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The Fractal Structure and Layered Recursion of Contemporary Science — The Hierarchical Unfolding of Scientific Systems Through the Universal Law of Point (•), Line (｜), and Circle (Ο)

6/3/2026

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。

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The Fractal Structure and Layered Recursion of Contemporary Philosophy — The Hierarchical Unfolding of Philosophical Systems Through the Universal Law of Point (•), Line (｜), and Circle (Ο)

6/3/2026

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Abstract:

For centuries, philosophy has been studied through historical traditions, cultural backgrounds, and schools of thought. However, from a structural perspective, major philosophical systems may also be understood as manifestations of recurring organizational patterns.
This article explores philosophy through the framework of Point (•), Line (｜), and Circle (Ο), proposed in Universal Law. It suggests that the I Ching tradition may be viewed as a Point-oriented philosophy emphasizing origin and generation; Western philosophy as a Line-oriented philosophy emphasizing reasoning and development; and Confucian philosophy as a Circle-oriented philosophy emphasizing order, harmony, and systemic integration.
Furthermore, each philosophical tradition appears to contain its own internal point-line-circle structure, producing a recursive and fractal-like hierarchy. Through this perspective, philosophy is interpreted not merely as a collection of doctrines, but as a continuously unfolding structural system. The study argues that apparent differences among philosophical traditions may conceal deeper structural commonalities, and that the concepts of Point, Line, and Circle may provide a reusable language for understanding the recursive organization of human thought.

Keywords: Universal Law; Philosophy; Recursive Structure; Fractal Philosophy; I Ching; Western Philosophy; Confucianism; Point-Line-Circle Structure.

________________________________________
I. The Overall Triadic Structure of Philosophy

From a macroscopic perspective, the major traditions of human philosophy may be viewed as exhibiting three primary structural tendencies:

Universal Law
Structural Characteristic
Representative Tradition

• Point
Origin, Ontology, Heavenly Principle

I Ching Tradition

｜ Line
Reasoning, Logic, Development

Western Philosophy

Ο Circle
Order, Relationships, Wholeness
Confucian Philosophy

1.1 Point Philosophy (•)

Representative Tradition: I Ching (Book of Changes)
Core Structure: Tai Chi → Yin and Yang → Four Symbols → Eight Trigrams → Ten Thousand Things
Emphasis:

·    Origin
·    Generation
·    Beginning

Corresponding Idea: One gives rise to Two; Two gives rise to Three; Three gives rise to the ten thousand things.
Therefore, the I Ching may be viewed as a philosophy of cosmic generation—a philosophical system that derives the universe from a single originating point.

1.2 Line Philosophy (｜)

Representative Tradition: Western Philosophy
From:

·    Socrates
·    Plato
·    Aristotle

To:

·    Descartes
·    Kant
·    Hegel

A characteristic progression emerges: Proposition → Reasoning → Conclusion → Structure
Emphasis:

·    Logic
·    Causality
·    Argumentation

Therefore, Western philosophy may be viewed as a philosophy of pathways, in which truth unfolds through reasoning and logical development.

1.3 Circle Philosophy (Ο)

Representative Tradition: Confucian Philosophy
Core Structure: Self-Cultivation → Family Regulation → State Governance → Harmony Under Heaven
Emphasis:

·    Relationships
·    Balance
·    Social Order
Ultimately leading toward: Heaven – Earth – Humanity as an integrated whole.
Therefore, Confucianism may be viewed as a philosophy of order, in which individual and collective existence together form a harmonious system.

________________________________________
II. Recursive Unfolding Within Philosophical Systems

As observed in religious systems, each philosophical tradition also contains recurring Point–Line–Circle structures within itself.

2.1 Internal Structure of the I Ching

Overall: I Ching → •
Internal Structure:

• Tai Chi
｜ Yin–Yang Transformation
Ο Trigram and Hexagram System

Correspondence:

·    Point: Tai Chi
·    Line: Yin–Yang Transformation
·    Circle: The Complete System of Sixty-Four Hexagrams

2.2 Internal Structure of Western Philosophy

Overall: Western Philosophy → ｜
Internal Structure:

• Being
｜ Reasoning
Ο System

Examples:

·    Point: Ontology
·    Line: Logic
·    Circle: System Philosophy

2.3 Internal Structure of Confucian Philosophy

Overall: Confucianism → Ο
Internal Structure:

• Ren (Humaneness)
｜ Li (Ritual and Social Order)
Ο Datong (Great Harmony)

Correspondence:

·    Point: Humaneness
·    Line: Social Process and Ethical Practice
·    Circle: Great Harmony Under Heaven

________________________________________
III. The Fractal Structure of Philosophy

The recursive structure may be represented as follows:

Philosophy

├─ Point Philosophy
│ ├─ Point
│ ├─ Line
│ └─ Circle
├─ Line Philosophy
│ ├─ Point
│ ├─ Line
│ └─ Circle
└─ Circle Philosophy
├─ Point
├─ Line
└─ Circle

Further Expansion:

Point
↓
Point–Line–Circle

Line
↓
Point–Line–Circle

Circle
↓
Point–Line–Circle

This recursive process may continue indefinitely.
Thus, every structure contains a miniature reflection of the whole. Such self-similarity is a defining characteristic of fractal systems.

________________________________________
IV. Correspondence with the Three-Book Framework

An interesting correspondence also appears in the structure of our own trilogy:

Golden Classic
↓
Universal Law
↓
Grand Ultimate Theory

This may be interpreted as:

Universal Law
Philosophical Function
Work

• Point
Inquiry into Origins
Golden Classic

｜ Line
Structural Unfolding
Universal Law

Ο Circle
Systemic Unification
Grand Ultimate Theory

Together they form a philosophical recursion: Point → Line → Circle

________________________________________
V. Conclusion

If religion emphasizes sacred structures, philosophy emphasizes structures of thought.
From the perspective of Point (•), Line (｜), and Circle (Ο):

·    The I Ching focuses on how the universe begins.
·    Western philosophy focuses on how truth unfolds.
·    Confucian philosophy focuses on how wholes become stable and harmonious.

These traditions are not mutually exclusive. Rather, they approach the same fundamental questions from different directions:

·    How does existence emerge?
·    How does existence evolve?
·    How does existence become an integrated whole?

Final Summary

The differences among philosophical traditions lie in their modes of thinking, yet their deeper structure may reflect the same recursive language: The Point seeks origins; the Line unfolds meaning; the Circle establishes order; and every Circle ultimately gives birth to a new Point.

Therefore, this interpretation does not seek to replace traditional philosophical classifications. Instead, it proposes a structural perspective through which the I Ching, Western philosophy, and Confucianism may be understood as three distinct yet interconnected pathways within a larger recursive framework.

________________________________________
       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). Golden Classic.

Classical Philosophical Sources

4.Laozi. Tao Te Ching.
5.Confucius. The Analects.
6.The I Ching (Book of Changes).
7.Plato. The Republic.
8.Aristotle. Metaphysics.
9.René Descartes. Discourse on the Method.
10.Immanuel Kant. Critique of Pure Reason.
11.G. W. F. Hegel. Phenomenology of Spirit.

Related Studies

12.Joseph Needham. Science and Civilisation in China.
13.Fung Yu-lan. A History of Chinese Philosophy.
14.Bertrand Russell. History of Western Philosophy.
15.Mircea Eliade. The Quest: History and Meaning in Religion.
16.Gregory Bateson. Mind and Nature: A Necessary Unity.
17.Ludwig von Bertalanffy. General System Theory.
18.Benoit Mandelbrot. The Fractal Geometry of Nature.

当今哲学的分形结构和分层递归—--从“点•、线｜、圆Ο”宇宙法则看哲学系统的层级展开

摘要：

几个世纪以来，哲学一直被置于历史传统、文化背景和思想流派的框架下进行研究。然而，从结构的角度来看，主要的哲学体系也可以被理解为反复出现的组织模式的体现。
本文以《宇宙法则》中提出的点（•）、线（｜）、圆（Ο）框架来探讨哲学。文章指出，《易经》传统可以被视为一种以点为导向的哲学，强调起源和生成；西方哲学可以被视为一种以线为导向的哲学，强调推理和发展；而儒家哲学则可以被视为一种以圆为导向的哲学，强调秩序、和谐与系统整合。
此外，每一种哲学传统似乎都包含其自身的内部点-线-圆结构，从而形成一种递归的、类似分形的层级结构。通过这种视角，哲学不再仅仅是一系列学说的集合，而是一个不断演进的结构系统。该研究认为，不同哲学传统之间表面上的差异可能掩盖了更深层次的结构共性，而点、线、圆的概念或许能为理解人类思维的递归组织提供一种可重复使用的语言。

关键词：普遍规律；哲学；递归结构；分形哲学；易经；西方哲学；儒家思想；点-线-圆结构。

________________________________________
一、哲学的整体三元结构

从宏观角度观察，人类哲学传统可以呈现三种主要结构倾向：

宇宙法则
结构特征
代表体系

• 点
起源、本体、天道
《易经》体系

｜线
推理、逻辑、展开
西方哲学

Ο 圆
秩序、关系、整体
儒家哲学

1.1   点哲学（•）

代表：《易经》
核心特点：太极两仪四象八卦万物
强调：

·     本源
·     生发
·     起点

对应：一生二，二生三，三生万物

因此：《易经》更像：宇宙生成哲学
即：从一个点推演整个宇宙。

1.2 线哲学（｜）

代表：西方哲学
从：

·     苏格拉底
·     柏拉图
·     亚里士多德

到：

·     笛卡尔
·     康德
·     黑格尔

形成：命题推理结论结构。
强调：

·     逻辑
·     因果
·     论证

因此：西方哲学更像：道路哲学
即：真理通过推理展开。

1.3 圆哲学（Ο）

代表：儒家
核心：修身齐家治国平天下
强调：

·     关系
·     平衡
·     整体秩序

最终形成：天，地，人统一。
因此，儒家更像：秩序哲学
即：个体与整体共同构成圆满系统。

________________________________________
二、哲学内部的递归展开

与宗教一样。每种哲学内部仍然出现：点，线，圆，三种结构。

2.1 《易经》内部

整体：I Ching → •
内部：

• 太极:
｜阴阳变化
Ο 八卦系统

对应：

点:太极
线: 阴阳变化
圆: 六十四卦整体

2.2 西方哲学内部

整体：Western Philosophy → ｜
内部：

• 存在
｜推理
Ο 体系

例如：

点: 本体论, Ontology

线: 逻辑学, Logic

圆:系统哲学, System Philosophy

2.3 儒家内部

整体：Confucianism → Ο
内部：

• 仁
｜礼
Ο 大同

对应：

点: 仁, Humaneness
线: 礼,Social Process
圆: 天下大同, Great Harmony

________________________________________
三、哲学的分形结构

结构图：

Philosophy

├─ Point Philosophy
│
│   ├─ Point
│   ├─ Line
│   └─ Circle
│
├─ Line Philosophy
│
│   ├─ Point
│   ├─ Line
│   └─ Circle
│
└─ Circle Philosophy
    │
    ├─ Point
    ├─ Line
    └─ Circle

进一步：

Point
↓
Point-Line-Circle

Line
↓
Point-Line-Circle

Circle
↓
Point-Line-Circle

不断递归。

________________________________________
四、与三部书的对应

这里也有个很有意思的思路。按照我们现在的著作结构：

Golden Classic
↓
Universal Law
↓
Grand Ultimate Theory

恰好也可以对应：宇宙法则
哲学功能著作

•
本源追问
Golden Classic

｜
结构展开
Universal Law

Ο
系统统一
Grand Ultimate Theory

形成：Point Line Circle 的哲学递归。

________________________________________
五、总结

如果宗教强调：神圣结构
那么哲学强调：思想结构
从点•、线｜、圆Ο的角度看：

·     《易经》更关注宇宙如何开始；
·     西方哲学更关注真理如何展开；
·     儒家更关注整体如何稳定。

三者并非互相排斥，而是在不同方向上探索同一个问题：
存在如何生成？
存在如何演化？
存在如何形成整体？

最终总结一句：哲学的差异存在于思维路径，而其深层结构可能体现为同一种递归语言——点寻找起源，线展开意义，圆形成秩序，而每一个圆又孕育新的点。
所以，我们认为这篇哲学更加清晰，因为《易经》、西方哲学、儒家本来就是三种非常明显不同的思想传统，而我们这里只是提供一种“结构观察法”。

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The Fractal Structure and Layered Recursion of Contemporary Science — The Hierarchical Unfolding of Scientific Systems Through the Universal Law of Point (•), Line (｜), and Circle (Ο)

The Fractal Structure and Layered Recursion of Contemporary Philosophy — The Hierarchical Unfolding of Philosophical Systems Through the Universal Law of Point (•), Line (｜), and Circle (Ο)

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