Logicomix

Logicomix: An Epic Search for Truth is a graphic novel created by Apostolos Doxiadis and Christos H. Papadimitriou about Bertrand Russell and his quest to get to the core of logical certainty. The novel is most biographical about Russell's education and life, with tangents into the logical and mathematical issues that he and other scholars were struggling with in the early Twentieth Century.

One of the themes of the book is the relationship between mathematics and insanity, since so many great mathematicians have gone insane. Does one cause the other? Does the search for more and more absolute knowledge cause one to lose the foundations of reality? Russell also struggles with this at times, espcially since there is madness in his own family.

Russell sees great promise in the mathematics of set theory, and seeks to expand it to create the foundations of arithmetic and thus all mathematics. He comes up with what is known as Russell's paradox: he defines a set that contains all sets that do not contain themselves, then asks, does this set contain itself? This is better known as the barber paradox. In a town, all men either shave themselves, or if they don't shave themselves, are shaved by the barber. This question is, who shaves the barber? If he does not shave himself, then he is shaved by the barber, but since he is the barber, he would be shaving himself. This paradox gets to the core of the nature of self-referential definitions.

Russell spends years with his friend and fellow mathematician Alfred North Whitehead to create the Principia Mathematica, a scholarly work whose goal is to define the foundations of mathematics and logic. One interesting setback is when the publisher can't find anyone who will be paid to proofread the book so decides that if nobody will be paid to read it, nobody will pay to read it. Reluctantly they paid for its publication and it proves to be an important scholarly work. Of course, Kurt Gödel publishes his discovery that no such system can be complete and provable, that in any complete system there are unprovable statements. This was a major setback to Russell and Whitehead, and it shook the world of mathematics.

Reading this book made me want more math in it, for it is light on the math and only provides a few simple examples so that the lay reader will understand the scope of the problems involved. This is not like Gödel, Escher, Bach, which is a much deeper dive into the issues of sets and the nature of self-reference. This is mostly biography and deals with Russell's personal relationships such as his marriages and his friendship with Whitehead's son. The framing story is Russell's speech at an American university, but the story also makes references to the current day as the authors jump in to make explanations or provide more context. Sometimes they discuss the questions of madness or how the mathematical questions impact us. The end contains a performance of teh end of Aeschylus' trilogy the Oresteia, wherein Athena transforms the history of revenge killings into a system of state-supported justice. While an interesting coda, I didn't quite understand the relevance to mathematics and logic and Russell's great issues. But the book is an interesting look at Russell's life and the logical questions that he proposed and tried to answer. A-

The Drunkard's Walk

The Drunkard's Walk: How Randomness Rules Our Lives, written by Leonard Mlodinow, is one of those books that makes an arcane subject understandable. Mlodinow explains statistics and probability in very clear language, with many examples and counter examples.

He tracks the history of probability theory from when gamblers started analyzing the games they played in an effort to improve their chances. Different people analyzed dice and cards and came up with algorithms to predict different odds. One gambler analyzed the different roulette wheels at a casino and discovered one that landed on certain numbers more often than other numbers. He used his findings to place large bets and won big until the casino got rid of the offending machine.

There is a good discussion of the rules of large numbers, including a description of Benford's Law. Benford's Law is an observation about numbers in real life that says that smaller digits are more likely to occur than larger digits. There is also a long discussion of how difficult it is to estimate probabilities with small sample sizes. And some mention is made of the difference between statistics, which describes a set of measurements in the real world, and probability, which takes those measurements and tries to make predictions based on it. He also discusses the concept of randomness and whether it implies equal likelihood of the outcomes.

I learned a lot about probability (even though I think I'm already pretty educated about it) when Mlodinow explained some of the contradictions and counterintuitive results in probability. He explains the Monty Hall problem well enough that I think I actually understand it now (and believe it's true). He also explains related paradoxes such as the Two Daughters question by showing how to expand all the possibilities of the sample space. Some of the solutions can be shown not only by deductive logic but by looking at actual results in the population.

Mlodinow also discusses how our minds interpret randomness and make a sort of order out of it, whether correct or not. A long succession of heads for coin flips or a long hitting streak in baseball is not necessarily a non-random event. Given enough chances, a lot of different outcomes can be expected. The streak of a Wall Street analyst can be explained by showing that the population of analysts can be expected to produce at least one such winning streak over a long enough time period. However we see numbers and understand them differently for individual events that happen to us. A story with a lot of detail is more likely to be remembered than one without. Combinations of events can appear more likely than the events separately, which is impossible. I appreciated this psychological look at how numbers and chance are processed in the mind.

I also appreciated the explanation of false positives: how a test with small chance of a mistake doesn't necessarily mean that the results are certain. Indeed, after listening to this audiobook I have a much better understanding of certainty and chance. It is important to appreciate the vast numbers that are relevant to our lives. This book gives a great understanding to how numbers and randomness work in real life. I highly recommend it. A