Book Review: "How Not to Be Wrong" by Jordan Ellenberg

I've recently read the book How Not to Be Wrong by Jordan Ellenberg. As the author states in the introduction, it is an exposition of simple yet profound ideas in mathematics, meant for laypeople. Topics include nonlinear phenomena (in opposition to naïve linear extrapolation), probability, Bayesian reasoning, and statistical testing of hypotheses. All chapters refer to many examples in politics, economics, and everyday life to make the concepts easier for laypeople to digest.

I found the book to be fairly easy to follow. I can't say that I learned much in terms of concepts, as these are all concepts that I've come across one way or another in school, college, graduate school, or my work now, though I did appreciate the discussion of how conspiracy theorists like to add hypotheses after the fact to make a conspiracy theory harder to fully disprove, how the fact that random fluctuations in many phenomena observed over time are time-reversal invariant implies that the phenomenon of regression toward the mean is also time-reversal invariant in a probabilistic sense, and the intuitive explanations of common causes & common effects in leading to correlations between random variables that are otherwise not causally connected. Additionally, I felt like this book did a better job than the book Algorithms to Live By by Brian Christian & Tom Griffiths (which I have reviewed on this blog before [LINK]) in having some structure in the progression from one chapter to the next and in using topics from earlier chapters in later chapters even though this book, unlike that book, didn't pretend to have a unified message. My only quibbles are the claim that the impossibility of accurately running the fundamental equations describing atmospheric & oceanic dynamics for more than 2 weeks implies impossibility in forecasting through other methods (like machine learning models looking for patterns in weather effects & progression) and the fact that the chapter connecting ideas from probability, geometry, and signal processing (particularly around error correction) took me a fair bit of effort to follow (unlike the other chapters, which tells me that laypeople will likely struggle with that chapter much more). Additionally, I think readers should be aware that the author often makes reference to sports that are mostly popular in the US and to US politics and that the author at a few points espouses more liberal or progressive political views (though I think such espousal is not gratuitous but is done in a way that fits well with broader discussions of assumptions underlying mathematical, political, and legal judgments). Overall, I think the author has done a good job of fulfilling the goal of communicating these ideas to a lay audience, so I recommend this book to anyone who might be interested in these ideas.

Book Review: "Algorithms to Live By" by Brian Christian & Tom Griffiths

I've recently read the book Algorithms to Live By by Brian Christian & Tom Griffiths. This book shows how many problems & heuristics in computer science can be applied to explain or improve human decision-making. Each chapter focuses on a certain class of problems or issues. Such classes include the optimal stopping problem, the multi-armed bandit problem, searching & sorting, task scheduling, Bayesian inference, overfitting data, constraint relaxation, random stimulus, communication protocols, and social interaction. Additionally, most chapters try to show how results from computer science can either improve or justify certain human behaviors.

This book was frustrating for me to read. If it had fully met my expectation that it would show, in a unified & consistent way, how these computer science problems apply to human behavior and connect to each other, I would be singing its praises. If it had completely failed, I'd be happy to rhetorically trash this book. Instead, I found that each chapter would be a great vignette on its own, and each chapter showed the great potential of what the book could have been, but the book failed to live up to that potential. First, there was very little connection among the chapters, and any acknowledgment that the authors did make of such connections was almost always superficial instead of deeply insightful. For example, the respective chapters about the optimal stopping problem, caches, and overfitting each could have been so much better with greater discussion about the connection to social pressure & game theory, yet those topics were discussed only in the last chapter, which I think was a mistake. Second, only in the concluding section did the authors make clear that they wanted to either improve or justify human behavior with each class of problems or issues. This because clear over the course of reading the book, yet there was very little guidance in each chapter about whether improvement versus justification would be the goal. Perhaps the worst offender was the chapter about constraint relaxation, as there was little connection to human behavior in a way that would be obvious to lay readers. These problems meant that reading the last numbered chapter (about game theory) and the conclusion felt simultaneously wonderful for finally seeing these concepts discussed clearly and maddening for knowing that the book could have been so much better if these ideas had been more consistently executed through the book.

There are two other minor criticisms I have of the book too. First, the chapter about overfitting seems to use the word "overfitting" to mean too many different things, which is ironic and undermines any clarity that the discussion could have provided. Second, the chapter about randomized algorithms attempts to make a tenuous connection between randomized algorithms used in computer science and the way that random mental stimuli can produce very creative responses in people, but it never makes clear whether the latter result is true at an individual level or only holds statistically for large populations.

Overall, I think the author's goals were laudable and that each chapter is interesting to read in isolation. However, other readers may be disappointed, as I was, in the way that the authors fail to synthesize many of the ideas across chapters in a smooth & unified manner. Thus, I would advise that readers who may be interested in these topics go into this book with lower expectations.

Classical Phase Space Densities for One or a Few Particles

This is the first time in several years that I've done a post about physics that didn't have to do with my research. This came about from thinking about applying techniques in statistical physics to game theory; although I still have a lot more to learn about that and need to do more to flesh out those ideas, it occurred to me in the process that I never had such a good intuition for the phase space density in classical mechanics, and notes that I've found online focus almost exclusively on the phase space density of a large number of particles in an explicitly statistical treatment. I intend to use this post to shed light on why this may be the case, help build intuition for how things like the Liouville equation work for simple systems of one or a few particles, and reinforce the notion that there is no classical analogue to the phenomenon of a multi-particle entangled quantum state yielding a mixed single-particle state under a partial trace. Follow the jump to see more.

Book Review: "The Evolution of Cooperation" by Robert Axelrod

I've recently read the book The Evolution of Cooperation by Robert Axelrod. (Note: this is somewhat of a technical book, so I will dive right into the review with jargon, with more on this point at the end of the review.) It's a primer on results from that time showing how in an iterated prisoners' dilemma, tit-for-tat strategies are remarkably robust for their combination of simplicity, clarity, tendency toward cooperation and forgiveness, and prompt & effective retaliation when needed, and that such strategies can effectively propagate environments even where other strategies are in place, provided that those who play the tit-for-tat strategies can find & cluster around each other to interact often enough, and provided that the value each player places on the next round compared to a given round in an iterated game is not too small. The author also uses examples from trench warfare in World War I, biological evolution, and international trade policy to illustrate the seeming universality of the principles of the prisoners' dilemma and its iterated variant.

Although this book was written in the 1980s, making it a little dated in terms of the complexity of models that could be tested on computers and the formalism of game theory itself, it was great to see the author anticipate a lot of more recent developments by discussing the importance of clustering, stereotypes, reputation, regulations, et cetera. Additionally, while the author stresses that cooperation can take place even among egotistical (non-altruistic) or antagonistic individuals in the absence of central authority, the author does take care to convey the nuance that this is not always a good thing per se, rather than taking the utopic view of libertarian philosophy; such cooperation is detrimental to the public at large in situations like economic collusion in an oligopoly, while the incentives to cooperate or not change such that government (or other societal) intervention is needed to do things like collect taxes & deter evaders to fund public goods, correct historical (and present) racist marginalization of minority groups, mediating conflicts among heterogeneous populations in large cities, et cetera. It was also cool for me to understand that any iterated game where the players are unsure of when the game will end but others controlling the game know it will end after a finite number of rounds can be rewritten as a similar game where the players believe the repetition will be infinite but with a different discount factor. My only minor complaints are that while the author does acknowledge that changing parameters of a social interaction can change the prisoners' dilemma into a different sort of game altogether, it would have been nice to see a more nuanced discussion of the degree to which the prisoners' dilemma is really a universal feature of human interactions as opposed to being culture-specific, given its seeming universality in other domains, and that the author rather glibly claims that sequential versus simultaneous play by players in each round of an iterated prisoners' dilemma doesn't make much of a difference, which I find suspicious in the absence of further explanation/context in the book itself. Overall, I enjoyed reading this and could read it quickly because of my minor in economics in college & interest in the subjects of economics, game theory, and network science, so it may be appropriate to others with similar interests & backgrounds as myself; it is a fairly technical book, so it may not be appropriate to general readers without this background, while specialists in the fields of evolution, game theory, or complexity science may find this book to be too dated.