning. If I have failed to convince you on this because my ability of writing those concepts in terms of philosophy has failed myself.
Although Yijing is much more advanced than the modern quark theory in some ways, it, nonetheless, is not a science. Yijing did not give rise to the modern technology. Yijing did not prevent China to became an under-developed country 200 years ago.
In fact, because no one was able to find any error in Yijing and Five Walk theory for two thousand years and because no error can be found in them even today, there was no chance for China to develop a western style science. That is, Yijing and Five Walk theory were not a blessing for China for the past 2000 years.
However, this paper points out that not only the East and the West share the same living planet but are sharing the same knowledge sphere. My aim is to bridge the difference between the East and the West and to enrich each other in both theories and practices. Starting by bridging the difference between the knowledge, we can then bridge the difference between cultures. Now, it is the time to do this. Now, we are able to do this. Let us do this together.