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拉马努金的直觉与现实矩阵
用高维数学与物理方程解构人类命运
Ramanujan's Intuition and the Matrix of Reality: Reading Human Destiny through Higher-Dimensional Mathematics and the Equations of Physics
DOI10.5281/zenodo.23640761摘要
拉马努金（1887—1920）几乎全靠自学，却留下了数千条公式，其中许多在他去世几十年后才被证明，并出现在统计物理与弦论里。本书十章，每章取他的一个数学结构——拉马努金求和、零与无穷、仿 θ 函数、1/π 级数、嵌套根式、欧拉–马斯刻若尼常数、主定理、黎曼 ζ 零点、兰道–拉马努金常数、罗杰斯–拉马努金恒等式——与道家、佛家、儒家或瑜伽传统中的一句教法并置，并由此提出一套关于注意力与行动的练习：减、观、令。
每章分为故事、陷阱与协议、进阶三篇。书中另以标注框区分作者的诠释与已确立的知识：证据框给出处，推导框给公式与可运行的 Python 验证代码，二者与作者观点不一致处一律直说。本书是诠释与实践之书，不是医疗、心理或财务建议。
关键词：拉马努金；拉马努金求和；仿θ函数；黎曼ζ函数；罗杰斯–拉马努金恒等式；道德经；心经；修行
Abstract
Ramanujan (1887–1920) was almost entirely self-taught, yet he left thousands of formulas, many proved only decades after his death and later found in statistical physics and string theory. Each of this book's ten chapters takes one of his structures (Ramanujan summation, zero and infinity, the mock theta functions, the series for 1/π, the nested radical, the Euler–Mascheroni constant, the Master Theorem, the zeros of the zeta function, the Landau–Ramanujan constant and the Rogers–Ramanujan identities) and sets it beside a teaching from the Daoist, Buddhist, Confucian or yogic traditions, building from them a practice of attention and action: subtract, observe, command.
Each chapter has three parts: story, trap and protocol, and an advanced practice. Throughout, marked boxes separate the author's interpretation from established knowledge: evidence boxes give sources, calculation boxes give the formulas with runnable Python checks, and where the two disagree the box says so. This is a book of interpretation and practice, not medical, psychological or financial advice.
Keywords: Srinivasa Ramanujan; Ramanujan summation; mock theta functions; Riemann zeta function; Rogers–Ramanujan identities; Daodejing; Heart Sutra; contemplative practice
目录 · Contents
- 序：直觉也可以被检验English 中文Preface: Intuition Can Be Tested
- 第一章 拉马努金求和English 中文Chapter 1: Ramanujan Summation
- 第二章 零与无穷English 中文Chapter 2: Zero and Infinity
- 第三章 仿 θ 函数English 中文Chapter 3: Mock Theta Functions
- 第四章 π 的无穷级数English 中文Chapter 4: Infinite Series for Pi
- 第五章 嵌套根式常数English 中文Chapter 5: Nested Radical Constant
- 第六章 欧拉–马斯刻若尼常数English 中文Chapter 6: Euler-Mascheroni Constant
- 第七章 拉马努金主定理English 中文Chapter 7: Ramanujan's Master Theorem
- 第八章 黎曼 ζ 函数的零点English 中文Chapter 8: Riemann Zeta Function Zeroes
- 第九章 兰道–拉马努金常数English 中文Chapter 9: Landau-Ramanujan Constant
- 第十章 罗杰斯–拉马努金恒等式English 中文Chapter 10: Rogers-Ramanujan Identities
- 尾声：求道者之死English 中文Epilogue: The Death of the Seeker
How to cite · 引用
Fan, Y. (2026). Ramanujan's Intuition and the Matrix of Reality: Reading Human Destiny through Higher-Dimensional Mathematics and the Equations of Physics [拉马努金的直觉与现实矩阵] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23640761
BibTeX
@book{fan2026ramanujan,
title = {{Ramanujan's Intuition and the Matrix of Reality}: Reading Human Destiny through Higher-Dimensional Mathematics and the Equations of Physics},
author = {Fan, Yafu},
year = {2026},
publisher = {5D Library},
edition = {Version 1.0.0},
doi = {10.5281/zenodo.23640761},
url = {https://doi.org/10.5281/zenodo.23640761},
note = {Chinese title: 拉马努金的直觉与现实矩阵}
}
| DOI | https://doi.org/10.5281/zenodo.23640761 |
|---|---|
| DOI（全部版本 all versions） | https://doi.org/10.5281/zenodo.23640760 |
| ORCID | https://orcid.org/0009-0004-3519-1203 |
| 5D Library ID | 5DL-B-001 |
| 版本 Version | 1.0.0 · 中英双语版 Bilingual edition |
| 出版日期 Date | 2026-10-25 |
| 网址 Online | https://5dlibrary.com/books/ramanujan-reality-matrix/ |
| SHA-256 · ramanujan-reality-matrix_bilingual_v1.0.0.pdf | e769a33cd9c54f647d559c1d2c0a7d228394b5a042d1b3d1ba042d3596d573a7 |
| SHA-256 · ramanujan-reality-matrix_en_v1.0.0.pdf | 78794b61a9c9b15c8536337f0cc1979074332cef1c56243edcc4eb0d7c26683a |
| SHA-256 · ramanujan-reality-matrix_zh_v1.0.0.pdf | dd8bb6b174f8bbfe273030bf1855af1f6a08c58c49ff78ebee1499bb0185ca62 |
| Licence · 许可 | Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). https://creativecommons.org/licenses/by-nc-nd/4.0/ |
Disclosure. 5D Library belongs to the same group as sacredcubit.com and tensorcoil.com. The library of sound frequencies mentioned in Chapter 4 is the author's own project.