Transformation
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Transformation

Commonality, Form, and Mechanism — How Civilization Rewrites the World to Gain Power

When a problem is hard in the form it arrives in, we do not usually get stronger. We carry the problem, as carefully as we can, into another form — one where our existing tools can reach it. We solve it there. Then we carry the answer back. This book traces that move through seventeen chapters: from Descartes' coordinates and Fourier's spectra through Boolean circuits, writing, maps, word embeddings, musical notation, the genetic code, and double-entry bookkeeping — and then examines where it ends.

Citation
@book{weng2026transformation, title = {Transformation: Commonality, Form, and Mechanism — How Civilization Rewrites the World to Gain Power}, author = {Weng, Gene}, year = {2026}, note = {\url{https://geneweng.github.io/transformation-book/}} }
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v1.0 · 2026 Last updated: April 17, 2026

About this book

The English edition is a substantial rewrite — not a translation — of an earlier Chinese manuscript. Seventeen chapters trace one recurring move (rewriting a hard problem into a tractable form, solving it, and carrying the answer back) across mathematics, engineering, biology, economics, linguistics, and cognitive science. The book argues that this move is not a metaphor but a method, that every use of it pays specific and nameable costs, and that some phenomena do not admit it at all.

Each case chapter instantiates a shared diagram — Source Domain and Target Domain linked by three arrows for transform, solve, and transform back — and works through the four terms the book uses to describe any bridge: commonality, form, mechanism, and cost. The final three chapters ask where the method reaches its limits.

Table of Contents

Introduction
  1. Why the World Can Always Be RewrittenBorges
Part I · Foundations
  1. Commonality: The Structure Beneath DifferenceCassirer
  2. Form Is Not a GarmentMcLuhan
  3. Mechanism: From Insight to InfrastructureWhitehead
Part II · Core Cases
  1. Curves and EquationsDescartes
  2. Time and FrequencyFourier
  3. Logic and CircuitsLeibniz
  4. Language and WritingPlato
  5. Terrain and MapsKorzybski
  6. Text and VectorsFirth
Part III · Supplementary Cases
  1. Sound and NotationDebussy
  2. DNA and ProteinWatson & Crick
  3. Double-Entry BookkeepingGoethe
Part IV · Boundaries
  1. Brain and ComputerTuring
  2. The Cost of TransformationGoodhart
  3. The UntransformablePolanyi
Epilogue
  1. Transformation Is a MethodWittgenstein

Build

The book is written as per-chapter Markdown, assembled by Pandoc with XeLaTeX, and rendered through Chicago author-date CSL from a BibTeX file. Source is on GitHub; a compiled PDF is mirrored alongside this page.

cd english make # produces book.pdf make chapter FILE=chapters/05_time_and_frequency.md make clean

Requirements: Pandoc ≥ 3, XeLaTeX, and a serif font (Baskerville by default; change mainfont in english/book.yaml to substitute).

Acknowledgements

This edition builds on a Chinese manuscript preserved in the repository. Thanks to the many sources — Descartes, Fourier, Shannon, Turing, Polanyi, Chalmers, Scott, Goodhart, and others — whose work the book uses as material, and to the traditions of mathematics, engineering, linguistics, biology, and philosophy from which each case chapter is drawn.