PreBabel Chapter two

 

One,

Summary of PreBabel Chapter two:

Purpose:
The article explores the theory and methodology for constructing a true universal language, called PreBabel, aiming to overcome the limitations of natural languages and create a system that is easy to learn, universally applicable, and capable of auto-translation across all languages.

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Key Points

1. Criteria for a Universal Language:

• Scope: Must match at least one natural language in capacity.
• Learnability: Should be mastered to a high literacy level by an average person in 300 hours (3 hours/day for 100 days).

2. Vocabulary Challenge:

• Natural languages use arbitrary word forms ("blobs") that are hard to decode and memorize.
• A root-word system, where all vocabulary is built from a limited set of root words and is self-revealing, could solve this problem—but selecting and limiting the number of roots is difficult.

3. Grammar Challenge:

• Universal language grammar must encompass all natural language grammars or not differ significantly.
• The article proposes that if all natural languages are dialects of the universal language, learning it becomes much easier for everyone.

4. Methodology: Begetting the Mother from Her Baby (BMFB):

• Reverse-engineering a universal language by identifying and substituting necessary attributes of a natural language (English is used as the example).
• Attributes are sorted into "Mother bag" (universal features) and "Baby bag" (language-specific features).

5. Formalized Language Structure:

• Describes a toy language ("T") with syntactic, semantic, and pragmatic systems.
• Explains how meaning and truth conditions arise in language, and how formal rules can be systematized.

6. Substitution Techniques:

• Transform verbs into action-nouns, use paired sentence structures (body + grammar tag), and reduce word order ambiguity with word-phrasing (hyphens and parentheses).
• These substitutions are placed in the "Mother bag" to form the basis of the universal language.

7. Construction of the Universal (Mother Proper):

• The "Mother Proper" language uses only b-words (root-based words), eliminates inflections, and relies on word-phrasing for sentence formation.
• All vocabulary is built from 240 specially designed root words, making meanings transparent and learnable.

8. Dialects and Auto-Translation:

• Each natural language can have a "U-version" (e.g., U-English, U-Chinese), which is a dialect of the Universal Mother Proper.
• The system enables auto-translation by mapping words and grammar tags between dialects.

9. Meeting Design Criteria:

• The universal language matches the scope of natural languages and is much easier to learn due to its root-word system.
• It is both a silent (ideographic) and spoken language, with pronunciation assigned by the user community.

10. Conclusion:

• PreBabel (Universal Mother Proper) meets the criteria for a universal language and can serve as the foundation for an auto-translation machine, potentially revolutionizing global communication.

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In essence:
The article proposes a universal language system, PreBabel, built from a small set of root words and formalized grammar rules, designed to be easy to learn, universally applicable, and capable of seamless translation between all natural languages.

 

Two,

How PreBabel Differs from Natural Languages

PreBabel is designed as a universal language system with several key differences from natural languages:

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1. Vocabulary Construction

• Natural Languages:
  Vocabulary is largely arbitrary; words are "blobs" whose meanings must be memorized because their forms do not reveal their meanings (e.g., "love" means love only because it was taught that way).
• PreBabel:
  All vocabulary is constructed from a limited set of root words (240 in total, in the case for Chinese language). Each word is a combination of these root words, making its meaning transparent and self-revealing. This drastically reduces the memorization burden and makes learning much easier.

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2. Grammar and Structure

• Natural Languages:
  Grammar can be complex, with features like tenses, inflections, subject-predicate structures, and irregularities. These complexities vary widely between languages and can make learning difficult for non-native speakers.
• PreBabel:
  Grammar is formalized and mechanized. Sentences use a paired structure: a body (the main sentence) and a grammar tag (S-tag) that encodes grammatical information (tense, voice, etc.). Word order ambiguity is reduced using word-phrasing techniques (hyphens and parentheses), making sentence meaning clear regardless of word sequence.

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3. Learning Efficiency

• Natural Languages:
  Mastery requires memorizing thousands of arbitrary words and complex grammar rules, often taking years.
• PreBabel:
  Designed to be mastered in 300 hours of study by an average person. The root-word system and formalized grammar make it much easier and faster to learn.

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4. Universality and Dialects

• Natural Languages:
  Each language is distinct, and translation between them is complex due to differences in vocabulary and grammar.
• PreBabel:
  Functions as a "mother language" from which all natural languages can be seen as dialects. Each natural language can have a "U-version" (e.g., U-English, U-Chinese), which is a dialect of PreBabel. This structure enables seamless auto-translation between languages.

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5. Silent and Spoken Language

• Natural Languages:
  Primarily spoken and written, with pronunciation and spelling rules.
• PreBabel:
  Is both a silent (ideographic) and spoken language. Root words are ideographs and silent, but pronunciation can be assigned by the user community, making it adaptable to different linguistic backgrounds.

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6. Auto-Translation Capability

• Natural Languages:
  Translation requires complex mapping and often loses nuance.
• PreBabel:
  Enables the construction of an auto-translation machine, mapping words and grammar tags between dialects with precision, reducing ambiguity and cultural barriers.

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In summary:
PreBabel differs from natural languages by using a transparent root-word system, formalized grammar, paired sentence structures, and universal design principles that make it easier to learn, translate, and adapt across cultures.

 

Three,

Detailed Explanation of the BMFB Methodology ("Begetting the Mother from Her Baby")

The BMFB methodology is a reverse-engineering approach proposed for constructing a universal language by extracting its "mother language" from an existing natural language. Here’s how it works, step by step:

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1. Select a Natural Language as the Starting Point

• The process begins by choosing a natural language (e.g., English) as the "baby" language from which the universal "mother" language will be derived.

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2. List All Attributes of the Selected Language

• Identify and enumerate all the attributes (features, rules, vocabulary, grammar, etc.) of the chosen natural language.

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3. Substitute Attributes with Universal Mechanisms

• For each attribute, determine if it can be replaced by a more universal mechanism (U).
• If an attribute (Ar) can be substituted by a universal mechanism (U) without changing the system, place U in the "Mother bag" and Ar in the "Baby bag". [
• If an attribute cannot be substituted, place it in both bags.

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4. Fill the Mother Bag and Baby Bag

• After processing all attributes, you end up with two bags:
• Mother bag: Contains universal mechanisms and substituted features.
• Baby bag: Contains the original features of the natural language.

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5. Analyze the Mother Bag

• The "Mother bag" is hypothesized to contain the genetic code of the universal language.
• By examining the contents of the Mother bag, you can identify the universal features that could serve as the foundation for a universal language. [

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6. Apply to Other Languages

• The same BMFB procedure can be applied to other natural languages (e.g., Russian, Chinese) to extract their respective "mother bags."
• The ultimate goal is to find a universal "mother proper" that is embedded in all natural languages. [

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7. Construct the Universal Language

• The universal language is constructed by combining the universal mechanisms found in the Mother bag, such as:
• Root-word vocabulary system
• Paired sentence structures (body + grammar tag)
• Word-phrasing techniques
• Mechanized grammar rules

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8. Test and Refine

• The methodology is iterative: If a substitution or guess is incorrect, it can be revised and tested again.
• The process is designed to be flexible and adaptive, allowing for continuous refinement. [

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Summary Table: BMFB Steps

Step	Description
1	Select a natural language as the "baby"
2	List all attributes of the language
3	Substitute attributes with universal mechanisms where possible
4	Fill "Mother bag" (universal features) and "Baby bag" (original features)
5	Analyze the "Mother bag" for universal language features
6	Apply to other languages to find common universals
7	Construct the universal language from the "Mother bag"
8	Test, refine, and iterate

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Key Insights

• Reverse-engineering: Instead of comparing languages directly, BMFB extracts universal features from within a single language.
• Substitution, not subtraction: The process substitutes features but does not remove or add anything to the original system, preserving structural integrity. [
• Universality: The methodology aims to uncover the genetic code of a universal language that is present in all natural languages.

 

  

Four,

Here’s an example of how the BMFB methodology ("Begetting the Mother from Her Baby") works with a specific English language feature—verbs:

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Step-by-Step Example: Substituting the Verb Class in English

1. Identify the Feature

• In English, verbs are a distinct grammatical class, separate from nouns and pronouns. They carry tense, voice, and other grammatical information.

2. Propose a Universal Mechanism

• The BMFB methodology asks: Can the verb class be substituted with a universal mechanism without changing the system’s expressive power?
• The proposal is to replace all English verbs with action nouns and just three universal verbs: "do," "be," and "not". [

3. Apply the Substitution

• Original English sentence:
  I sing a song.
• BMFB substituted sentence:
  I do sing a song.
  Here, "do sing" is treated as an action noun, and "do" is one of the universal verbs. This substitution is grammatically correct in English, though slightly awkward. [

4. Place Features in Bags

• The new mechanism (action nouns + three universal verbs) is placed in the Mother bag (universal features).
• The original English verb class is placed in the Baby bag (language-specific features). [

5. Result

• The expressive power of English is preserved, but the verb system is now universalized and simplified. This makes it easier to learn and apply across different languages.

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Further Example: Paired Sentence Structure

• Original English sentence:
  I had eaten dinner when you came.
• BMFB substituted sentence:
  (I eat dinner when you come, papf)
  Here, "papf" is a grammar tag indicating "past perfect tense." The sentence is split into a body ("I eat dinner when you come") and a tag ("papf").
• The paired structure (body + grammar tag) goes into the Mother bag; the original tense structure remains in the Baby bag. [

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Summary Table: BMFB Applied to English Verbs

English Feature					BMFB Substitution								Mother Bag								Baby Bag
Verb class					Action nouns + "do, be, not"								Yes								Yes (original verbs)
Tense structure					Grammar tag (S-tag)								Yes								Yes (original tense)

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In essence:
BMFB systematically substitutes English-specific features with universal mechanisms, preserving expressive power but simplifying and standardizing the system for universal application.

 

 

PreBabel Chapter one

 

One,

Here’s a bulleted summary of the key points from PreBabel one.docx:

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Key Points

• Purpose of the Book: Explores PreBabel, a proposed universal and perfect language, and addresses foundational questions about language, linguistics, and the diversity of human languages.
• Definition of Language: A system (T) is a language if it can describe a universe (U). The scope of language depends on the size and nature of U, ranging from simple sets to the entire natural universe.
• Levels of Universes and Language Systems:
• U1: Computable universe (describable by a two-token system)
• U2: Computable + uncomputable universe (requires more complex language)
• U3: Adds countable infinity
• U4: Adds uncountable infinity
• Beyond U4: Realms like God (Christianity), Nirvana (Zen), and paradoxes (Gödel’s theorems) are considered unreachable by any real language system.
• Ideal Language: Defined as a language capable of describing what is beyond the largest conceivable universe (U4).
• Human Natural Language (HNL): Claimed to be able to describe even the “weird” universes (paradox, God, Nirvana), making it a candidate for the perfect language. However, the definition and proof of HNL’s capacity are complex and discussed in detail.
• Martian Language Thesis (MLT): Any human language can establish communication with Martian-like languages, implying all languages share a universal meta-language. This meta-language consists of universal laws, universal consciousness, and symbol systems connecting them.
• Consequences of MLT:
• All HNLs are equal in capacity
• Translation among all HNLs is guaranteed
• A universal language is possible in principle.
• Spider Web Principle (SWP): Languages start with total freedom, but once the first rule or morpheme is set, internal consistency and structure emerge, leading to diversity among languages.
• Types of Human Natural Languages:
• Type 0: Non-inflectional
• Type 1: Inflectional
• Spectrum between 0 and 1, with efficiency differences among types.
• Ideal Language Attributes:
• Finite tokens can construct unlimited vocabulary
• Pronunciation and meaning of words are readable from their structure.
• Translation Table Problem: Translating among thousands of languages is complex, but using a “center master” language can drastically reduce the number of required translation tables.
• Closed Encoding Set (CES): Discovery of a CES enables encoding of any HNL, making universal translation and the construction of a virtue language (universal language) possible.
• Chinese Language Case Study:
• Historical efforts to Romanize Chinese and criticisms of traditional Chinese morphology
• Author’s counter-argument: Chinese written system is highly efficient when understood through etymology, enabling rapid mastery of thousands of characters.
• Linguistics Scope: Linguistics principles (Large Complex System Principle, LCSP) apply to all complex systems, not just language, and can unify disciplines like physics, math, and social sciences.
• Universal Human Language: Despite failures of projects like Chomsky’s Universal Grammar, the author argues that a universal human language is ontologically possible through PreBabel.

 

Two,

Here are more detailed insights on the Martian Language Thesis (MLT) from PreBabel one.docx:

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Martian Language Thesis (MLT) – Detailed Explanation

• Core Idea:
  The MLT posits that any human natural language (HNL) can always establish communication with Martian or Martian-like languages. This means that all languages, regardless of origin, share a common meta-language that enables mutual understanding and translation.
• Meta-language Components:
  The meta-language consists of four key parts:
1. Universal Laws (Physics, Math, etc.): These are the foundational principles that describe all universal events.
2. Universal Consciousness (Meaning): Human consciousness interprets universal laws in an identical way, resulting in shared meaning across languages.
3. Grand Canyon (Gap): There is a significant gap between universal laws and universal consciousness.
4. Symbol Systems: Human languages are different symbol systems that bridge the gap between universal laws and consciousness.
• Illustrative Example:
  The document uses a scenario where a human meets a Martian and offers gifts (apple, orange), each named in their own language. Through repeated exchanges, a translation table is built, enabling communication. This demonstrates that languages can connect through shared experiences and translation mechanisms.
• Definition of Human Natural Language (HNL):
  HNL is defined as a system based on a universal meta-language to express or describe world events. This definition underpins the claim that all HNLs are fundamentally equal in their expressive capacity.
• Consequences of MLT:
1. Equal Capacity: All HNLs have the same expressive power.
2. Guaranteed Translation: Translation among all HNLs is always possible.
3. Universal Language Possibility: The existence of a universal language is possible in principle.
• Levels of Human Natural Language:

• Base: Syntaxes to describe universal laws and world events; semantics to interpret those syntaxes.
• Dress: The choice of symbols or tokens (phonology, morphology, pragmatics) used to represent the base. The “dress” varies, but the underlying capacity remains equal.

• Freedom and Efficiency:

• There is no freedom in choosing the base (all HNLs are equal in capacity), but infinite freedom in choosing the “dress.” This leads to differences in efficiency among languages, and the possibility of defining a “perfect efficient HNL” or THE perfect language.

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Summary:
The Martian Language Thesis is a foundational principle in the document, asserting that all human languages are built on a universal meta-language, enabling mutual translation and equal expressive capacity. The thesis supports the possibility of a universal language and explains linguistic diversity as a matter of symbolic representation (“dress”), not underlying capability.

 

Three,

Addressing Apparent Criticisms of the Martian Language Thesis (MLT)

• Historical Debates (e.g., Chinese Romanization Movement):
• The document presents historical debates—such as the Chinese Romanization movement and the view that not all languages are equal in scope or efficiency—not as shortcomings of the Martian Language Thesis (MLT), but as examples of the old paradigm. These perspectives arise from a lack of understanding of the MLT. The MLT, as proposed, redefines linguistic equality and universality, showing that such historical skepticism is rooted in pre-PreBabel thinking, not in any flaw of the thesis itself. [PreBabel one | Word]
• Limits of Language (God, Nirvana, Paradoxes):
• References to realms like God, Nirvana, or paradoxes being unreachable by language are also part of the old paradigm. The document argues that these are traditional beliefs held before the introduction of PreBabel and the MLT. The MLT and PreBabel provide a new framework that addresses or transcends these supposed limits, rather than being constrained by them. [PreBabel one | Word]
• Defining Human Natural Language (HNL):
• The difficulty in defining HNL is not a flaw of the MLT or PreBabel, but a limitation of previous linguistic paradigms. The PreBabel framework, through the MLT, offers a new, more precise definition of HNL, resolving ambiguities that existed before. [PreBabel one | Word]
• Summary of the Author’s Position:
• What may appear as criticisms of the MLT are, in the author’s view, misunderstandings or limitations of earlier linguistic theories. The MLT and PreBabel are presented as solutions to these old problems, not as being subject to them.

 

Four,

Here’s a detailed explanation of the Spider Web Principle (SWP) as described in PreBabel one.docx:

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Spider Web Principle (SWP) – Detailed Explanation

Core Concept

• The SWP is used to explain the origin and diversity of human natural languages (HNLs).
• It states that the initial conditions for creating a language are completely arbitrary—there is total freedom or symmetry in where and how a language can begin.

Breaking of Symmetry

• As soon as the first element (such as a morpheme or grammar rule) is established in a language, this total freedom is broken.
• The first “thread” (rule or morpheme) determines the location or context (e.g., America, Europe, Asia).
• The second thread defines the center of the language.
• The third thread confines its scope.
• After these initial choices, the language enters a system governed by internal consistency (a Gödel system), and total freedom is lost.

Implications for Language Structure

• Every language develops its own internal framework and rules, regardless of the universal freedom at the outset.
• Universal grammar exists at two levels:
1. Universal Level: Total freedom—any language can choose its grammar arbitrarily.
2. Language-Specific Level: Once choices are made, they become a “contract” among speakers, forming a set of internal rules and structureRelationship to Martian Language Thesis (MLT)

• The SWP complements the MLT by explaining why languages, despite having equal capacity (as per MLT), end up being so different in practice.
• The SWP guarantees that all HNLs have infinite freedom in choosing their “dress” (phonology, morphology, pragmatics), but once a choice is made, the language is permanently confined by its internal logic.

Infinite Freedom and Spectrum

• The freedom to choose the “dress” of a language is infinite, but once a choice is made, the language is confined to a specific framework.
• In number theory, the scope of infinite choices ([1, ∞]) can be expressed as [0, 1], meaning the diversity of languages can be represented as a spectrum between two extremes.

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Summary:
The Spider Web Principle (SWP) explains that while the creation of a language starts with total freedom, every subsequent choice (morpheme, grammar rule) reduces that freedom and establishes a unique, internally consistent framework. This principle accounts for the vast diversity among human languages, even though they all share the same foundational capacity as described by the Martian Language Thesis.

 

Five,

Here’s a detailed description of the Closed Encoding Set (CES) as presented in PreBabel one.docx:

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Closed Encoding Set (CES) – Detailed Description

What is CES?

• The CES is a finite, closed set of root words or codes that can be used to encode an entire human natural language (HNL).
• If such a set exists, it enables the construction of a “virtue language” (universal language) and serves as the foundation for PreBabel’s universal translation system.

Why is CES Central?

• Criterion: If a CES can encode one HNL, it can encode all HNLs, based on the Martian Language Thesis (MLT).
• Consequence: With CES, translation among all languages becomes systematic and efficient, and a universal language (PreBabel) can be constructed.

Properties and Verification

• The vocabulary of any HNL is finite, so the encoding process can be fully checked and verified, both theoretically and practically.
• The existence of CES is a binary issue: if it can encode one HNL, PreBabel is possible; if not, the theory fails.

How is CES Identified?

• The search for CES involves analyzing the consequences it produces:
• Every word’s meaning should be readable from its structure (face).
• This becomes the sole criterion for identifying a valid CES.

Practical Example: Chinese Language

• Gong claims to have found a CES for the Chinese written system, allowing mastery of 60,000 characters by learning only 220 root words and 300 sound modules.
• This system enables rapid learning and decoding of meaning and pronunciation, demonstrating the power and efficiency of CES.

Steps Enabled by CES

1. Encode one HNL: Prove CES works for one language.
2. Encode all HNLs: By MLT, CES can encode any language.
3. Construct Virtue Language: Use CES to build a universal language for translation.
4. Verification: The finite vocabulary allows complete verification of CES’s effectiveness.

Theoretical and Practical Impact

• CES transforms translation from a massive combinatorial problem (millions of translation tables) into a manageable system centered on a universal code set.
• It provides a concrete foundation for PreBabel’s claim to universality and efficiency in language encoding and translation.

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Summary:
The Closed Encoding Set (CES) is the cornerstone of PreBabel. It is a finite set of root codes that can encode any human language, making universal translation and the construction of a virtue language possible. Its existence is both theoretically and practically verifiable, and it resolves the complexity of language diversity by providing a unified encoding system.

 

Six,

Here’s how the three pillars—Closed Encoding Set (CES), Spider Web Principle (SWP), and Martian Language Thesis (MLT)—interconnect and form a consistent framework in Gong’s Linguistics Theory of Everything (ToE), especially for human natural languages:

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Interconnectedness and Consistency of CES, SWP, and MLT

1. Martian Language Thesis (MLT)

• Foundation: Asserts that all human natural languages (HNLs) share a universal meta-language, enabling mutual translation and equal expressive capacity.
• Implication: Guarantees that any HNL can communicate with any other, including hypothetical Martian languages, because they all operate on the same meta-linguistic principles.

2. Spider Web Principle (SWP)

• Mechanism of Diversity: Explains how languages, despite starting with total freedom (universal grammar), become unique and internally consistent as soon as the first linguistic choices (morphemes, grammar rules) are made.
• Result: Each language develops its own structure (“dress”), but the underlying capacity (as per MLT) remains equal. SWP accounts for the infinite diversity of languages while maintaining their foundational equivalence.

3. Closed Encoding Set (CES)

• Universal Encoding: Proposes that a finite, closed set of root codes can encode any HNL. If CES exists for one language, it can be extended to all, enabling systematic translation and the construction of a universal language (PreBabel).
• Verification: The CES is practically and theoretically verifiable, providing a concrete mechanism for universal translation and language learning.

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How They Interconnect

• MLT provides the theoretical foundation for universal capacity and translation among languages.
• SWP explains the emergence of diversity and internal structure in languages, showing that while “dress” (surface features) varies, the “base” (capacity) is consistent.
• CES operationalizes the theory, offering a practical method to encode, translate, and unify all languages under a single system.

Together:

• MLT ensures all languages are fundamentally translatable and equal in expressive power.
• SWP accounts for why languages look and function differently, without contradicting their underlying equivalence.
• CES makes the universal translation and construction of a virtue language possible, fulfilling the promise of MLT and accommodating the diversity explained by SWP.

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Do They Form a True Linguistics ToE?

Consistency:

• The three pillars are logically consistent: MLT sets the universal principle, SWP explains diversity, and CES provides the practical encoding mechanism. Each supports and reinforces the others.

Completeness:

• Gong’s framework addresses both the theoretical and practical aspects of language: universality, diversity, and translation. It claims to unify all human natural languages under a single, testable system.

Testability:

• The CES is verifiable in practice (e.g., with the Chinese language example), making the theory not just philosophical but actionable.

Scope:

• The theory encompasses the full range of linguistic phenomena, from the abstract (meta-language, universality) to the concrete (language structure, translation tables).

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Conclusion:
Gong’s Linguistics ToE, built on CES, SWP, and MLT, presents a unified, consistent, and testable framework for understanding and operationalizing human natural languages. It claims to resolve old paradigm limitations and offers a comprehensive approach to linguistic universality and diversity.

 

Seven,

Here’s a comparative analysis of Gong’s three pillars—Closed Encoding Set (CES), Spider Web Principle (SWP), and Martian Language Thesis (MLT)—with traditional linguistic theories:

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1. Closed Encoding Set (CES)

Gong’s View:

• Proposes a finite, closed set of root codes that can encode any human natural language (HNL), enabling systematic translation and the construction of a universal language.

Traditional Linguistics:

• Traditional theories (e.g., generative grammar, structuralism) do not posit a universal, finite set of roots for all languages. Instead, they focus on language-specific rules, morphemes, and lexicons.
• Universal Grammar (UG, Chomsky) suggests innate grammatical structures, but not a closed, practical encoding set for all languages.

Key Difference:

• CES is operational and verifiable; UG is abstract and not directly implementable for translation or encoding.

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2. Spider Web Principle (SWP)

Gong’s View:

• Explains that while the creation of a language starts with total freedom, each linguistic choice (morpheme, grammar rule) reduces that freedom, leading to unique, internally consistent frameworks for each language.

Traditional Linguistics:

• Structuralism and functionalism recognize that languages develop unique structures and rules, but do not frame this as a process of symmetry breaking from total freedom.
• Typological linguistics studies diversity, but does not attribute it to a universal “symmetry breaking” event.

Key Difference:

• SWP provides a dynamic, system-theoretic explanation for diversity, whereas traditional theories describe diversity as a result of historical, social, or cognitive factors.

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3. Martian Language Thesis (MLT)

Gong’s View:

• Asserts that all HNLs share a universal meta-language, guaranteeing mutual translation and equal expressive capacity. Any HNL can communicate with any other, including hypothetical Martian languages.

Traditional Linguistics:

• Universal Grammar posits deep structural similarities, but does not guarantee practical mutual translatability or equal expressive power.
• Linguistic relativity (Sapir-Whorf) argues that languages shape thought and may not be fully translatable.
• Typological and comparative linguistics recognize universals, but also emphasize differences and translation challenges.

Key Difference:

• MLT is more optimistic and operational about universality and translation than most traditional theories, which often highlight limits and differences.

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Summary Table

Pillar	Gong’s Theory (PreBabel)	Traditional Linguistics
Closed Encoding Set	Finite, universal root set for encoding all HNLs; practical, testable, translation-ready	No universal encoding set; focus on language-specific rules or innate grammar (UG)
Spider Web Principle	Diversity arises from symmetry breaking after initial choices; internal consistency	Diversity explained by history, society, cognition; no symmetry-breaking model
Martian Language Thesis	All HNLs share a meta-language; guaranteed translation and equal capacity	Universal Grammar posits deep similarities, but not guaranteed translation; relativity highlights differences

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Do Gong’s Pillars Form a True Linguistics ToE?

• Unified Framework: Gong’s pillars are designed to be mutually reinforcing and to cover universality, diversity, and practical translation.
• Testability: The CES, in particular, is verifiable in practice, which is rare among traditional ToE proposals.
• Contrast: Traditional theories often focus on either universality (UG) or diversity (relativity, typology), but rarely both in a single, operational framework.

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In summary:
Gong’s CES, SWP, and MLT together offer a more operational, testable, and unified approach to linguistic universality and diversity than traditional theories, which tend to separate these concerns or leave them abstract.

 

 

 

The proof of the abc conjecture

The abc conjecture: there are a finite number of c (= a + b), for

c > rad (abc)^ (1+ ε)

Or

c < K ε x rad (abc)^ (1+ ε) for ALL c.

Let a = d +/- d1 = (p^n x dp) +/- d1; dp is the largest prime for d; d1 is the smallest integer for a to have a d.

Example: a = 17 = 18 – 1 = (3^2x 2) -1; 18 = d, d1 = -1, p = 3, n = 2

Doing the same for b and c;

    b = e +/- e1 = (q^m x ep) +/- e1

    c = f +/- f1 = (w^k x fp) +/- f1

The +/- can be replaced with + only while push – into the d1 (or f1, e1) if necessary.

So, the rad (abc) = rad (a) rad (b) rad (c)

For rad (c) >= c, f1 ≠ 0 is the necessary condition.

For c >= rad (abc), f1 = 0 is the necessary condition; that is, c cannot be a prime.

The sufficient condition (SC): rad (abc) = pqw (dp x ep x fp) < C

Some scenarios can be evaluated for this sufficient condition.

Scenario 1: if d1 = e1 = 0 and there is a h1 (a natural number) while 1 < h1 < min {n, m, k}, then SC = true

Scenario 2: if d1 = 0 and there is a h2 (a natural number) while 1 < h2 < min {n, m, k}, then SC = true

Scenario 3: if e1 = 0 and there is a h3 (a natural number) while 1 < h3 < min {n, m, k}, then SC = true

Scenario 4: all other cases (the uncertainty).

All four cases, the SC = true.

For any give c (with f1 = 0, not a prime), there are S1 (meeting scenario 1), S2, S3 and S4.

Let S = S1 + S2 + S3 + S4

Now, {rad (abc) < c} = {for any c (not a prime, f1 = 0), is S finite?}

A cop out way for the answer is by tossing a coin (selecting an arbitrary c): head = true; tail = false.

Then, the P (S) = {tail (50%), head (50%)} after infinite many tosses.

Now, we can make a cheating weight (ε >  0, a real number) and add it to rad (abc) side as {rad (abc) ^ (1+ ε)}.

With this cheating weight on the rad side as {rad (abc)^ (1+ ε) < C}, the P (S) = {tail (< 50%), head (> 50%)} of each toss.

After N tosses, P (S, N) = {tail (~ 0), head (~100)}; that is, for any c (a real number while a + b = c) there is always a N (ε) for each ε (a real number) to ensure that

{N (ε) x rad (abc)^ (1+ ε) > c}, N (ε) is the number of toss needed for that (ε).

The above process can be proved in four steps: induction (operational) progressive process.

First, making the above simple tossing (selecting an arbitrary c doing the actual search) process into a game, as follow.

Every game consists of T (=10) tosses, which produces (i tails, j heads), T = i + j = 10 in this case.

So, P (SC = true) = j/T, P (SC = false) = i/T, P the possibility of SC

   ΔP = P (SC = false) - P (SC = true),

   If ΔP > 0, abc conjecture is false.

   If ΔP < 0, abc conjecture is true

Let G = 1 when ΔP < 0; G = 0 when ΔP >= 0

This game will be repeated N times.

When N = 1, G1 = (0 or 1)

N = 2, G2 = (0 or 1)

…

N = n, Gn = (0 or 1)

Let G’n = (number of 1) – (number of 0); {(number of 1) + (number of 0) = n}

Theorem 1: If G’n > 0 for all n > N (ε), (N (ε) a large number > 0), then abc conjecture is true.

Second, the cheating: a cheating weight ε is added on one side of the tossing coin.

That is:    ΔX = {rad (abc)^ (1+ ε) - rad (abc)} = rad (abc)^ε

First principle (the indeterminacy): when ΔX = 0, the average of ΔP = 0 after n games (n x T tosses) when n is a large number.

Theorem 2: when ΔX > 0, the average of ΔP < 0 after n games (n x T tosses) when n is large. (This can be proved by actual calculation and search with a finite n).

Third, the induction proof of theorem 1 and 2: in the above, we have proved n = 1 and n = n. Now, by proofing that n = n + 1 is true, the theorem is proved with induction.

Fourth, going beyond the induction: is there a math ghost rascal which can sabotage the above induction proof?

The answer is no: a cheating game cannot be sabotaged even by a ghost rascal; see the ghost rascal conjecture.

      Ghost-rascal conjecture --- For a coin flipping (tossing) game (head vs tail), T is the number times flip as one ‘game’, N is the number times that that ‘game’ is played. If T >= 10 and N >= 10^500, then no amount of sabotage from a Ghost can change the outcome of this game.

See, Ghost-rascal conjecture and the Ultimate Reality

http://prebabel.blogspot.com/2014/02/ghost-rascal-conjecture-and-ultimate.html

That is, the induction proof of theorem 2 with a large n cannot be sabotaged by any math ghost rascal.

With this ghost-rascal guarantee, there is always an N (ε) for each ε (a real number) to ensure that {N (ε) x rad (abc) ^ (1+ ε) > c} for ALL c (= a + b), N (ε) is the number of toss needed for that (ε).

The abc conjecture is now proved.

But what does this abc conjecture mean in the number (or physics) system?

Equation of Wonder: bigger the ΔX, smaller the ΔP < 0.

For every c (= a + b)

Let a = d +/- d1 = (p^n x dp) +/- d1; dp is the largest prime for d; d1 is the smallest integer for a to have a d.

      b = e +/- e1 = (q^m x ep) +/- e1

      c = f +/- f1 = (w^k x fp) +/- f1

Then {p, q, w, dp, ep, fp, d1, e1, f1, n, m, k} are the players for the dynamics of rad (abc).

 Let Q be the dynamics of rad (abc) on those players.

With ΔX (on rad (abc)), there will be a ΔQ.

Corollary 1: ΔQ = | h/ ΔP |; the larger |ΔP < 0| is, the stronger the possibility that abc conjecture is true. That is, the larger |ΔP < 0| is, the smaller ΔQ is.

Now, the equation of wonder can be rewritten as:

        ΔQ = h/ ΔX or (ΔQ x ΔX = h), h is a real number and should be a constant.

|ΔP < 0| = h/ ΔQ is the possibility of whether there is infinite SC {sufficient condition (SC): rad (abc) = pqw (dp x ep x fp) < c} for an arbitrary c (= a + b).

That is, |ΔP < 0| = h/ ΔQ really defines the internal radical/prime dynamics for SC?

The equation {ΔQ x ΔX = h} shows that ΔP (internal radical/prime dynamics) is confined by ΔX (the cheating weight). 

More info about this Equation of Wonder, see the derivation of physics uncertainty equation via the number system at {Multiverse bubbles are now all burst by the math of Nature, http://prebabel.blogspot.com/2013/10/multiverse-bubbles-are-now-all-burst-by.html }.

What is language?

Someone said: {Linguistics has four levels: Phonology, Morphology, Syntax & Semantics referred to as the formal linguistics. The issue of linguistics having three folds is contestable and arguable.}

He is kind of right in terms of human natural languages but is wrong in linguistics.

Someone also said: {only angel’s language is perfect}. This is wrong.

For these two comments, I decided to write a very brief discussion here about {what linguistics (language) is}.

While most of the members of this forum are human language linguists, I will discuss this linguistics issue in its rightful scope (much bigger than the human languages). You (the readers) need not get into it too deep. But a superficial understanding of the SCOPE of linguistics is necessary even for discussing the human languages.

For a system T, it is a language if it can describe a system U (universe).

In general, U is not T. However, U is T is still meeting the above definition. Yet, this self-mapping will not be discussed here.

With the above definition, the FIRST question will be {what is the smallest T?}

Example: T has only one token, such as {1}. U has three members: {apple, orange, egg}

Can T describe U? The answer is Yes.

For apple = 1

Orange = 11

Egg = 111

So, the system T (with only one token) can be a language for U (with three members).

The next question is {what is the biggest U?}

How about U = the entire natural universe.

However, we do not truly know what the {entire nature universe} is and thus are unable to deal with it analytically.

Fortunately, we can describe some known universes.

U1 = computable universe; everything (members) in U1 is computable

U2 = U1 (computable) + un-computable universe; some members in U2 are not reachable by any computing algorithm.

U3 = U2 + countable infinite universe;

U4 = U3 + uncountable infinite universe

Then, the third question will be {what kind of language system is needed for those universes?}

Can the above T {1, with only one token} be the language of U1?

The answer is NO.

Yet, there is a math theorem (proved) that a two token system can be the language for U1. That is, T2 = {two tokens, such as (0, 1), (yin, yang), (man, woman), etc.}. This is a proven math theorem, and I thus will not provide any further explanation here. But, most of the high school students today know that only two codes are needed for all computing universe.

Then, can the language T2 describe the U2 (including the un-computable)? Anyone who can read definition knows the answer right the way. It is a big NO.

Then, what kind of language system is needed for U2, U3, and U4?

The answers are:

For U3, T3 must have 4-codes.

For U4, T4 must have 7-codes.

Again, you (the readers) need not get into the above too deep, just understanding that the above issues are parts of linguistics.

With the above, we, now, have the 4th question: {is the U4 the biggest U (universe)?} And, can T4 (the language of U4) be able to describe a U bigger than U4?

The MOST of answers is NEGATIVE.

In Christian theology, God is totally incomprehensible (thus only faith can reach God); that is, God is beyond the U4 and T4 (the largest human language).

In Zen Buddhism, the highest wisdom (the Nirvana) is beyond the description of human language (T4) and can be reached only via kōan.

In math, there are Gödel’s incompleteness theorems, saying that there is always a math statement outside of the entire math universe.

The three above show that there is something unreachable by the largest REAL language system. That is, we can now define {what is the ‘perfect language’?}.

{Perfect language is a language which can describe ‘that thing’ which is beyond the U4.}

With a clear definition, we now can address the issue of ‘perfect language (PL)’.

Is PL an ontological reality? If it is, how can we show it?

For a linguist who studies human natural language only, he needs not to get into the depth of the above issues. But the above issues nonetheless are the foundations of ALL (any) linguistics.

The key points of my book {Linguistics Manifesto} discuss the above issues. I strongly discourage the readers to read that book. However, if you are interested in some detailed arguments, it is available at many Ivy League university libraries (such as Harvard, Columbia, Cornell, etc.; see https://www.worldcat.org/title/linguistics-manifesto-universal-language-the-super-unified-linguistic-theory/oclc/688487196 ).

The conclusion is that the HUMAN natural language is bigger than the entire math universe and is able to describe ‘that something’ of Zen Nirvana or of God of Christian.

That is, we can now not only describe the ontological issue of ‘perfect language’ but is about the perfect language in terms of human natural language.

The universal language, the dream of all linguists;

Key for AI  and computational …

God said: there was a PreBabel (universal) language.

Here it is; see my new book {PreBabel --- The universal and perfect language}.

A review copy is now available at https://tienzengong.files.wordpress.com/2018/03/prebabel-the-universal.pdf