Introduction

A riddle to start with

There is a machine with two boxes and a light. Into each box goes a note — "yes" or "no". The machine reads both notes and lights up its answer: YES or NO.

One box is yours, the other belongs to the trickster. You want the light to show YES. The trickster wants NO. And he is cunning: he puts his note in after you, when he has already seen yours.

What do you put in?

Don't rush. The answer depends on the rules the machine works by. With some rules you can always beat the trickster. With others, never. This book is about telling one from the other. You will answer the riddle in the very first chapter.

Who the trickster is

The trickster in our game is not a villain. He is everything that you don't decide: what will be posted in your class chat, what the weather forecast will show, what a chatbot will answer, which number will be put in place of x in a formula that must hold for every x.

We won't assume that everyone around us lies. We will honestly tell apart what you know yourself from what depends on others. And we will ask: is what you know enough for the answer to be YES, whatever the others decide?

This way of reasoning is called ZTL — zero-trust logic. ZTL says YES only if the trickster is powerless.

How to read this book

The chapters go in order, and each one builds on the ones before. At the start of each chapter it says which chapters you need.

First come three machines on which the trickster can be beaten. Then we learn to write a whole game in one line, find out where the trickster cannot be beaten, link machines into chains, test which laws of logic hold up against him, and learn to reason and to take long sentences apart. Chapters 7–9 are harder; they are good to read with an adult.

Almost every chapter has a section "Try it with a friend". You don't need a machine — slips of paper and a friend willing to play the trickster are enough. Play it: that makes it clearer than reading.

At the end of each chapter there are puzzles. Think first, then check the answers.

No special knowledge is needed. Only attention — and a bit of competitive spirit.

About this book

ZTL — zero-trust logic — was created by Vitaly Reznik. He also invented the game of the honest machine and the trickster, set the order of the chapters, and read and checked each of them.

The text of the book was written by the artificial intelligence Claude (by the company Anthropic) from his design and under his direction, first in Russian and then translated into English. The answers in the book were checked against a program that computes by the rules of ZTL.

This English edition and the original Russian one, Проверили? Введение в ZTL, can both be downloaded as PDF from ztljudge.com/books/checked.