The Equation of Knowledge : From Bayes' Rule to a Unified Philosophy of Science book cover
1st Edition

The Equation of Knowledge
From Bayes' Rule to a Unified Philosophy of Science

ISBN 9780367428150
Published June 19, 2020 by Chapman and Hall/CRC
460 Pages 12 B/W Illustrations

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Book Description

The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science introduces readers to the Bayesian approach to science: teasing out the link between probability and knowledge.

The author strives to make this book accessible to a very broad audience, suitable for professionals, students, and academics, as well as the enthusiastic amateur scientist/mathematician.

This book also shows how Bayesianism sheds new light on nearly all areas of knowledge, from philosophy to mathematics, science and engineering, but also law, politics and everyday decision-making.

Bayesian thinking is an important topic for research, which has seen dramatic progress in the recent years, and has a significant role to play in the understanding and development of AI and Machine Learning, among many other things. This book seeks to act as a tool for proselytising the benefits and limits of Bayesianism to a wider public.


  • Presents the Bayesian approach as a unifying scientific method for a wide range of topics
  • Suitable for a broad audience, including professionals, students, and academics
  • Provides a more accessible, philosophical introduction to the subject that is offered elsewhere

Table of Contents

Sction I. Pure Bayesianism.  1. On A Transformative Journey.  2. Bayes Theorem.  3. Logically Speaking... 4. Let’s Generalize!  5. All Hail Prejudices.  6. The Bayesian Prophets.  7. Solomonoff’s Demon.  Section II. Applied Bayesianism.  8. Can You Keep A Secret?  9. Game, Set and Math.  10. Will Darwin Select Bayes? 11. Exponentially Counter-Intuitive.  12. Ockham Cuts to the Chase.  13. Facts Are Misleading.  Section III. Pragmatic Bayesianism.  14.  Quick And Not Too Dirty.  15. Wish Me Luck.  16. Down Memory Lane.  17. Let’s Sleep On It.  18. The Unreasonable Effectiveness of Abstraction.  19. The Bayesian Brain.  Section IV. Beyond Bayesianism.  20. It’s All Fiction.  21. Exploring The Origins Of Beliefs.  22. Beyond Bayesianism.

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Lê Nguyên graduated from the École Polytechnique de Montréal with a PhD in applied mathematics, before working as a post-doctoral researcher at MIT. Since 2016, he has been working as a science communicator at EPFL. He also has his own YouTube channel Science4All (in French), with over 170k subscribers. 


"Each chapter is opened with a fascinating epigraph quoting famous persons, and is completed by the most recent references. There are multiple illustrations, and the Bayes’ formulae are many times presented via various funny symbols of emoji kind. The book is addressed to a wide audience of students, professionals, and actually any reader interested to be better acquainted with modern ideas in various sciences and philosophy of science, and their Bayesian statistical description and interpretation."
— Stan Lipovetsky, Technometrics (Volume 63, 2021 - Issue 1)

"[. . . ] Trained in the hard school of online videos, Le Nguyen Hoang has found a new tone to talk about science, a tone that is both rigorous and narrative, where examples illuminate the most abstract questions."
— From the Foreword by Gilles Dowek, Professor at École Polytechnique and researcher at the Laboratoire d'Informatique de l'École Polytechnique and the Institut National de Recherche en Informatique et en Automatique (INRIA).

Lê Nguyên Hoang takes us on a fascinating intellectual journey into Bayesianism, cutting across many social and natural sciences. The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science is a real page turner.
— George Zaccour, HEC Montréal and co-author of Handbook of Dynamic Game Theory

"Making math accessible to everyone, showing its connections with dozens of different domains, narrating scientific discovery as a personal human adventure, and sharing impressive enthusiasm: there is definitely something of Greg Chaitin's Meta Math! in Lê Nguyên Hoang's book!"
— Rémi Peyre, École des Mines de Nancy

"A remarkable piece of work, broad and insightful at the same time. This book is unique in that it gives an accessible journey from subtle probabilistic puzzles to the most advanced concepts at the heart of the machine learning revolution; with unrivalled clarity, it exposes deep ideas that have remained very confidential outside of specialized circles, and that yet are becoming fundamental in the way we understand our world."
— Clément Hongler, Associate Professor and Chair of Statistical Field Theory, EPFL

"As someone who practices research and publishes academic papers, it is frustrating to note how little we, scientists, are trained in epistemology. ‘How do we know that we know?’ This question is often neglected or taken for granted. The recent controversies about reproducibility of scientific publishing might be one of the tips of a larger iceberg. This book will, in my opinion, be remembered as one of those that helped melt the iceberg."  
— El Mahdi El Mhamdi, École Polytechnique Fédérale de Lausanne.

"The book has a lively writing style, rather like you are listening to an inspiring lecturer. Indeed the author has a French YouTube channel and is clearly enthusiastic about exposition. It is overtly an account of what the author personally finds interesting. [. . .] In teaching a basic college course, focused on the mathematical setup and on the analysis of data, I often find there is one student who comes to office hours and is interested in seeing connections with broad scientific fields, or in conceptual issues of the philosophy of science. I could certainly recommend this book to such a student. Similarly, for the MAA community it could be an innovative basis for an undergraduate seminar course, in which students would choose a topic from the book and delve deeper into it."
— David Aldous, Mathematical Association of America