2 The Fundamental Principles of Tao
The Principle of Oneness and Field-Being Philosophy
Laotzu begins the Tao Te Ching with a concise architecture of Tao philosophy. He describes Tao in terms of its manifestations as Wu 無 and Yu 有。 He clearly states that Tao has two levels of appearances to us: we can talk about Tao at one level but the true Tao is at a higher level. He says:
道可道也非恒道也； |
Tao may be spoken but it is not the Eternal Tao. |
名可名也非恒名也。 |
Name may be given but it is not the eternal name. |
This two-level architecture is fundamental in Tao philosophy and will be treated explicitly in our formulation. There is considerable confusion in defining these two levels. Some associate these two levels of Tao with Wu and Yu and we hope to clarify the relationship of these two levels to Wu and Yu.
Let us follow Laotzu by accepting that Tao manifests itself in two modes as Wu and Yu. One mode is with the unlimited and the other mode is with the limited. Here we interpret Wu as Wu-Chi無極, which means beyond all bounds. Yu as multifaceted appearances in the world that have limits and are bound by their appearances.
Laotzu proclaims that heaven and earth begins with the Boundless and that the ten-thousand things begin with their appearances:
無，名天地之始； |
As Wu, it marks the beginning of heaven and earth; |
有，名萬物之母。 |
As Yu, it is the mother of ten thousand things. |
The boundless Wu is overwhelmingly holistic so it may seem to be absent to us. Nevertheless, Wu is not a nothing and we can immediately and certainly apprehend Wu as the Tzujan自然。 Yu can be apprehended as the appearances of the world. Both Wu and Yu are real and can be secured in our thought. These are the classical states of Tao and are can probably be described with our ordinary language.
The reality is more complicated, since Wu and Yu are not independent of each other. Their inter-dependency is hard to describe since it is beyond our ordinary senses. Laotzu manages to express this critical feature in a simple way:
恒無，欲以觀其所妙； |
In Wu, it is to show its transmuting appearance (into Yu); |
恒有，欲以觀其所徼。 |
In Yu, it is to show its transmuting disappearance (into Wu) |
This verse describes a process of disclosure of Yu and Wu in each other. Wu and Yu areco-arising and co-producing in each other. This is the fundamental dynamics of Tao philosophy. The relationship between Wu and Yu goes beyond co-arising. Laotzu proclaims that they are two simultaneous manifestations of the same Tao:
兩者同出， |
The two manifests at the same time; they are |
This concise statement reveals the Oneness <太一 of Tao. The intrinsic interactions between Wu and Yu give rise to a state of profundity 玄。 Understanding of this state of profundity is the ultimate doorway to all the mysteries of Tao:
玄之又玄， |
It is profound upon profound. |
It is the purpose of this paper to show the transcendence or profundity nature of Tao in a systematic way.
Tao manifests as Wu and Yu within bounds of Oneness. In order to model this Oneness of Tao, we may follow a common practice in sciences to �divide and then re-combine� an entity in order to reveal its structure. To follow Laotzu, we demonstrate this basic procedure by dividing Oneness of Tao into Wu and Yu, and then show how Oneness can be preserved. This is shown in Figure 1.
Let us begin with an observation of the manifestations of Wu and Yu far from the Oneness state. At this level, we can describe Tao in terms of the Classical States 傳統狀 of Yu and Wu � as the limited and the unlimited. This is the level where we may classically speak of Tao (道可道). However, we realize that these states by themselves cannot represent the true states of Tao (非恒道也). There are unsettling interactions between these classical states that make them appear certain and constantly changing.
When these two classical states are properly brought together, we may return to the Oneness state of Tao, as shown in Figure 1.
When this is achieved, the true Wu and Yu states with Oneness are called the Actual States 真實狀。 These actual states preserve the Oneness of the eternal Tao 恒道。
Figure 1 The Profound State of Oneness
The actual states are transcendental and are beyond our ordinary description. It is important to emphasize that philosophers often consider the states with Oneness as real. This is similar to the Being (What-Is) in the Greek philosophy. As emphasized by Parmenides, we should only pursue what really exists. However, such actual states exist in a transcendental way and are thus very perplexing to our ordinary senses.
The classical states may appear to our senses as concrete experiences and can be described with clarity in our ordinary language. The classical states provide a convenient way to define a domain and scope for our understanding of the world. As we shall show, these classical states should not be taken as outright illusionary, but should be treated properly with their mutual interactions. We shall introduce a model to show how Oneness can be preserved when we re-combine the classical states back into the actual states with Oneness. We call this process actualization of Oneness.
In Figure 2, we show how the two classical states of Wu and Yu interact with an interaction V to become the actual states. The classical Wu and Yu states are shown as W_{0} and Y_{0} respectively, in (a). These classical states are not stable due to the interaction. When the interaction is harmonized, the states become the actual states, as shown in (b). If the harmonization process is complete, the interaction vanishes (V_{R} =0) and the actual states become stable.
Therefore, the process of actualization is to achieve Oneness by harmonizing the interactions of the classical states. The action of harmonization is described, for example, in Chapter 4 and 10 by Laotzu as:
挫其銳解其紛 |
Blunt its sharpness and unravel its entanglements. |
[We have selected only a few verses from the Tao Te Ching as illustrations in this paper. There are many other verses to the same effect.]
Figure 2 Actualization of the Classical States
Because of the interaction, the actual states are superpositions, or mixtures, of the classical states. For this reason, the actual states may appear paradoxical to us. A reality becomes a mixture of opposites and has an uncertain nature. For example is in Chapter 58:
禍，福之所倚； |
A misfortune is where a fortune lies; |
It is confusing to describe the actual states with our everyday language because of their transcendental nature. Fortunately, the interaction model shown in Figure 2 allows us to derive a mathematical representation of such a transcendental relationship.
The classical states interact with each other, so they are inter-mixed. Similar to a quantum theory treatment of two interacting states, the actual states may be related to the Quantum Theory treatment of two interacting states, the actual states may be related to the classical states by the following mathematical expressions:
W = a W_{0} + b Y_{0} |
Eq. 1(a) |
Y = -b W_{0} + a Y_{0} |
Eq. 1(b) |
Here W and Y are the actual states of Wu and Yu, respectively. They are shown as superpositions of the classical states W_{0} and Y_{0, }of Wu and Yu respectively. The parameters, a and b, are determined by the interaction. If the interaction is strong, we have a = b, and, if the interaction is weak, we have a = 1 and b = 0.
Mathematically the actual states of Wu and Yu differ only by a phase. To draw an analogy with the holographic effect [TA92], Tao may appear as a hologram of Oneness when Tao is manifested by these two �lights of different phases.� This is an interesting way to visualize how Wu and Yu together can reconstruct Oneness of Tao.
It is also interesting to see, if we treat Tao states in a way similar to the quantum states, the measurable properties of a state are in the �probability density� (square of the state function). For example, the properties of Wu may be expressedas:� |W|^{2} = a^{2} |W_{0}| ^{2 �}+ b^{2} |Y_{0 }| ^{2 }�+ 2 ab<W_{0}|Y_{0}>. Here we have a cross term <W_{0}|Y_{0}> showing the �transmutations of the Wu and Yu.� Such property of the actual states appears mathematically and transcends our direct experiences. A mathematical representation may be our language to describe the actual states completely and consistently. The mathematical relationship presented above provides a convenient way to show the nature of Oneness.
The abstract mathematical representation should not appear intimidating to us. Eq. [1] is simply our familiar Tai-Chi 太極or Yin-Yang Diagram or �Tai-Chi Diagram 太極圖�, as shown in Figure 3. The Tai-Chi diagram represents our ancient efforts to overcome the limitations of our language by introducing such a symbol. It is indeed an accurate description of the Oneness state of Tao in terms of the actual Wu and Yu states. Figure 3 is a visual and symbolic representation of Oneness and Eq. [1] is an imageless, abstract, and formal representation of Oneness. The advantage of an abstract mathematical relationship is that we may manipulate the mathematical expression to show other relations not obvious to our direct observations.
Figure 3 Symbolic Representation of Oneness
This is a symbol that can represent the Oneness relationship between any two interacting opposites, such as Yin and Yang or Wu and Yu. The interconnection between Wu and Yu is a result of Yin-Yang interchange and preserve the same relationship shown in this diagram.
As in any scientific theory, symmetry plays a fundamental part. In our model, Oneness has a complete symmetry in Wu and Yu. Such symmetry is formally shown in this paper, but it has been recognized in [WA04] as a way to produce a more consistent interpretation of the Tao Te Ching. With such observation, we may interpret Chapter 11 with clarity:
卅輻共一轂， |
With thirty spokes connected to the hub, |
This symmetry of Oneness should be recognized in Tao philosophy. Our model may be extended to all pair-wise categories, such as Tao and vessel 道與器, substance and function 體與用, name and essence 名與實, body and soul, etc.�
Our interaction model can adequately represent Laotzu�s concept of two-level Tao philosophy. The actual states transcend above the classical states. We may view the classical states as our horizontal experiences and theactual states as the vertical transcending experiences. The classical states appear impermanent and the actual states appear as unchanging reality. There is no inconsistency in seeing an unchanging reality together with the ever-changing appearances. For a mathematical illustration of this, sin(x) and cos(x) curves never cease to change, but their combination, sin^{2}(x) + cos^{2}(x) =1, is a constant. It is not inconceivable that a transcendental reality remains constant while our classical experiences are always in flux.
We have stated that the classical states are not necessarily illusionary. However, if we let the classical states assume their own independent realities, we violate the Principle of Oneness. Paradoxes will appear when Oneness is not observed.
As an example, let�s use the familiar �chicken and egg� paradox. We commonly divide the whole �chicken-egg� entity into two classical forms of chicken and egg and assume they are distinct and exclusive of each other. In this case, the paradoxical question of �which comes first?� will appear as though with plausible meaning.
We may now understand this paradox occurs because we have violated the Principle of Oneness by ignoring the inherent interactions between �chicken� and �egg.� Separated chicken and egg are illusionary. Their actual forms must preserve the concept of wholeness: a chicken bearing the seed for egg and an egg bearing the seed for chicken. They are always encoded within each other. The paradox arises only due to the limitations of our language, which is built on the classical experience of our daily life. At the actual state level, the paradoxes will not occur.
Many other paradoxes may be shown as due to the same fallacy with broken Oneness. Even the famous paradoxes of Zeno may be shown simply due to the fact that time, speed, and distance are treated as independent. If time, speed, and distance were treated with Oneness, the paradoxes will not appear.