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The Equation of Knowledge

Lê Nguyên Hoang
Chapman and Hall/CRC
Publication Date: 
Number of Pages: 
[Reviewed by
David Aldous
, on
I once heard a pronouncement that the three necessities for success in the 21st century are Python, Bayes Rule, and Mandarin. And in a June 2020 key policy speech, senior U.K. government minister Michael Gove said "We need to ensure more policy makers and decision makers feel comfortable discussing the Monte Carlo method or Bayesian statistics ....."  So a non-technical book on Bayesianism might be timely.
This book contains 22 chapters, each with roughly 10 two-page sections. It touches briefly on a huge range of topics. In the author's words,  
We discuss numerous fundamental concepts of mathematics, logic, statistics, computer science, artificial intelligence, and even notions of physics, biology, neuroscience, psychology, and economy. We explain logarithms, contraposition, p-values, Solomonoff complexity, and neural networks, as well as entropy, Darwinian evolution, false memory, cognitive biases, and financial bubbles.  
By including such a huge range of topics, the discussion of each is necessarily rather superficial, and there is little mathematics beyond some definitions and some elementary toy models. Writing a clear one-page verbal description of (for instance) Latent Dirichlet Allocation is impressive but the "read and quickly move on" style likely does not provide the reader with any permanent understanding. Anyway, such descriptions are more usefully placed on Wikipedia.
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. The author sees Bayes everywhere, though many of the connections strike me as strained. As the title implies, the author is mostly concerned with "theories of knowledge", leading occasionally to statements of elusive significance such as "The Bennett logical depth of our universe thus seems to be the key to explain the unreasonable effectiveness of abstraction." In other words, there is little connection with what actual statisticians spend their days working on.
For the latter reason, this book does not seem helpful for someone completely unfamiliar with Probability and Statistics. 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 ( is retired from U.C. Berkeley after 39 years but retains interests in theoretical and applied probability and in the popular exposition of probability in the real world.