Jason Karpeles · The Mathematics of AI Agents

Laboratory readers

Each chapter has four illustrated demonstrations drawn from its equations. Choose a value, watch the figure and the numbers change, and check a prediction before reading the answer.

27 of 27 chapters available. Each reader runs in your browser.

Every example in these readers is a constructed teaching example. The probabilities, utilities and cases are declared inputs chosen to make the mathematics visible. They are not measurements of any deployed agent, product or team.

Chapters

  1. Chapter 1When a Score Becomes a SkillFour illustrated demonstrations
  2. Chapter 2How to Measure EmergenceFour illustrated demonstrations
  3. Chapter 3How to Predict EmergenceFour illustrated demonstrations
  4. Chapter 4The Path from Prediction to ActionFour illustrated demonstrations
  5. Chapter 5What the Model Becomes Inside an AgentFour illustrated demonstrations
  6. Chapter 6The Price of a ChoiceFour illustrated demonstrations
  7. Chapter 7The Equation That Looks AheadFour illustrated demonstrations
  8. Chapter 8Acting in the DarkFour illustrated demonstrations
  9. Chapter 9Searching the FutureFour illustrated demonstrations
  10. Chapter 10Plans Within Plans: Hierarchical Actions and Reusable SkillsFour illustrated demonstrations
  11. Chapter 11The Mathematics of CuriosityFour illustrated demonstrations
  12. Chapter 12Credit for ConsequencesFour illustrated demonstrations
  13. Chapter 13Learning to Choose: Training an Agent from TrajectoriesFour illustrated demonstrations
  14. Chapter 14Building a World InsideFour illustrated demonstrations
  15. Chapter 15What an Agent Should Remember: Retrieval, Compression, and ExperienceFour illustrated demonstrations
  16. Chapter 16Thought as SearchFour illustrated demonstrations
  17. Chapter 17State and ConsequenceFour illustrated demonstrations
  18. Chapter 18When an Action Has CoordinatesFour illustrated demonstrations
  19. Chapter 19When Another Mind Becomes Part of the WorldFour illustrated demonstrations
  20. Chapter 20Messages, Beliefs, and ConsensusFour illustrated demonstrations
  21. Chapter 21Markets, Teams, and InstitutionsFour illustrated demonstrations
  22. Chapter 22Safe Enough to ActFour illustrated demonstrations
  23. Chapter 23When the Environment Gives Instructions: The Mathematics of Agent SecurityFour illustrated demonstrations
  24. Chapter 24How Much Capability Have We Extracted?Four illustrated demonstrations
  25. Chapter 25Improving an Agent Without Trusting the ImprovementFour illustrated demonstrations
  26. Chapter 26How Much More Could the System Become?Four illustrated demonstrations
  27. Chapter 27The Mathematics of DelegationFour illustrated demonstrations