The Formal Language

THE FORMAL LANGUAGE OF THE METAPHYSICAL

by Sun Yu-li

'So-called space is actually something which can be held by man. It is something that is created by man. However, how can man show the presence of space? It can only be done when he introduces Metaphysical Moulds into his world. Metaphysical Moulds link the mind and the form. The application is the birth of language. Shi Zuo-Cheng

THE UNFOLDING OF SPACE
- Zero-Dimensional Space
  It is a non-space. It has no elements. Nothing can be registered.
- One-Dimensional Space
  It is a linear space. its element is a dot. A position can be registered.
- Two-Dimensional Space
  it is a planar space. Its elements are a dot and a line. A length can be registered
- Three-Dimensional Space
  it is a volumed space. its elements are a dot, a line and a plane. An area can be registered.
THE COMPONENTS OF SPACE
- Space is the co-existence of two sub-spaces which are different but complementing in nature.
  Topological Space -- a conceptual space (C-Space)
  
  Geometrical Space --a structural space (S-Space)
THE ELEMENTS OF C-SPACE AND S-SPACE
1. C-Space Elements
  - The Conceptual Dot (CD)
    A CD only indicates a position in a space. It has no length, width nor depth.
  - The Conceptual Line (CL)
    A CL is formed when a CD extends itself. It has a length but has no width nor depth.
  - The Conceptual Plane (CP)
    A CP is formed when a CL extends sideway. It has a length and a width but has no depth.
    
    Fig.1
2. S-Space Elements
  - The Structural Plane (SP)
    The SP is the surface of a three-dimensional volume in space. It has a length and a width but has no depth.
  - The Structural Line (SL)
    The SL is the meeting line of two SPs. It has a length but has no width nor depth.
  - The Structural Dot (SD)
    The SD is the meeting point of three SPs. It has no length, width nor depth.
    
    Fig.2
THE RELATIONSHIP BETWEEN C-SPACE AND S-SPACE ELEMENTS
- Twin Genesis of the Basic Elements
  The initial two CD and SD co-exist infinitely close to each other as different but complementing dots. The CD is a condensation of the Topological or C-Space and the SD is the condensation of the Geometrical or S-Space.
  
  The two dots, CD and SD, are the Basic Elements because it is from them that the respective lines, CL and SL, and planes, CP and SP, are derived.
- Active and Reactive Nature of the Basic Elements
  a. The CD is an Active Element. It always initiates a change.
  
  b. The SD is a Reactive Element. It always and only reacts to a change initiated by a CD.
- Derivative Elements (CL, SL, CP AND SP)
  The constructing and transforming of the Basic Elements and the Derivative Elements form:
  
  Conceptual Graph (C-Graph) in C-Space
  
  Structural Graph (S-Graph) in S-Space
RULES OF CONSTRUCTION AND TRANSFORMATION
1. Rules of Construction for Conceptual Graphs (C-graph)
  - A CD can remain at its position, unchanged (Fig. 1, Fig. 2).
  - A CD can extend from its position, forms a CL(Fig. 1, step 1), stops at another position, and establishes another CD(Fig. 1, step 2).
    
    Fig.3
  - A CD can extend from its position, forms a CL, loops back to its original position(Fig. 2, step 1), and establishes another CD which merges with the original CD, and a CP is created(Fig. 2, step 2).
    
    Fig.4
2. Rules of Transformation for Structural Graphs (S-graph)
  - An SD will always remain at its position, unchanged and will always and only react to a change initiated by a CD(Fig. 3, Fig. 4).
  - A CL formed must be intersected once and only once by an SL formed by a reacting SD which loops back to its original position(Fig.' 3, step 1), and establishes another SD which merges with the original CD and a SP is created(Fig. 3, step 2).
  - In every CP, there should exist one and only one SD which cuts across CL(Fig. 4, step 1), stops at another position, and establishes another SD(Fig.4. step 2).
There is a type of Graph called " Planar Graph and its Dual ". Any given pair of corresponding Planar Graph and its Dual Graph should respectively satisfy the Rule : D + P-2 = L. This type of Graph with its Rule was found by 18th Century mathematician Leonnard Euler. The C-graph is in fact Euler's planar Graph and the S-graph Euler's Dual Graph. So the CS-graph is Euler's Planar Graph with its Dual.

There are tens of other type of Graphs, each with dots, lines and planes as elements and all have their own expanding rules in Graph Theory. However, Planar Graph and its Dual is the only type of Graph that no mathematician has ever been able to find the formula which can calculate the possible number of Planar Graph and its Dual in existence, given a fixed number of dots, lines and planes. May this formula never be known to man? The reason behind it is intriguing.
DERIVING THE FRAMEWORK OF THE FORMAL LANGUAGE
The framework below shows how C-graphs and S-graphs are derived, and combined as a CS- graphs, by applying the Rules that have been established.

*representing a stabilized Graph

a stabilized C-graph should satisfy the Rule: CD+CP-2=CL

a stabilized S-graph should satisfy the Rule: SD+SP-2=SL

a stabilized CS-graph is obtained only when both C-graph and S-graph are stabilized.

According to Graph Theory, a CD or SD, outside of a stabilized graph, is at infinity(oo).
THE BASIC METAPHYSICAL MOULDS
The combined stabilized CS-graphs are the basic Metaphysical Moulds.
THE FORMAL LANGUAGE OF THE METAPHYSICAL
The Metaphysical Moulds are infinite in number and are the concrete forms of the Formal Language of the Metaphysical.

The CLs or SLs, outside of the Metaphysical Moulds (Stabilized CS-graph), are linked to one (and only one) CD or SD at infinity(oo).

Reference : "Topological Organization of Architectural Spaces" by Jean Cousin

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