I picked up Logicomix in Moe’s Books in Berkeley yesterday. It’s a graphic novel that tells the story of Bertrand Russell’s tortured quest to discover the logical foundations of mathematics. It is fascinating because it focuses in such detail on the torment of these great minds who spent their lives chasing after an impossibility. Russell’s ultimate goal was to begin with a set of well-defined axioms and prove all mathematical truths from those axioms. The goal of this program was to eliminate all paradox and uncertainty from the foundation of mathematics, generally represented by the “obvious” statements that had been used in proof before Russell’s time.
Russell first ruins the foundations of set theory with a paradox: does the set of all non-self-referential sets contain itself? I love the way the book describes Russell’s emotion toward his discovery though. It says that Russell felt like a devout Catholic journalist uncovering the Pope’s ignominy. The rest of Russell’s story follows the same path: ups and downs tormented by the impossibility of a universal set of axioms. For some reason the graphic novel format, with its incredibly detailed comics, does a phenomenal job of telling the story. I have not been able to put it down. It’s a quick, fun, intriguing read that really gets into the character of Russell.
The Black Swan by Nassim Nicholas Taleb is a warning about the unforeseen risk inherent in any complex model and the ways we blind ourselves to said risk. To illustrate his point, Taleb presents two polar worlds: the one we perceive he dubs “mediocristan” while the world we experience is “extremistan.” Bell-curve and average describe mediocristan, a place where deviations from the norm are readily explained by null hypotheses and standard deviations. Taleb convincingly argues, however, that we should focus more on Extremistan, a place where a single observation greatly affects the average.
Wealth is one such example. Take Bill Gates’ wealth and add it to 100 middle class family net worths. The average clearly tells us little about the true nature of the situation. In this example, Bill Gates is a Black Swan, an ultra-rare, highly impactful event that greatly influences our observations.
What causes our blindness to these Black Swans? Among many reasons, Taleb accuses the study of history. By packaging events into neat cause-effect relationships, we lose sight of their true randomness. We are also subject to the ludic fallacy — Taleb’s term for when we mistake the model for the real thing. And, along with others, we almost always trust anecdote to empirical data. That is, we are more likely to be influenced by stories of our friends tell rather than fact.
This was the best book I’ve read this year so far. Highly recommended!