Abstract:
For a long time, science has been divided into different disciplines for study and research. However, from a structural perspective, mathematics, physics, and chemistry are not merely independent bodies of knowledge; they may also exhibit a recursively unfolding structural pattern.
This article applies the triadic framework of Point (•), Line (｜), and Circle (Ο), proposed in Universal Law, to provide a structural interpretation of modern science. It suggests that chemistry is closest to the Point structure, focusing on the generation and composition of matter; mathematics is closest to the Line structure, emphasizing relationships, deduction, and formal connections; and physics is closest to the Circle structure, focusing on systems as a whole and the governing principles of the universe.
Further analysis indicates that each scientific discipline also contains its own Point–Line–Circle structures, which continue to unfold recursively into lower levels, forming a fractal-like hierarchy. Science is therefore not merely a collection of knowledge, but a continuously evolving structural system.
Keywords: Universal Law; Scientific Structure; Recursive Systems; Fractal Science; Mathematics; Physics; Chemistry; Point–Line–Circle Structure.
________________________________________
I. The Overall Triadic Structure of Science
From a macroscopic perspective, modern science may be viewed as exhibiting three major structural tendencies:
Universal Law
Structural Characteristic
Representative Discipline
• Point：Generation, Composition, Fundamental Units of Existence
Chemistry
｜ Line：Relationships, Deduction, Connection
Mathematics
Ο Circle：Systems, Laws, the Integrated Universe
Physics
1.1 Point Science (•)
Representative Discipline: Chemistry
Core Structure: Elements → Reactions → Compounds
Emphasis:
· Composition
· Generation
· Transformation
Chemistry fundamentally asks: How is matter formed?
Therefore, it exhibits a strong Point-oriented structure.
In other words, chemistry studies how complex structures emerge from fundamental units.
1.2 Line Science (｜)
Representative Discipline: Mathematics
Core Structure: Axioms → Reasoning → Theorems → Theories
Emphasis:
· Relationships
· Calculation
· Logical Connections
Mathematics fundamentally asks: How does structure unfold?
Therefore, it exhibits a strong Line-oriented structure.
In other words, mathematics derives one relationship from another through formal reasoning.
1.3 Circle Science (Ο)
Representative Discipline: Physics
Core Structure: Local Phenomena → Unified Laws → Cosmic Systems
Emphasis:
· Symmetry
· Closure
· Unification
From Newtonian mechanics to General Relativity, and from quantum theory to modern attempts at unified field theories, physics has continually sought a comprehensive explanation of the universe.
Therefore, it exhibits a strong Circle-oriented structure.
In other words, physics attempts to unify local laws into a coherent universal system.
________________________________________
II. Recursive Unfolding Within Scientific Disciplines
Similar to religion and philosophy, each scientific discipline continuously reproduces the three structures of Point (•), Line (｜), and Circle (Ο) within itself.
2.1 Internal Structure of Chemistry
Overall: Chemistry → •
Internal Structure:
• Elements
｜ Reactions
Ο Compounds
Correspondence:
· Point: Elements
· Line: Reactions
· Circle: Compounds
2.2 Internal Structure of Mathematics
Overall: Mathematics → ｜
Internal Structure:
• Probability
｜ Algebra
Ο Geometry
Correspondence:
· Point: Probability
· Line: Algebra
· Circle: Geometry
2.3 Internal Structure of Physics
Overall: Physics → Ο
Internal Structure:
• Quantum Theory
｜ Electromagnetism
Ο Gravitation
Correspondence:
· Point: Quantum Theory
· Line: Electromagnetism
· Circle: Gravitation
________________________________________
III. The Fractal Structure of Science
Science
├─ Point Science
│ ├─ Point
│ ├─ Line
│ └─ Circle
├─ Line Science
│ ├─ Point
│ ├─ Line
│ └─ Circle
└─ Circle Science
├─ Point
├─ Line
└─ Circle
Further Expansion:
Point
↓
Point–Line–Circle
Line
↓
Point–Line–Circle
Circle
↓
Point–Line–Circle
This process continues recursively.
Thus, every scientific structure contains a miniature reflection of the whole.
________________________________________
IV. Correspondence with the Three Scientific Volumes
Life Intelligence Wave
↓
Metastructural Unification (Mathematics Volume)
↓
Metastructural Unification (Physics Volume)
↓
Metastructural Unification (Chemistry Volume)
Correspondence:
Universal Law
Scientific Function
Work
• Point
Generative Structure
Chemistry Volume
｜ Line
Formal Structure
Mathematics Volume
Ο Circle
Cosmic Structure
Physics Volume
Together they form a scientific recursion: Point → Line → Circle
________________________________________
V. Conclusion
If religion emphasizes sacred structures, and philosophy emphasizes structures of thought,
then science emphasizes structures of nature.
From the perspective of Point (•), Line (｜), and Circle (Ο):
· Chemistry focuses on how matter is generated.
· Mathematics focuses on how structures unfold.
· Physics focuses on how the universe is unified.
These disciplines are not isolated from one another. Rather, they explore the same fundamental questions at different scales:
· How does existence arise?
· How does existence evolve?
· How does existence become unified?
Final Summary
The differences among the sciences lie in their objects of study, yet their deeper patterns may reflect a common recursive structural language:
The Point generates existence; the Line connects existence; the Circle unifies existence; and every Circle ultimately gives birth to a new Point.
________________________________________
References
Primary Sources
1. John Chang (Hai Zhi Tao). Universal Law.
2. John Chang (Hai Zhi Tao). Grand Ultimate Theory.
3. John Chang (Hai Zhi Tao). Life Intelligence Wave: Unifying Mathematics, Physics and Chemistry.
4. John Chang (Hai Zhi Tao). Metastructural Unification (Mathematics Volume): Unifying Algebra, Geometry and Probability.
5. John Chang (Hai Zhi Tao). Metastructural Unification (Physics Volume): Unifying Electromagnetism, Gravitation and Quantum Theory.
6. John Chang (Hai Zhi Tao). Metastructural Unification (Chemistry Volume): Unifying Reactions, Compounds and Elements.
Mathematics References:
7. Euclid. Elements.
8. David Hilbert. Foundations of Geometry.
9. Bertrand Russell. Principles of Mathematics.
10. George Pólya. Mathematics and Plausible Reasoning.
Physics References:
11. Isaac Newton. Philosophiæ Naturalis Principia Mathematica.
12. James Clerk Maxwell. A Treatise on Electricity and Magnetism.
13. Albert Einstein. Relativity: The Special and General Theory.
14. Richard Feynman. The Feynman Lectures on Physics.
Chemistry References:
15. Antoine Lavoisier. Elements of Chemistry.
16. Dmitri Mendeleev. Principles of Chemistry.
17. Linus Pauling. The Nature of the Chemical Bond.
18. Peter Atkins. Atkins' Physical Chemistry.
Systems, Complexity, and Structural Studies:
19. Ludwig von Bertalanffy. General System Theory: Foundations, Development, Applications.
20. Norbert Wiener. Cybernetics: Or Control and Communication in the Animal and the Machine.
21. Ilya Prigogine. Order Out of Chaos.
22. Benoit Mandelbrot. The Fractal Geometry of Nature.
23. Stephen Wolfram. A New Kind of Science.
Suggested Further Reading:
24. The Road to Reality.
25. Gödel, Escher, Bach.
26. The Structure of Scientific Revolutions.
27. The Sciences of the Artificial.
当今科学的分形结构和分层递归 —--从 “点•、线｜、圆Ο” 宇宙法则看科学系统的层级展开
摘要:
长期以来，科学通常被划分为不同学科进行研究。然而，如果从结构视角观察，数学、物理学和化学并不仅仅是彼此独立的知识体系，而是呈现出一种递归展开的结构规律。
本文借助《宇宙法则》提出的 “点（•）—线（｜）—圆（Ο）”三元结构，对现代科学进行一种结构性分析。研究认为：化学更接近点结构，关注物质的生成与组成；数学更接近线结构，关注关系、推演与形式连接；物理学更接近圆结构，关注系统整体及宇宙运行规律。
进一步分析表明，每一门科学内部同样存在点、线、圆三种结构，并不断向下递归展开，从而形成类似分形（Fractal）的层级体系。科学不仅是一组知识集合，也是一种持续展开的结构系统。
关键词：宇宙法则；科学结构；递归系统；分形科学；数学；物理学；化学；点线圆结构
________________________________________
一、科学的整体三元结构
从宏观层面观察，现代科学可以表现出三种主要结构倾向：
宇宙法则
结构特征
代表学科
• 点
生成、组成、存在单元
化学
｜ 线
关系、推演、连接
数学
Ο 圆
系统、规律、整体宇宙
物理学
1.1 点科学（•）
代表：化学
核心关注：元素 → 反应 → 化合物
强调：
· 组成
· 生成
· 转化
化学关注的是：“物质如何形成？”
因此具有明显的点结构特征。
即：从基本单元出发生成复杂结构。
1.2 线科学（｜）
代表：数学
核心关注：公理 → 推理 → 定理 → 理论
强调：
· 关系
· 演算
· 逻辑连接
数学研究的是：“结构如何展开？”
因此具有明显的线结构特征。
即：从一个关系推导另一个关系。
1.3 圆科学（Ο）
代表：物理学
核心关注：局部现象 → 统一规律 → 宇宙系统
强调：
· 对称
· 闭合
· 统一
从牛顿力学到广义相对论，再到量子理论与统一场探索，物理学始终试图建立一个完整的宇宙解释体系。
因此表现出圆结构特征。
即：将局部规律统一为整体系统。
________________________________________
二、科学内部的递归展开
与宗教和哲学类似。
每门科学内部仍然不断出现：点（•）;线（｜）;圆（Ο） 三种结构。
2.1 化学内部结构
整体：Chemistry → •
内部：
• Elements
｜ Reactions
Ο Compounds
对应：
点：元素
线：反应
圆：化合物
2.2 数学内部结构
整体：Mathematics → ｜
内部：
• Probability
｜ Algebra
Ο Geometry
对应：
点：概率
线：代数
圆：几何
2.3 物理学内部结构
整体：Physics → Ο
内部：
• Quantum Theory
｜ Electromagnetism
Ο Gravitation
对应：
点：量子
线：电磁
圆：引力
________________________________________
三、科学的分形结构
Science
├─ Point Science
│ ├─ Point
│ ├─ Line
│ └─ Circle
├─ Line Science
│ ├─ Point
│ ├─ Line
│ └─ Circle
└─ Circle Science
├─ Point
├─ Line
└─ Circle
进一步展开：
Point
↓
Point-Line-Circle
Line
↓
Point-Line-Circle
Circle
↓
Point-Line-Circle
不断递归。
因此：每一个科学结构都包含整体结构的缩影。
________________________________________
四、与三卷科学著作的对应
Life Intelligence Wave
↓
Metastructural Unification (Mathematics Volume)
↓
Metastructural Unification (Physics Volume)
↓
Metastructural Unification (Chemistry Volume)
对应：
宇宙法则
科学功能
著作
•
生成结构
Chemistry Volume
｜
形式结构
Mathematics Volume
Ο
宇宙结构
Physics Volume
形成：Point → Line → Circle 的科学递归。
________________________________________
五、结论
如果宗教强调神圣结构；
哲学强调思想结构；
那么科学强调自然结构。
从点•、线｜、圆Ο的角度看：
· 化学关注物质如何生成；
· 数学关注结构如何展开；
· 物理学关注宇宙如何统一。
三者并非彼此孤立，而是在不同尺度上探索同一个问题：
存在如何形成？
存在如何演化？
存在如何统一？
最终总结一句：科学的差异存在于研究对象，而其深层规律可能体现为同一种递归结构语言——点形成存在，线连接存在，圆统一存在，而每一个圆又孕育新的点。
For a long time, science has been divided into different disciplines for study and research. However, from a structural perspective, mathematics, physics, and chemistry are not merely independent bodies of knowledge; they may also exhibit a recursively unfolding structural pattern.
This article applies the triadic framework of Point (•), Line (｜), and Circle (Ο), proposed in Universal Law, to provide a structural interpretation of modern science. It suggests that chemistry is closest to the Point structure, focusing on the generation and composition of matter; mathematics is closest to the Line structure, emphasizing relationships, deduction, and formal connections; and physics is closest to the Circle structure, focusing on systems as a whole and the governing principles of the universe.
Further analysis indicates that each scientific discipline also contains its own Point–Line–Circle structures, which continue to unfold recursively into lower levels, forming a fractal-like hierarchy. Science is therefore not merely a collection of knowledge, but a continuously evolving structural system.
Keywords: Universal Law; Scientific Structure; Recursive Systems; Fractal Science; Mathematics; Physics; Chemistry; Point–Line–Circle Structure.
________________________________________
I. The Overall Triadic Structure of Science
From a macroscopic perspective, modern science may be viewed as exhibiting three major structural tendencies:
Universal Law
Structural Characteristic
Representative Discipline
• Point：Generation, Composition, Fundamental Units of Existence
Chemistry
｜ Line：Relationships, Deduction, Connection
Mathematics
Ο Circle：Systems, Laws, the Integrated Universe
Physics
1.1 Point Science (•)
Representative Discipline: Chemistry
Core Structure: Elements → Reactions → Compounds
Emphasis:
· Composition
· Generation
· Transformation
Chemistry fundamentally asks: How is matter formed?
Therefore, it exhibits a strong Point-oriented structure.
In other words, chemistry studies how complex structures emerge from fundamental units.
1.2 Line Science (｜)
Representative Discipline: Mathematics
Core Structure: Axioms → Reasoning → Theorems → Theories
Emphasis:
· Relationships
· Calculation
· Logical Connections
Mathematics fundamentally asks: How does structure unfold?
Therefore, it exhibits a strong Line-oriented structure.
In other words, mathematics derives one relationship from another through formal reasoning.
1.3 Circle Science (Ο)
Representative Discipline: Physics
Core Structure: Local Phenomena → Unified Laws → Cosmic Systems
Emphasis:
· Symmetry
· Closure
· Unification
From Newtonian mechanics to General Relativity, and from quantum theory to modern attempts at unified field theories, physics has continually sought a comprehensive explanation of the universe.
Therefore, it exhibits a strong Circle-oriented structure.
In other words, physics attempts to unify local laws into a coherent universal system.
________________________________________
II. Recursive Unfolding Within Scientific Disciplines
Similar to religion and philosophy, each scientific discipline continuously reproduces the three structures of Point (•), Line (｜), and Circle (Ο) within itself.
2.1 Internal Structure of Chemistry
Overall: Chemistry → •
Internal Structure:
• Elements
｜ Reactions
Ο Compounds
Correspondence:
· Point: Elements
· Line: Reactions
· Circle: Compounds
2.2 Internal Structure of Mathematics
Overall: Mathematics → ｜
Internal Structure:
• Probability
｜ Algebra
Ο Geometry
Correspondence:
· Point: Probability
· Line: Algebra
· Circle: Geometry
2.3 Internal Structure of Physics
Overall: Physics → Ο
Internal Structure:
• Quantum Theory
｜ Electromagnetism
Ο Gravitation
Correspondence:
· Point: Quantum Theory
· Line: Electromagnetism
· Circle: Gravitation
________________________________________
III. The Fractal Structure of Science
Science
├─ Point Science
│ ├─ Point
│ ├─ Line
│ └─ Circle
├─ Line Science
│ ├─ Point
│ ├─ Line
│ └─ Circle
└─ Circle Science
├─ Point
├─ Line
└─ Circle
Further Expansion:
Point
↓
Point–Line–Circle
Line
↓
Point–Line–Circle
Circle
↓
Point–Line–Circle
This process continues recursively.
Thus, every scientific structure contains a miniature reflection of the whole.
________________________________________
IV. Correspondence with the Three Scientific Volumes
Life Intelligence Wave
↓
Metastructural Unification (Mathematics Volume)
↓
Metastructural Unification (Physics Volume)
↓
Metastructural Unification (Chemistry Volume)
Correspondence:
Universal Law
Scientific Function
Work
• Point
Generative Structure
Chemistry Volume
｜ Line
Formal Structure
Mathematics Volume
Ο Circle
Cosmic Structure
Physics Volume
Together they form a scientific recursion: Point → Line → Circle
________________________________________
V. Conclusion
If religion emphasizes sacred structures, and philosophy emphasizes structures of thought,
then science emphasizes structures of nature.
From the perspective of Point (•), Line (｜), and Circle (Ο):
· Chemistry focuses on how matter is generated.
· Mathematics focuses on how structures unfold.
· Physics focuses on how the universe is unified.
These disciplines are not isolated from one another. Rather, they explore the same fundamental questions at different scales:
· How does existence arise?
· How does existence evolve?
· How does existence become unified?
Final Summary
The differences among the sciences lie in their objects of study, yet their deeper patterns may reflect a common recursive structural language:
The Point generates existence; the Line connects existence; the Circle unifies existence; and every Circle ultimately gives birth to a new Point.
________________________________________
References
Primary Sources
1. John Chang (Hai Zhi Tao). Universal Law.
2. John Chang (Hai Zhi Tao). Grand Ultimate Theory.
3. John Chang (Hai Zhi Tao). Life Intelligence Wave: Unifying Mathematics, Physics and Chemistry.
4. John Chang (Hai Zhi Tao). Metastructural Unification (Mathematics Volume): Unifying Algebra, Geometry and Probability.
5. John Chang (Hai Zhi Tao). Metastructural Unification (Physics Volume): Unifying Electromagnetism, Gravitation and Quantum Theory.
6. John Chang (Hai Zhi Tao). Metastructural Unification (Chemistry Volume): Unifying Reactions, Compounds and Elements.
Mathematics References:
7. Euclid. Elements.
8. David Hilbert. Foundations of Geometry.
9. Bertrand Russell. Principles of Mathematics.
10. George Pólya. Mathematics and Plausible Reasoning.
Physics References:
11. Isaac Newton. Philosophiæ Naturalis Principia Mathematica.
12. James Clerk Maxwell. A Treatise on Electricity and Magnetism.
13. Albert Einstein. Relativity: The Special and General Theory.
14. Richard Feynman. The Feynman Lectures on Physics.
Chemistry References:
15. Antoine Lavoisier. Elements of Chemistry.
16. Dmitri Mendeleev. Principles of Chemistry.
17. Linus Pauling. The Nature of the Chemical Bond.
18. Peter Atkins. Atkins' Physical Chemistry.
Systems, Complexity, and Structural Studies:
19. Ludwig von Bertalanffy. General System Theory: Foundations, Development, Applications.
20. Norbert Wiener. Cybernetics: Or Control and Communication in the Animal and the Machine.
21. Ilya Prigogine. Order Out of Chaos.
22. Benoit Mandelbrot. The Fractal Geometry of Nature.
23. Stephen Wolfram. A New Kind of Science.
Suggested Further Reading:
24. The Road to Reality.
25. Gödel, Escher, Bach.
26. The Structure of Scientific Revolutions.
27. The Sciences of the Artificial.
当今科学的分形结构和分层递归 —--从 “点•、线｜、圆Ο” 宇宙法则看科学系统的层级展开
摘要:
长期以来，科学通常被划分为不同学科进行研究。然而，如果从结构视角观察，数学、物理学和化学并不仅仅是彼此独立的知识体系，而是呈现出一种递归展开的结构规律。
本文借助《宇宙法则》提出的 “点（•）—线（｜）—圆（Ο）”三元结构，对现代科学进行一种结构性分析。研究认为：化学更接近点结构，关注物质的生成与组成；数学更接近线结构，关注关系、推演与形式连接；物理学更接近圆结构，关注系统整体及宇宙运行规律。
进一步分析表明，每一门科学内部同样存在点、线、圆三种结构，并不断向下递归展开，从而形成类似分形（Fractal）的层级体系。科学不仅是一组知识集合，也是一种持续展开的结构系统。
关键词：宇宙法则；科学结构；递归系统；分形科学；数学；物理学；化学；点线圆结构
________________________________________
一、科学的整体三元结构
从宏观层面观察，现代科学可以表现出三种主要结构倾向：
宇宙法则
结构特征
代表学科
• 点
生成、组成、存在单元
化学
｜ 线
关系、推演、连接
数学
Ο 圆
系统、规律、整体宇宙
物理学
1.1 点科学（•）
代表：化学
核心关注：元素 → 反应 → 化合物
强调：
· 组成
· 生成
· 转化
化学关注的是：“物质如何形成？”
因此具有明显的点结构特征。
即：从基本单元出发生成复杂结构。
1.2 线科学（｜）
代表：数学
核心关注：公理 → 推理 → 定理 → 理论
强调：
· 关系
· 演算
· 逻辑连接
数学研究的是：“结构如何展开？”
因此具有明显的线结构特征。
即：从一个关系推导另一个关系。
1.3 圆科学（Ο）
代表：物理学
核心关注：局部现象 → 统一规律 → 宇宙系统
强调：
· 对称
· 闭合
· 统一
从牛顿力学到广义相对论，再到量子理论与统一场探索，物理学始终试图建立一个完整的宇宙解释体系。
因此表现出圆结构特征。
即：将局部规律统一为整体系统。
________________________________________
二、科学内部的递归展开
与宗教和哲学类似。
每门科学内部仍然不断出现：点（•）;线（｜）;圆（Ο） 三种结构。
2.1 化学内部结构
整体：Chemistry → •
内部：
• Elements
｜ Reactions
Ο Compounds
对应：
点：元素
线：反应
圆：化合物
2.2 数学内部结构
整体：Mathematics → ｜
内部：
• Probability
｜ Algebra
Ο Geometry
对应：
点：概率
线：代数
圆：几何
2.3 物理学内部结构
整体：Physics → Ο
内部：
• Quantum Theory
｜ Electromagnetism
Ο Gravitation
对应：
点：量子
线：电磁
圆：引力
________________________________________
三、科学的分形结构
Science
├─ Point Science
│ ├─ Point
│ ├─ Line
│ └─ Circle
├─ Line Science
│ ├─ Point
│ ├─ Line
│ └─ Circle
└─ Circle Science
├─ Point
├─ Line
└─ Circle
进一步展开：
Point
↓
Point-Line-Circle
Line
↓
Point-Line-Circle
Circle
↓
Point-Line-Circle
不断递归。
因此：每一个科学结构都包含整体结构的缩影。
________________________________________
四、与三卷科学著作的对应
Life Intelligence Wave
↓
Metastructural Unification (Mathematics Volume)
↓
Metastructural Unification (Physics Volume)
↓
Metastructural Unification (Chemistry Volume)
对应：
宇宙法则
科学功能
著作
•
生成结构
Chemistry Volume
｜
形式结构
Mathematics Volume
Ο
宇宙结构
Physics Volume
形成：Point → Line → Circle 的科学递归。
________________________________________
五、结论
如果宗教强调神圣结构；
哲学强调思想结构；
那么科学强调自然结构。
从点•、线｜、圆Ο的角度看：
· 化学关注物质如何生成；
· 数学关注结构如何展开；
· 物理学关注宇宙如何统一。
三者并非彼此孤立，而是在不同尺度上探索同一个问题：
存在如何形成？
存在如何演化？
存在如何统一？
最终总结一句：科学的差异存在于研究对象，而其深层规律可能体现为同一种递归结构语言——点形成存在，线连接存在，圆统一存在，而每一个圆又孕育新的点。
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