Day fifty-three -- Constructed linguistic universe (VI)

      From Tienzen:
      Thus far, we have made the following points.
      A. The constructed language universe has three layers of hierarchy.

      First, we should have a bird eyes view on this constructed language universe first. In fact, it has three layers (levels) of hierarchy.
         1. The pre-word layer (pw - sphere) -- this sphere is, in fact, not defined thus far in this constructed language universe. Yet, it will be the vital sphere for PreBabel. And, it will be added later.
         2. The word/sentence layer (ws - sphere) -- this sphere has three sub-layers
               1. the word sphere
               2. the phrase sphere
               3. the sentence sphere
            This ws-sphere is governed (or delineated) by two operators, "Operator" of composite (Opc) and "Operator" of dot (Opd).
         3. The post-sentence layer (ps - sphere) -- this sphere is context and culture laden or centered. In fact, the Sapir-Whorf hypothesis is defined in this sphere, and thus it is a major interest of our discussion. This ps-sphere is governed by the "Operator" of accumulation (Opa).

      Thus, each sphere is governed or delineated by operators. In this post, I will discuss only the ws-sphere. And, we can "derive" some theorems and laws now. [/quote]

      The pw-sphere is not yet defined. The ps-sphere is context (history, culture, etc.) centered, and thus, there should be some fundamental differences among different languages in this ps-sphere.

      B. Thus far, our discussion is centered on ws-sphere, and I have reached the following points.
         1. There are different languages which have different language structures, ranging from "type 0" to "type 1".
         2. By introducing two operators, "Operator of pidginning" and "Operator of creoling", the great divide between the "type 0" and the "type 1" can be bridged over. That is,
               1. The "type 0" is the ground (or default) state.
               2. The "type 1" is the excited (or higher energy) state. And, the transition between the two states can be achieved with two operators, "Operator of pidginning" and "Operator of creoling". Thus, a "hypothesis one" is suggested.

      Tienzen: Hypothesis one -- this "constructed linguistic universe" forms a linear language spectrum, ranging from the "type 0" to the "type 1". That is, all natural languages are distributed in this language spectrum, and this "constructed linguistic universe" encompasses the entire "real" linguistic universe. [/quote]

      In order to prove that the "Hypothesis one" is true, we must construct a theory for it. And, I will start this with a definition.

      Definition eleven (11) -- Lx and Ly are different sets (with different symbols and different numbers of symbols). Z is a Range Set. F is a (arbitrary) function.
      if, F (Lx) = Z, (F maps Lx to Z)
      and F(Ly) = Z, then
      Lx and Ly are "functionally equal". And it is written as, Lx (=F=) Ly

      With this definition on (=F=), functionally equal, we can make a new postulate.

      Postulate three -- Lx and Ly are different natural languages in the ws-sphere, then
      Lx (=F=) Ly
      That is, the major known natural languages, at least the Big 6, are functionally equal in the ws-sphere.

      Note: This "postulate three" does not cover other spheres, as the Lx and Ly might not be functionally equal in the ps-sphere which is history and culture centered.

      The "postulate three" will play a vital role in our construction of this "constructed linguistic universe" and in our process of verifying the "hypothesis one."

Signature --
PreBabel is the true universal language, it is available at