Preface: What the Mirror Shows

Note

How this book was made. This book is itself an example of the workflow it discusses. The author defined the question, the framework of each chapter and the cross-field hypotheses; an AI model drafted the text, the boxes and the code; the author reviewed the drafts, and the sources, quotations and calculations were checked before publication. Where checking changed a claim the author had proposed, the book says so. Readers should judge the book by its sources, its code and its tests, not by how it was written.

Two people can ask the same language model about the same subject and come away with opposite impressions. One finds it shallow and evasive; the other finds it a tireless collaborator that opens new lines of thought. Some of the difference lies in the model, which is better at some things than others. But much of it lies in the question: what the asker brings, how precisely they frame it, and what they are able to check.

This book develops one idea about that difference and tests it from several directions. A language model is, to a first approximation, a learned conditional distribution: given a context, it assigns probabilities to what comes next, shaped by the text it was trained on and by later fine-tuning. What it returns therefore depends heavily on the context it is given. In that limited but important sense it behaves like a mirror: it reflects, and recombines, what the question points it towards. The book calls this the algorithmic mirror, and asks what follows from it for people who use these systems to think.

What this book claims and does not claim

The mirror is an analogy, and it can be pushed too far. A model is not only a mirror: it has its own errors, it can state false things fluently, it carries the biases of its training data and of the people who fine-tuned it, and it can be more capable than its user at many tasks. The book therefore separates three kinds of claim. Some are mathematics, such as the definitions of conditional entropy and attention, or Ashby’s law of requisite variety. Some are published findings, such as the effects of fine-tuning on output diversity, model collapse under recursive training, and the mixed record of human–AI teams. And some are the author’s hypotheses about what these mean for human users. Those are in hypothesis boxes, each with the result that would refute it.

How to read the boxes

As in the other books of the 5D Library, different kinds of statement are kept apart.

Evidence

Evidence boxes report published findings, with their sources.

Calculation

Calculation boxes give formulas and short Python programs. Every program runs as printed with a standard Python 3 installation and nothing else, and its output is shown underneath it.

Hypothesis · not established

Hypothesis boxes hold the author’s ideas. They are labelled “not established”, and they say what result would show them to be wrong.

Source text

Source text boxes quote the classical texts, with the author’s translation.

Note

Note boxes give cautions and explain choices.

The plan of the book

The machine as a conditional distribution. Entropy, conditional entropy and mutual information, and what a vague prompt and a constrained one do to the distribution of answers.
The geometry of self-attention. Scaled dot-product attention implemented from scratch, and a toy model of queries that stay in one field or reach across several, read beside the Record of Learning’s image of the bell.
Ashby’s law of requisite variety. Why only variety can absorb variety, and a model of how much a user can verify of what a generator produces.
Projection, the Barnum effect and confirmation. Precision-weighted belief updating and biased assimilation, applied to how readers see themselves in ambiguous text, whether they love or distrust the machine.
Echo chambers and model collapse. Recursive training on generated data, the loss of the tails, and why fresh real data prevents it.
Centaur intelligence. From freestyle chess to the jagged frontier, and what a meta-analysis of human–AI teams actually found.
Mirrors in the classics. Zhuangzi’s mirror of the perfected person, the Record of Learning’s bell, Indra’s net of the Huayan school, and the Yogācāra account of consciousness.
Practice and a pre-registered trial. A four-step audit of the information in a prompt or research brief, and a blinded randomised trial comparing single-domain prompts with cross-field structured prompts.

This edition

This is version 1.0.0, the first complete edition: a preface and eight chapters, in Chinese and English. Corrections, and references the author has missed, are welcome through the 5D Library website.

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 promotes no AI product or service. As described above, the book was produced with an AI model under the author’s direction. All the code and the trial protocol are published openly for anyone to check.

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 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).