The Grammar
for PreBabel, the true Universal Language
Copyright © July 2009 by Tienzen (Jeh-Tween) Gong

U (English), the universal language in English, is a language that its vocabulary is encoded from the natural English with the PreBabel root words while its word inflection and English grammar stay the same. For example,
I am ing the natural English and the U (English) now.

The grammar of U (English) is the same as the grammar of its source language, the natural English. And this is the case for U (Russian), U (German), U (French), U (Chinese), etc..

However, for the U (Mother Proper), the PreBabel Proper, it should have its own grammar. As we have known, a grammar consists of two parts:
  1. list of symbols
  2. formation rules for symbols (words, terms, expressions, sentences, etc.)
For PreBabel, these two are linked together; the symbols are constructed with the formation rules. There is no way to separate the symbols from their formation rules. This is significantly different from the English grammar. The inflection of English vocabulary is, indeed, playing a big part in the formation of English sentence. However, the English sentence formation rules come alive with an own life force, and the vocabulary inflection plays only the supporting role now.

Twenty years ago, a new mathematics was invented and was called Fractal. With Fractal, a virtual universe can be constructed. In fact, the real universe was constructed with the Fractal principle, the Self-Similarity Transformation, which is a logic algorithm that replays itself over and over in many different levels. The entire PreBabel formation rule is by applying the Fractal principle, the Self-Similarity Transformation, with the following steps:
  1. initial state --- a set of roots (240 root words)
  2. forming words --- composed from root words
  3. becoming radicals --- words become radical of new words
  4. forming large words --- the word phrases, consists of a few stand alone words
  5. forming sentences --- composed of words and word phrases.
In the above formation processes, a body and a soul come alive: By definition, the Self-Similarity Transformation is a repeating process to ad infinitum. Should this process be stopped at one point, such as at the sentence level? In fact, sentence is just a larger symbol comparing to a word symbol in any linguistic system. Why should it be different from its smaller relative? In PreBabel, there is, in fact, no difference between the two in terms of their formation rule.

However, from our experience in English, the formation rules between vocabulary and sentences are completely different. The symbol form and symbol meaning of English vocabulary are brutally given as "you told me so." On the other hand, the meaning of a sentence can never be clear and certain if some additional grammatical rules are not followed.

Yet, can any sentence of PreBabel Proper always have a unique meaning without the assistance of an English-like grammar?

In the PB word formation, the sub-elements of every symbol are, in general, less than three (three roots or two radicals while each radical itself can have two to three roots). There is a little chance to mis-read the meaning from a two radical symbol. If a symbol becomes ambiguous because of its large number of roots or radicals, it should be divided into word phrases. With this strategy, the number of symbols (words or word phrases) in a sentence should not go above five. Yet, in reality, a PB sentence could be quite lengthy as each word phrase could contain three to five words while each word contains three to five radicals and each radical with three to five root words.

Yet, are we always able to guarantee a unique meaning from a five symbol (or less) sentence without the assistance of an English-like grammar?

The answer is yes. In fact, the choice of 5 is quite arbitrary while a long sentence (more than 7) do loose its elegance, not its clarity in PreBabel. And, this answer Yes does have a strong theoretical foundation, not just an opinion. The following discussion is a bit technical with some mathematic concepts. However, it could be understood by anyone who is not a mathematician.

Let's define the followings first:
With the above definitions, we now are able to answer the question "what kind of sentence will always have an attractor?" In Fractal mathematics, it provides the answer for this question with the following simple concepts and theorems.
  1. contractive --- every member in a given field converges to a fixed point (its meaning), it is contractive
  2. iterated function system (IFS) --- a process being applied repeatedly in a system
  3. Collage theorem:
    • the symbols, (a, b, c, d, e, f, g) are members of this field and are contractive
    • S is a sentence composed of those symbols S (a, b, c, d, e, f, g)
    • S is a sentence composed of those symbols S (a, b, c, d, e, f, g)
    • we can find a set of transformations (IFS) with the coefficients (s, q, u, v, w, x, y), and SF = (sa, qb, uc, vd, we, xf, yg) points to a fixed point A (in the field). "A" is the attractor of S. In terms of linguistics, it means that SF has a unique meaning.
    In fact, the word inflection, the tense, the subject-predicate structure, the numbers, etc. of English grammar are the coefficients of the above contraction operation, forcing the SF pointing to a unique attractor.
  4. Shadow theorem:
    If all members of S are contractive, and S is a random dynamical system, S is always a shadow of a deterministic system with an attractor A.

    With this shadow theorem, a S, however chaotic, is always having an attractor as long as its members are contractive.
Obviously, the inflected English words are contractive. However, it might not be the case if the inflection is removed from English vocabulary system. Thus, without the inflection, English might not be able to apply the shadow theorem. On the contrary, all PB symbols (words, radicals, word phrases, sentences, etc.) are constructed with the self-similarity operations, and they are all innately contractive. The "PB Proper" sentence can always apply the shadow theorem. In short, the PreBabel grammar consists of: Thus, the "PB Proper" sentence does not need a support of an English-like grammar for guaranteeing an attractor.