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The Equation of Knowledge
The Equation of From Bayes' Rule to a Unified Philosophy of Science introduces readers to the Bayesian approach to 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. Features
- GenresMathematics
460 pages, Hardcover
Published June 19, 2020
4 people are currently reading
36 people want to read
About the author
Lê Nguyên Hoang
11 books13 followersLê Nguyên Hoang est vidéaste et médiateur scientifique à l'EPFL. Diplômé de l'Ecole Polytechnique (X2007), il est docteur en mathématiques de Polytechnique Montréal et ancien chercheur postdoctorant du MIT. Il est l'auteur de la chaîne Science4All (160 000 abonnés sur YouTube), des podcasts Axiome et Probablement, et du livre la formule du savoir (EDP sciences).
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Displaying 1 - 3 of 3 reviews
January 2, 2025
First, the good: What is most impressive about this book is its immense scope and breadth. I can’t imagine anyone knows more applications of Bayes’ theorem than LN Huong. While I was already a well convinced Bayesian before picking up this book (and arrived at this position for reasons related to my own research and thus different from Huong), I came to very similar conclusions. I found this book based on a search to see who else had made the connection between Godel and Bayes, and this is one of literally hundreds of connections the author makes. This makes it one of the most interesting and engaging books I've ever read.
Furthermore, this book is an easy read - not overly technical but technical enough when needed. My field is electrical and computer engineering and I understood every chapter. It takes a certain brilliance to explain so many concepts from so many disciplines (neuroscience, economics, computer science, statistics, epistemology) in a clear and intuitive way. Huong’s grasp of mathematics and his ability to distill these ideas is impressive. Each section and each chapter holds new insights and information. The book is written in a casual tone, with the author’s personal anecdotes and reflections contributing greatly to the experience. As a result, I wholeheartedly recommend this book for anyone even remotely interested in Bayes’ theorem, or philosophy, mathematics, and science in general.
So why four stars? Despite this book’s tremendous breadth, there are times it is inconsistent and at odds with itself. While some of this is perhaps inevitable given the size of this text, it is clear the author’s views were evolving as the book was written, and some editing could have improved the coherence of his overall argument. For instance, in Section 20.7, he writes “many seek to draw a line between science and pseudoscience, as if there were a natural boundary between the models that deserve all our credences, and those that deserve none. This boundary is not the truth; nor even the quest for truth.” This makes his pejorative use of the term “pseudo-scientific” in Section 10.1 quite puzzling. Huong seems to desperately want people to trust scientific consensus, despite providing several strong reasons for distrusting it, especially in controversial cases. He writes, “scientific peer review seems to judge the usefulness of scientific contributions more than their truth (or their validity),” and in the final chapter, writes, "\[S\]cientific hooliganism thus explains the requirement of a (yet illusory) objectivity and the acceptance of the “scientific method” even though the pure Bayesian and the pragmatic Bayesian would retort that it’s neither a good descriptive theory of how science works, nor a desirable normative theory.”
Furthermore, Huong ends the book by arguing for a kind of fictionalism about scientific theories (though I think instrumentalism or pragmatism would be a more appropriate term). Yet despite this, he constantly uses realist language when discussing Darwinian evolution throughout the book. This is problematic for two reasons. The first is that neo-Darwinian evolution appeals to "randomness" in a way that is incompatible to the Bayesian Huong advocates: according to the neo-darwinian synthesis, genetic mutations are "random," in way that is causal and not primarily epistemic. This "propensity" view of probability (which has been criticized by many philosophers of science, such as Eliot Sober) is at odds with the "degree-of-belief," and brutal criticisms have been lobbied against this view on both metaphysical and pragmatic grounds. If Huong wants to argue that probability is an epistemic concept, how can it play a causal role? What is the necessarily metaphyscial link between causality and epistemology he has in mind when he writes "By pure luck, chance made me live in other conditions?" We are left to guess, but it appears as if the author is (perhaps unknowingly) equivocating the world "chance" or "probability" when making these kinds of claims.
The second issue with this appeal is that despite his insistence on considering alternative models, he seems tied to metaphysical naturalism, refusing to engage with theistic, deistic, or pantheistic views of nature, or more broadly anything that would permit the injection of teleology. He consistently cites authors that come from an *a priori* philosophical to naturalism, such as Sean Carroll. My guess is this is what allows him to write the following sentence, "Knowledge and rationality are forbidden by the laws of our universe," which I found to be incredibly sloppy. First of all, we see Huong again shifting to a realism about scientific theories, rather than the fictionalism he later advocates for. If "all models are wrong," then clearly knowledge and rationality are only forbidden by the laws of the universe in question, which is a wrong model his own lights. Secondly, this statement betrays Huong's unfamiliarity with (what I would argue are) key concepts field of epistemology, despite his respect for the field and encouragement of people to learn it (which I do very much appreciate by the way).
For a book primarily dealing with epistemology (the word "knowledge" is in the title), we get very little of it: little discussion on what separates knowledge from belief, basically nothing on the nature of justification, and crucially, no engagement with externalist vs internalist theories. Epistemologists such as Bonjour and Plantinga (who tend to use Bayesian calculations in their philosophical work) would have much to say about some of the claims in the book, such as the one above. Perhaps in a newer edition, Huong could write about how foundationlist theories of knowledge can integrate into Bayesianism in the form of certain priors: properly basic beliefs (such as incorrigible beliefs) could be assigned full confidence (probability 1), and this can help fight radical skepticism. It is hard to fault Huong too much for his unfamiliarity in epistemology given his breadth of knowledge in so many other areas. However engagement with these ideas is the key way the book could be improved, despite its current length and scope. Given the author's respect and appreciation for philosophy (something I respect and appreciate *him* for) my guess is he would find books such as Warrant: The Current DebateWarrant: The Current Debate (and the rest of the trilogy) deeply thought provoking and engaging.
Huong's aversion to considering teleological explanations in nature extends to his discussion of morality. He claims "The two main approaches to prescriptive moral philosophy are deontology and consequentialism," without discussing virtue ethics which has exploded in popularity and relevance in recent years. Key figures in moral philosophy, such as Alasdair MacIntyre have revived virtue ethics into a thriving field with work such as After Virtue, and yet we get zero discussion of this (read After Virtue for how virtue ethics can link teleology to moral prescriptions, getting around G.E. Moore's Open Question Argument and David Hume's is-ought distinction).
His inclination to consequentialism/utilitarianism leads him to suggest a rational agent would atempt to maximize E_x good(x) | a, which I found to be objectionalble . Consider a scenario where a biased coin, with a 55% probability of landing heads and a 45% of landing tails, is flipped. If you choose to play, if the coin lands on heads, you get a million dollars. If the coin lands on tails, you are executed. Would Huong argue a rational agent would play the game, since the expected good of playing is larger than not playing? Would he play himself (and if not, argue he is irrational since he is morally obligated to do so)?
Finally, and this is only a small nitpick, I think an exploration on minimum description length (MDL) and its relationship to compatibility as well as Solmonoff/Kolmogorov complexity would have provided another point of agreement. This topic is heavily implied but I think stating it explicitly would have helped, and some other recent work in detection theory have used this to tie Bayesianism together with algorithmic information theory (see Dembski and Ewert - The Design Inference 2nd Edition and some work by George Montanez such as his 2018 paper A Unified Model of Complex Specified Information). Additionally, given the mention of Joseph Bertrand in Section 6.6, I’m surprised the author didn’t mention Bertrand’s Paradoxes, since these provide additional support for the Bayesian view (based on work by statistician and philosopher of statistics Alan Hajek and Van Fraasen’s classic text Laws and Symmetry).
Again, despite my concerns, I do 100% recommend reading picking up book if you have any interest in probability or topics in STEM and how they relate to philosophy. It really is an incredible achievement, and if you read it with a careful and skeptical eye (something I'm sure the author would also encourage), I am (almost) certain you will learn something useful and interesting from it.
Furthermore, this book is an easy read - not overly technical but technical enough when needed. My field is electrical and computer engineering and I understood every chapter. It takes a certain brilliance to explain so many concepts from so many disciplines (neuroscience, economics, computer science, statistics, epistemology) in a clear and intuitive way. Huong’s grasp of mathematics and his ability to distill these ideas is impressive. Each section and each chapter holds new insights and information. The book is written in a casual tone, with the author’s personal anecdotes and reflections contributing greatly to the experience. As a result, I wholeheartedly recommend this book for anyone even remotely interested in Bayes’ theorem, or philosophy, mathematics, and science in general.
So why four stars? Despite this book’s tremendous breadth, there are times it is inconsistent and at odds with itself. While some of this is perhaps inevitable given the size of this text, it is clear the author’s views were evolving as the book was written, and some editing could have improved the coherence of his overall argument. For instance, in Section 20.7, he writes “many seek to draw a line between science and pseudoscience, as if there were a natural boundary between the models that deserve all our credences, and those that deserve none. This boundary is not the truth; nor even the quest for truth.” This makes his pejorative use of the term “pseudo-scientific” in Section 10.1 quite puzzling. Huong seems to desperately want people to trust scientific consensus, despite providing several strong reasons for distrusting it, especially in controversial cases. He writes, “scientific peer review seems to judge the usefulness of scientific contributions more than their truth (or their validity),” and in the final chapter, writes, "\[S\]cientific hooliganism thus explains the requirement of a (yet illusory) objectivity and the acceptance of the “scientific method” even though the pure Bayesian and the pragmatic Bayesian would retort that it’s neither a good descriptive theory of how science works, nor a desirable normative theory.”
Furthermore, Huong ends the book by arguing for a kind of fictionalism about scientific theories (though I think instrumentalism or pragmatism would be a more appropriate term). Yet despite this, he constantly uses realist language when discussing Darwinian evolution throughout the book. This is problematic for two reasons. The first is that neo-Darwinian evolution appeals to "randomness" in a way that is incompatible to the Bayesian Huong advocates: according to the neo-darwinian synthesis, genetic mutations are "random," in way that is causal and not primarily epistemic. This "propensity" view of probability (which has been criticized by many philosophers of science, such as Eliot Sober) is at odds with the "degree-of-belief," and brutal criticisms have been lobbied against this view on both metaphysical and pragmatic grounds. If Huong wants to argue that probability is an epistemic concept, how can it play a causal role? What is the necessarily metaphyscial link between causality and epistemology he has in mind when he writes "By pure luck, chance made me live in other conditions?" We are left to guess, but it appears as if the author is (perhaps unknowingly) equivocating the world "chance" or "probability" when making these kinds of claims.
The second issue with this appeal is that despite his insistence on considering alternative models, he seems tied to metaphysical naturalism, refusing to engage with theistic, deistic, or pantheistic views of nature, or more broadly anything that would permit the injection of teleology. He consistently cites authors that come from an *a priori* philosophical to naturalism, such as Sean Carroll. My guess is this is what allows him to write the following sentence, "Knowledge and rationality are forbidden by the laws of our universe," which I found to be incredibly sloppy. First of all, we see Huong again shifting to a realism about scientific theories, rather than the fictionalism he later advocates for. If "all models are wrong," then clearly knowledge and rationality are only forbidden by the laws of the universe in question, which is a wrong model his own lights. Secondly, this statement betrays Huong's unfamiliarity with (what I would argue are) key concepts field of epistemology, despite his respect for the field and encouragement of people to learn it (which I do very much appreciate by the way).
For a book primarily dealing with epistemology (the word "knowledge" is in the title), we get very little of it: little discussion on what separates knowledge from belief, basically nothing on the nature of justification, and crucially, no engagement with externalist vs internalist theories. Epistemologists such as Bonjour and Plantinga (who tend to use Bayesian calculations in their philosophical work) would have much to say about some of the claims in the book, such as the one above. Perhaps in a newer edition, Huong could write about how foundationlist theories of knowledge can integrate into Bayesianism in the form of certain priors: properly basic beliefs (such as incorrigible beliefs) could be assigned full confidence (probability 1), and this can help fight radical skepticism. It is hard to fault Huong too much for his unfamiliarity in epistemology given his breadth of knowledge in so many other areas. However engagement with these ideas is the key way the book could be improved, despite its current length and scope. Given the author's respect and appreciation for philosophy (something I respect and appreciate *him* for) my guess is he would find books such as Warrant: The Current DebateWarrant: The Current Debate (and the rest of the trilogy) deeply thought provoking and engaging.
Huong's aversion to considering teleological explanations in nature extends to his discussion of morality. He claims "The two main approaches to prescriptive moral philosophy are deontology and consequentialism," without discussing virtue ethics which has exploded in popularity and relevance in recent years. Key figures in moral philosophy, such as Alasdair MacIntyre have revived virtue ethics into a thriving field with work such as After Virtue, and yet we get zero discussion of this (read After Virtue for how virtue ethics can link teleology to moral prescriptions, getting around G.E. Moore's Open Question Argument and David Hume's is-ought distinction).
His inclination to consequentialism/utilitarianism leads him to suggest a rational agent would atempt to maximize E_x good(x) | a, which I found to be objectionalble . Consider a scenario where a biased coin, with a 55% probability of landing heads and a 45% of landing tails, is flipped. If you choose to play, if the coin lands on heads, you get a million dollars. If the coin lands on tails, you are executed. Would Huong argue a rational agent would play the game, since the expected good of playing is larger than not playing? Would he play himself (and if not, argue he is irrational since he is morally obligated to do so)?
Finally, and this is only a small nitpick, I think an exploration on minimum description length (MDL) and its relationship to compatibility as well as Solmonoff/Kolmogorov complexity would have provided another point of agreement. This topic is heavily implied but I think stating it explicitly would have helped, and some other recent work in detection theory have used this to tie Bayesianism together with algorithmic information theory (see Dembski and Ewert - The Design Inference 2nd Edition and some work by George Montanez such as his 2018 paper A Unified Model of Complex Specified Information). Additionally, given the mention of Joseph Bertrand in Section 6.6, I’m surprised the author didn’t mention Bertrand’s Paradoxes, since these provide additional support for the Bayesian view (based on work by statistician and philosopher of statistics Alan Hajek and Van Fraasen’s classic text Laws and Symmetry).
Again, despite my concerns, I do 100% recommend reading picking up book if you have any interest in probability or topics in STEM and how they relate to philosophy. It really is an incredible achievement, and if you read it with a careful and skeptical eye (something I'm sure the author would also encourage), I am (almost) certain you will learn something useful and interesting from it.
November 10, 2020
Very interesting at one level. Full of details and ideas worth thinking on. It traverses the range from Bayes Equation to the applications of Bayesian thinking to problems of moral philosophy.
Which is where it diverges from the apparent goal of establishing a coherent explanation of Bayesianism as a philosophy of knowledge or science. It seems to present this form of reasoning as the answer to what we do with the knowledge we gain.
If one reads this book, please never take it at face value. It justifies the authors reasoning as to why he believes as he does, but does not constitute a proof that this is a right or even a good belief. He assumes what is good the justifies his Bayesianism as conforming to those beliefs. Many valid objections are raised to what has been defined Science for many years, but Bayesianism is just another approach with advantages and disadvantages.
And keep in mind that this book refers his version of Bayesianism. Not all who employ Bayesian Methods will agree with his moral conclusions.
Which is where it diverges from the apparent goal of establishing a coherent explanation of Bayesianism as a philosophy of knowledge or science. It seems to present this form of reasoning as the answer to what we do with the knowledge we gain.
If one reads this book, please never take it at face value. It justifies the authors reasoning as to why he believes as he does, but does not constitute a proof that this is a right or even a good belief. He assumes what is good the justifies his Bayesianism as conforming to those beliefs. Many valid objections are raised to what has been defined Science for many years, but Bayesianism is just another approach with advantages and disadvantages.
And keep in mind that this book refers his version of Bayesianism. Not all who employ Bayesian Methods will agree with his moral conclusions.
November 11, 2023
I have stopped reading after 280 pages (about ⅔ of the book). The book is a more mathematically than philosophically driven discussion about the application of Bayes’ theorem. It is quite interesting, and it has recommended to me important literature and web resources. But it suffers from a major shortcoming – at least for me: It reviews in each chapter influential conjectures, theorems and equations. Even if the author tries to explain the essence to an audience without much mathematical knowledge and even if I have already read about of theorems in some chapters, the book is overloaded with too much different information. To explain quantum mechanics, chaos theory, thermodynamics, Shannon’s redundancy, Kullback-Leibler divergence, Wassterstein’s metric and Generative Adversarial Networks (GANS) in one chapter was too much for me.
Displaying 1 - 3 of 3 reviews