Abstract:

Introduction and the table of content:

1. Definitions -- five definitions and three operators
   1. Five definitions:
      1. Definition one -- the set UL, it encompasses "all" languages, Lx, Ly, ....
      2. Definition two -- the set Vx, it encompasses all symbols of "one" language, Lx.
      3. Definition three -- the words
      4. Definition four -- the phrases
      5. Definition five -- the sentences
      These five definitions demarcate a linguistic universe.
      
   2. Three operators --
      1. Operator of composite
      2. Operator of dot (completion)
      3. Operator of accumulations
      These three operators delineate a three layer (sphere) hierarchy.
      1. the Pre-word sphere
      2. the word/sentence sphere
      3. the post-sentence sphere
2. Six axioms --
   1. Similarity transformation axiom -- Sa
   2. Predicative axiom -- Pa
   3. Inflection axiom -- Ia
   4. Redundancy axiom -- Ra
   5. Non-Communicative axiom -- Na
   6. Exception axiom -- Ea
   These six axioms identify the language type, "type 0" and "type 1". Then, can this great divide between these two types be bridged over?
   
3. The structure of a constructed linguistic universe
   1. Three layers of hierarchy
      1. the Pre-word sphere
      2. the word/sentence sphere (context free)
      3. the post-sentence sphere (context centered)
   2. Language types, ranging from "type 0" to "type 1"
4. Comparison with the real linguistic universe
   1. Introducing the concept of "apostrophe," the type degeneration or deviation.
   2. "Type" algebra (type operation table)
   3. Comparing English and Chinese
5. The language spectrum -- ranging from "type 0" to "type 1", and all languages are distributed in this language spectrum.
   1. Two more operators:
      1. Operator of pidginning
      2. Operator of creoling
   2. Two postulates:
      1. Postulate one -- the "Operator of pidginning" transforms a language Lx toward the direction to the "type 0" language.
      2. Postulate two -- the "Operator of creoling" transforms a pidgin (Lx) toward the direction to the "type 1" language.
   3. Two predications:
      1. Predication one -- the difference of the language structure in terms of "language type" between two pidgins is smaller than the difference between two original languages
      2. Predication two -- The difference of the language structure in terms of "language type" between two creoles is smaller than the difference between it and its parent language.
6. Operator of (=F=), the functional equal
   
   1. Definition of (=F=), functionally equal
   2. Postulate three: the major known natural languages, at least the Big 6, are functionally equal in the ws-sphere.
   3. Postulate four: the Transitive Property holds for the (=F=), the functional equal.
7. Linguistic theorems
   1. 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.
   2. Theorems -- all theorems of this "constructed linguistic universe" are applied on the "real" linguistic universe and to see whether they hold or not.
      1. Theorem 1: English is a "type 1" language.
      2. Theorem 2 -- the syntax sets of two natural languages are functionally equal.
         Corollary 2.1 -- Any two natural languages (Lx and Ly) are mutually translatable.
      3. Theorem 3 -- the word sets of two natural languages are functionally equal.
         Corollary 3.1 -- Wx (Chinese) has only about 60,000 characters and Wy (English) has about one million words. Yet, Wx (Chinese) is functionally equal to Wy (English).
8. The discovery of the PreBabel principle.
   1. Law 1: Encoding with a closed set of root words, any arbitrary vocabulary type language will be organized into a logically linked linear chain.
   2. Law 2: When every natural language is encoded with a universal set of root words, a true Universal Language emerges.
9. The PreBabel procedures -- the regressive encoding
10. The Benefits of PreBabel
    1. It revolutionizes the way of language acquisition.
    2. It creates a true universal language.
11. The Conclusion

1. Definition one: Set UL = {Lx; Lx is a natural language}. So, the members of set UL are natural languages.
2. Definition two: Set Vx = {syx; syx is a symbol in Lx}.
3. Definition three: Wx is a "word" in Lx if and only if the following two conditions are met.
   1. Wx is a syx of Lx.
   2. Wx has the following attributes:
      1. Wx has a unique topological form.
      2. Wx carries, at least, one unique completed sound note.
      3. Wx carries, at least, one unique meaning.
      
      Note: In a universe, some terms are known intuitively and are not defined. In general, these terms are known via some other disciplines. The following terms are undefined.
      1. Natural language
      2. Set, member and symbol
      3. topological form
      4. Completed sound note
      5. Meaning -- meaning is, in fact, a pointing function. When, F(wx) --> y, then, y is the meaning for wx.
4. Definition four: "Operator" of composite (Opc) -- set Vx is the domain and the range for Opc. Then, Opc (syx1, syx2, ...) = syxn
   Note: there can be some laws for Opc, such as, the Commutative, Associative, Distributive Laws.
5. Definition five: "Operator" of dot (Opd) -- Opd is placed at the utmost right position of a syx. Opc cannot have any operand which carries an Opd.
6. Definition six: Sx is a "sentence" in Lx if and only if the following two conditions are met.
   1. Sx must have, at least, two wx. That is, Sx = Opc (syxa, syxb, ...).
   2. Sx must be an operand of Opd. That is, Sx = Opd (Opc (syxa, syxb, ...)).
      Note: Definition 6.a -- If Sx has only one wx, Sx = Opd (wx) is a "degenerated" sentence.
7. Definition seven: Px is a "phrase" in Lx if and only if the following two conditions are met.
   1. Px must have, at least, two wx. Px = Opc (syxa, syxb, ...)
   2. Px must "not" be an operand of Opd.
8. Definition eight: "Operator" of accumulation (Opa) -- Only "sentences" of Lx can be the operands of Opa. Opa stacks "sentences" of Lx into a linear chain.

1. Similarity transformation axiom -- a rule (theorem or law) will repeat over and over in a domain or in different levels of its hierarchy. And, it has two values;
   1. Sa = 0, similarity transformation is not active.
   2. Sa = 1, similarity transformation is active.
2. Predicative axiom -- particles in a glob (a word, a phrase or a sentence) is distinguishable. And, it has two values;
   1. Pa = 0, PA is not active.
   2. Pa = 1, PA is active.
   
   When Pa = 1, a sentence "could" be first distinguished as the "Speaker" and the "others." If Sa = 1 also, then, the "others" can be further distinguished as,
   1. action (or state) words
   2. object (things or person) words
   3. pointing words, and these can be further distinguished as,
      1. pointing the action words
      2. pointing the object words
   4. gluing words
   5. others
3. Inflection axiom -- some tags are tagged at the end of words. And, it has two values;
   1. Ia = 0, IA is not active
   2. Ia = 1, IA is active
      
4. Redundancy axiom -- For a function F, it will be applied, at least, twice on its operand. And, it has two values;
   1. Ra = 0, RA is not active
   2. Ra =1, RA is active
   Examples:
   1. Ra = 0;
      I go to school "yesterday".
      I have "three" dog.
      I love He.
      She love I.
   2. Ra = 1;
      I "went" to school yesterday.
      I have three "dogs".
      I love him.
      She loves me.
5. Non-Communicative axiom -- for (a, b) and (b, a), they are "not" the same. And, it has two values;
   1. Na = 0, NA is not active
   2. Na = 1, NA is active
   For a sentence,
   1. when Na = 0,
      (I love you) = (love you I)
      Note: If a Lx has Na = 0, it will run into some problems. Is (I love you) and (You love I) the same? Yet, there are some ways to resolve this kind of issue, and I will discuss it later.
   2. when Na = 1, then the "word order" is a rule.
6. Exception axiom -- for every rule in the universe, there is one or some exceptions. And, it has two values;
   1. Ea = 0, EA is not active
   2. Ea = 1, EA is active

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).

1. English is inflected --> Ia = 1
2. English has a "subject -- predicate" structure --> Pa = 1
3. English has parts of speech, tense, numbers, etc. --> Ra =1
4. English has word order --> Na =1

1. Many words can represent many distinct parts of speech.
2. The correct part of speech for many words cannot be decided without understanding the semantics or even the pragmatics of the context.

1. Axiom -- it is a non-logical axiom and is selected arbitrary. Its purpose is to demarcate a domain.
2. Hypothesis -- it is a statement which must be proved, generally via a theory.
3. Postulate -- it is a statement that is assumed to be true without proof and to serve as a starting point for proving other statements. In practice, a postulate must have enough evidences to support (not to prove) its validity.

1. Postulate one -- the "Operator of pidginning" transforms a language Lx toward the direction to the "type 0" language.
   Definition 9 -- the "Operator of pidginning" transforms a language Lx to a pidgin (Lx).
2. Postulate two -- the "Operator of creoling" transforms a pidgin (Lx) toward the direction to the "type 1" language.
   Definition 10 -- the "Operator of creoling" transforms a pidgin (Lx) to a creole (Lx).

1. The pre-word layer (pw - sphere)
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. This ps-sphere is governed by the "Operator" of accumulation (Opa).

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.

1. There are three different vocabulary types.
   1. Type A -- chaotic data set, most of the member of the set are stand alone without any logic or genealogical connection with other members.
   2. Type B -- axiomatic data set, the "entire" (not partial) set can be derived from:
      1. a finite number of basic building blocks,
      2. a finite number of rules.
   3. Type C -- a hybrid data set, the mixing of type A and type B.
   There is an unsolved problems in linguistics, listed in Wikipedia.
   
   [quote="Wikipedia"] What fundamental reasons explain why ultimate attainment in second language acquisition is typically some way short of the native speaker's ability, with learners varying widely in performance?[/quote]
   
   With this new discovery, this unsolved problem is, in fact, removed. Please read the article "The New Paradigm of Linguistics," at;
   http://www.chinese-word-roots.org/nparadi.htm
   
   
2. The discovery of the PreBabel principle,
   If we can find a PB set, and PB (=F=) Wx (Chinese); PB is functionally equal to the entire Chinese character set, with the "postulate 4", the transitive of (=F=),
   
   Wx (Chinese) (=F=) Wy (English)
   PB (=F=) Wx (Chinese)
   then, PB (=F=) Wy (English)
   That is, Wy (English), all English vocabulary, can also be encoded with PB.

1. Law 1: Encoding with a closed set of root words, any arbitrary vocabulary type language will be organized into a logically linked linear chain.
   
2. Law 2: When every natural language is encoded with a universal set of root words, a true Universal Language emerges.

1. How to PreBabelize a word which is unique to a language?
2. How to PreBabelize words which have unique relations in a language?
3. How to PreBabelize words which are constructed with a unique culture tradition (with special myriad prefixes and suffices) in a language?

1. Encoding a giving language, and it again has three sub-steps.
   1. Ciphering the vocabulary -- that is, every symbol in that language is ciphered. if "du" means [you] in German, then "ev" = "du" also means [you]. If there are another million [you] in German, there are a million ciphers for [you] in German. There is not a single difference between the original German and the ciphered German in terms of its structure.
   2. "Before" the ciphering, every word is encoded with two (maximally 3) of its own words with a "regressive encoding process". In fact, this is a dictionary process. In dictionary, a word is explained, in general, with a sentence or with a synonym. In this PreBabel process, a word is encoded with two words of the same language. That is, we are "making" every vocabulary carries its own dictionary. The following is one example of this "regressive encoding,"
      
      electricity (lightning, energy)
      lightning (rain, energy)
      rain (sky, water)
      sky (above, mountain)
      above (dot, horizontal bar)
      
      dot, horizontal bar, mountain and water are roots.
      
   3. Only at the "final" stroke, a very small set of the Generation 1 (the bottom base) words are encoded with the PreBabel root set. This encoding might not be all that intuitive, such as, the (dot, stop) = "at". Then, all words are "progressively ciphered." Note: the issue that "at" can perform hundreds different kinds of acts, the (dot, stop) can do the same as it is simply a cipher for "at". The internal meaning of (dot, stop) has nothing to do with its external performances. It is simply a mnemonic dictionary for the word "at."
   
   These three sub-steps are done internally in a given language. And thus, all the unique linguistic and cultural features are completely (100%) preserved in its PreBabelized system.
   
   Because that every word carries its own dictionary, the PreBabelized system revolutionizes the way of language acquisition.
   
2. Emerging the PreBabel (Proper), the true universal language -- after many languages are PreBabelized, they are sharing the same PreBabel root set for their "word forms." And, they form a big mixing pot. Every PreBabel (language x) becomes a dialect of this big mixing pot. Although the PreBabel (language x) is 100% linguistic and cultural centered in the language x, the mixing pot can sort out the conflicts and remove the duplicates. Then, the PreBabel (proper) will emerge. This process can begin after two PreBabel (language x) are done.

1. It revolutionizes the way of language acquisition.
2. It creates a true universal language.

1. deposit the information
2. recall the information

1. temporary (or short term) memory, such as the RAM
2. Long term memory

1. anchoring -- burn-in the information and its indexing file
2. webbing -- associating the new information with the anchored data, and this reduces the burn-in energy and the recalling efforts for the new information.

1. the verbal is learned with brutal anchoring efforts without any previously anchored base.
2. the written is learned with the verbal as the anchored base.

1. Chinese college graduates learn about 6,000 Chinese characters.
2. Let memory energy on these 6,000 written words be 100
3. Let memory energy on these 6,000 words on verbal (word sounds) be 100

1. Only 220 roots (+50 variants) need to be memorized with the brutal anchoring efforts. That is,
   220 / 6000 = 0.037 = 3.7%
   Yet, these 220 are much easier than any of the 6,000.
2. The 300 sound modules can be learned as derived words, and the effort is about 1/10 of by learning with the old school way.
   (300 / 6000) x (1/10) = 0.005 = 0.5%
3. The remaining 5700 words are all derived words from the above (220 + 300), and the effort is less than 1/100 (in average) of by learning with the old school way. Note: after one point (about 1,000 words learned), zero energy is needed.
   (5700 / 6000) x (1/100) = 0.0095 = 0.95%

1. Reduce a huge data set to a very small root set, and thus reduce the memory energy about 95%.
2. Provide a memory anchor for learning the verbal in learning the second language.