Preface: Why Starting Is Harder than Continuing

Note

Please read this first. This book borrows the equations of classical and statistical mechanics to think about human action, procrastination and habit. Applied to people, every one of these equations is a cross-disciplinary analogy or simplified model: the “mass”, “friction coefficient”, “barrier” and “noise” in this book are not physical quantities that can be measured in a person, and the numbers in the programs are illustrative. This book is not psychotherapy or medical advice and diagnoses nothing. Persistent difficulty starting everyday tasks, a lasting low mood, or marked changes in sleep or appetite can belong to conditions such as depression or ADHD that need professional assessment; please seek help from a qualified doctor or mental-health professional rather than treating it as a matter of “too much friction”.

A block resting on a table is hardest to move with the first push; once it slides, less force keeps it going. A car on ice only spins its wheels, however strong its engine. A ball resting in one of two valleys will sooner or later be shaken over the ridge, but how long that takes depends on the height of the ridge and the strength of the shaking, and the dependence is exponential. Physics describes these things precisely. When people say “the first step is the hardest”, “keep going and you will win” or “giving up halfway”, they seem to be talking about the same kind of thing.

This book takes that “seem” and looks at it closely: what the physical equations actually say, what the behavioural evidence says, where the two agree and where they do not. Throughout, two kinds of statement are kept apart. The conclusions of physics itself can be tested in a laboratory. Applying them to people is analogy and modelling, which needs evidence of its own and often needs correcting. Several of the claims that prompted this book turned out, on checking, to need narrowing, and each chapter says so.

What this book is and is not

This is a book of models and reviews. Each chapter states a piece of established physics or mathematics, runs it in a short Python program whose parameters the reader can change, and then reviews the relevant behavioural research, showing where model and evidence agree and where they part. The book offers no “formula that changes your life”. It offers a set of testable questions and, in Chapter 8, a pre-registered trial that could prove the author’s idea wrong.

How to read the boxes

As in the other books of the 5D Library, different kinds of statement are marked separately.

Evidence

Evidence boxes report published findings, with their sources.

Calculation

Calculation boxes give formulas and short Python programs. Every program uses only the Python 3 standard library and runs as printed; its actual output is shown beneath it as comments.

Hypothesis · not established

Hypothesis boxes hold the author’s ideas, marked “not established”, together with the result that would prove them wrong.

Source text

Source text boxes quote classical texts, with notes.

Note

Note boxes give cautions and explain choices.

Plan of the book

Inertia and the status quo. The evidence on status quo bias, and a damped restoring model: a short hard push dies away, and only a sustained force moves the resting point.
Static and kinetic friction. Why starting takes more force than keeping going; stick-slip motion; and why a wheel needs friction to move forward — a section that also shows that “resistance” and “grip” are different things.
The double well and Kramers’ escape rate. How long it takes to cross a barrier from one stable state to another, and the different effects of lowering the barrier and of applying a steady outside force.
Hysteresis and tipping points. Why, in a bistable system, giving up halfway slides you back, while crossing the saddle-node lets you slide into the new state on your own.
Social coupling and learning by teaching. The evidence on learning in order to teach, network models of complex contagion, and an arithmetic problem hidden in the rule “help two classmates before you unlock the next stage”.
The cognitive energy budget and the ego-depletion debate. The large-scale failures to replicate ego depletion, and explanations in terms of motivation and opportunity cost.
East Asian philosophy of practice. The Book of Changes, Wang Yangming’s Instructions for Practical Living and a Chan (Zen) case, read beside the models of this book, with the limits of the analogy.
Practice and a pre-registered trial. A four-step barrier audit, and a pre-registered randomised controlled trial comparing self-study with a “teach two to unlock” rule.

About this edition

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

Disclosure

The author uses this book as the methodological basis of his community cognition courses, 5D Ascension Cards (Dimensional Shift Card Decks) and the Yafu AI knowledge base, and so has a direct commercial interest in its subject and in the result of the Chapter 8 trial. The book promotes no course, card deck or product and makes no health or therapeutic claim; the trial is designed to be run and analysed by researchers independent of the author’s business; all the code and the study protocol are published openly for anyone to check.

Fan, Y. (2026). Classical and Statistical Mechanics of Human Action: Psychological Inertia, Static Friction Thresholds, Kramers Escape Rate in Double-Well Potentials and Habit Phase Transitions, Read Beside East Asian Philosophy of Practice [行动的经典与统计力学] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23738774 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).