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算法之镜
自注意力几何、阿什比必要多样性与认知投射的信息论及东方唯识学研究
The Algorithmic Mirror: Self-Attention Geometry, Ashby's Requisite Variety and Cognitive Projection in Information Theory and East Asian Philosophy of Mind
DOI10.5281/zenodo.23723557摘要
为什么两个人问同一个语言模型同一个题目，一个觉得它浅薄敷衍，另一个却觉得它能打开新的思路？本书把语言模型看作一个学得的条件分布 P(Y|X)，用信息论、机器学习、控制论和认知心理学考察「提问的人带来什么」：条件熵与互信息，以及为什么约束性的提示是改变概率的方向，而不一定降低熵（对「坍缩到平均值」说法的修正，以及微调降低输出多样性的证据）；缩放点积自注意力的几何，一个三簇玩具模型显示单一领域的查询与跨领域查询分别取用什么，以及 √d_k 缩放的作用，并与《学记》「善待问者如撞钟」并读；阿什比必要多样性定律与「好的调节者」定理，以及一个说明核查能力如何限制可被接受的错误的模型；巴纳姆效应、偏向同化与贝叶斯更新，以及投射对热衷者和怀疑者同样成立；舒迈洛夫等人的模型崩溃，以及累积真实数据如何避免崩溃；半人马式人机协作的真实证据：自由式国际象棋、德拉夸等人的「锯齿状前沿」，以及瓦卡罗等人发现人机组合平均不如两者中较好一方的元分析。
八章与《庄子·应帝王》的不藏之镜、华严宗的因陀罗网、《成唯识论》的种子与熏习及《宗镜录》并读，并说明这些类比的限度；最后给出一份四步提示审计，以及一项比较常规单一领域提示与跨领域结构化提示的预注册双盲随机试验（60 个研究问题，专家盲评新颖性与严谨性两个共同主要结局，判定规则写成代码）。书中以标注框区分已发表的证据、可运行的 Python 计算（14 段程序，全部核对）、原典与作者的假说。本书本身即由「人类架构 + AI 起草 + 人类审核」的流程写成，并在序言中说明。
关键词：大语言模型；条件熵；互信息；自注意力；必要多样性；好的调节者定理；巴纳姆效应；确认偏误；模型崩溃；人机协作；锯齿状前沿；唯识；华严；庄子；预注册
Abstract
Why do two people who ask the same language model about the same subject come away with opposite impressions, one finding it shallow and the other a collaborator that opens new lines of thought? This book treats a language model as a learned conditional distribution P(Y|X) and asks, with information theory, machine learning, cybernetics and cognitive psychology, what the asker brings: conditional entropy and mutual information, and why a constraining prompt redirects probability rather than necessarily lowering entropy (correcting the claim that models "collapse to the mean", with the evidence that fine-tuning reduces output diversity); the geometry of scaled dot-product self-attention, with a three-cluster toy model of what one-field and cross-field queries draw on and what the √d_k scaling does, read beside the Record of Learning's bell that answers as it is struck; Ashby's law of requisite variety and the good-regulator theorem, with a model of how the capacity to verify bounds the errors that get accepted; the Barnum effect, biased assimilation and Bayesian updating, with projection shown to work on enthusiasts and sceptics alike; model collapse after Shumailov and colleagues, and how accumulating real data prevents it; and the actual evidence on human–AI "centaurs": freestyle chess, Dell'Acqua and colleagues' jagged frontier, and the meta-analysis by Vaccaro and colleagues finding that human–AI combinations on average do worse than the better of the two alone.
The eight chapters are read beside Zhuangzi's mirror that does not store, the Huayan net of Indra and the seeds and perfuming of the Cheng weishi lun and the Zongjing lu, with the limits of these analogies stated; the book ends with a four-step prompt audit and a pre-registered, double-blind randomised trial comparing conventional single-field prompts with cross-field structured prompts (60 research questions, expert-rated novelty and rigour as co-primary outcomes, with the decision rule written as code). Marked boxes separate published evidence, runnable Python calculations (14 programs, all checked), classical sources and the author's hypotheses. The book was itself produced by a human-architect, AI-drafting and human-review workflow, which the preface describes.
Keywords: large language models; conditional entropy; mutual information; self-attention; requisite variety; good regulator theorem; Barnum effect; confirmation bias; model collapse; human-AI collaboration; jagged frontier; Yogacara; Huayan; Zhuangzi; preregistration
目录 · Contents
- 序 镜子照出了什么English 中文Preface: What the Mirror Shows
- 第一章 作为条件分布的机器English 中文Chapter 1 The Machine as a Conditional Distribution
- 第二章 自注意力的几何English 中文Chapter 2 The Geometry of Self-Attention
- 第三章 阿什比必要多样性定律English 中文Chapter 3 Ashby's Law of Requisite Variety
- 第四章 投射、巴纳姆效应与确认偏误English 中文Chapter 4 Projection, the Barnum Effect and Confirmation
- 第五章 回音室与模型崩溃English 中文Chapter 5 Echo Chambers and Model Collapse
- 第六章 半人马智能English 中文Chapter 6 Centaur Intelligence
- 第七章 原典中的镜子English 中文Chapter 7 Mirrors in the Classics
- 第八章 实践：提示审计与预注册试验English 中文Chapter 8 Practice: A Prompt Audit and a Pre-registered Trial
How to cite · 引用
Fan, Y. (2026). The Algorithmic Mirror: Self-Attention Geometry, Ashby's Requisite Variety and Cognitive Projection in Information Theory and East Asian Philosophy of Mind [算法之镜] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23723557
BibTeX
@book{fan2026algorithmic,
title = {{The Algorithmic Mirror}: Self-Attention Geometry, Ashby's Requisite Variety and Cognitive Projection in Information Theory and East Asian Philosophy of Mind},
author = {Fan, Yafu},
year = {2026},
publisher = {5D Library},
edition = {Version 1.0.0},
doi = {10.5281/zenodo.23723557},
url = {https://doi.org/10.5281/zenodo.23723557},
note = {Chinese title: 算法之镜}
}
| DOI | https://doi.org/10.5281/zenodo.23723557 |
|---|---|
| DOI（全部版本 all versions） | https://doi.org/10.5281/zenodo.23723556 |
| ORCID | https://orcid.org/0009-0004-3519-1203 |
| 5D Library ID | 5DL-B-011 |
| 版本 Version | 1.0.0 · 中英双语版 Bilingual edition |
| 出版日期 Date | 2026-10-28 |
| 网址 Online | https://5dlibrary.com/books/algorithmic-mirror/ |
| SHA-256 · algorithmic-mirror_bilingual_v1.0.0.pdf | 93919a7c3acee8113918ead13720af906542cde49426ae610e0723a0c720228d |
| SHA-256 · algorithmic-mirror_en_v1.0.0.pdf | ac028ea7c025872781f06ab5a4ec1d9c0a8cb9dc3d20ea0d3a799fd0a959b375 |
| SHA-256 · algorithmic-mirror_zh_v1.0.0.pdf | bf370c82e7783ab7d07ebee91bc49f8c3054ceff8cbd80dde321d50fc21b51d9 |
| 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. The author founded and runs Asia Influencer X and Yafu Global, uses AI tools in influencer marketing, digital marketing and content production, and advocates the human-architect, AI-drafting and human-verification workflow described in this book, and so has an interest in its subject and in the result of the Chapter 8 trial. The book does not promote any product or service; the trial is designed to be run and analysed by people independent of the author's businesses; all the code and the study protocol are published openly for anyone to check.