Everything is Obvious.

Duncan Watts’ book Everything is Obvious *Once You Know the Answer: How Common Sense Fails Us fits in well in the recent string of books explaining or demonstrating how the way we think often leads us astray. As with Thinking Fast and Slow, by Nobel Prize winner Daniel Kahneman, Watts’ book highlights some specific cognitive biases, notably our overreliance on what we consider “common sense,” lead us to false conclusions, especially in the spheres of the social sciences, with clear ramifications in the business and political worlds as well as some strong messages for journalists who always seek to graft narratives on to facts as if the latter were inevitable outcomes.

The argument from common sense is one of the most frequently seen logical fallacies out there – X must be true because common sense says it’s true. But common sense itself is, of course, inherently limited; our common sense is the result of our individual and collective experiences, not something innate given to us by God or contained in our genes. Given the human cognitive tendency to assign explanations to every event, even those that are the result of random chance, this is a recipe for bad results, whether it’s the fawning over a CEO who had little or nothing to do with his company’s strong results or top-down policy prescriptions that lead to billions in wasted foreign aid.

Watts runs through various cognitive biases and illusions that you may have encountered in other works, although a few of them were new to me, like the Matthew Effect, by which the rich get richer and the poor get poorer. According to the theory behind it, the Matthew Effect argues that success breeds success, because it means those people get greater opportunities going forward. A band that has a hit album will get greater airplay for its next record, even if that isn’t as good as the first one, or markedly inferior to an album released on the same day by an unknown artist. A good student born into privilege will have a better chance to attend a fancy-pants college, like, say, Harfurd, and thus benefits further from having the prestigious brand name on his resume. A writer who has nearly half a million Twitter followers might find it easier to land a deal for a major publisher to produce his book, Smart Baseball, available in stores now, and that major publisher then has the contacts and resources to ensure the book is reviewed in critical publications. It could be that the book sells well because it’s a good book, but I doubt it.

Watts similarly dispenses with the ‘great man theory of history’ – and with history in general, if we’re being honest. He points out that historical accounts will always include judgments or information that was not available to actors at the time of these events, citing the example of a soldier wandering around the battlefield in War and Peace, noticing that the realities of war look nothing like the genteel paintings of battle scenes hanging in Russian drawing rooms. He asks if the Mona Lisa, which wasn’t regarded as the world’s greatest painting or even its most famous until it was stolen from the Louvre by an Italian nationalist before World War II, ascended to that status because of innate qualities of the painting – or if circumstances pushed it to the top, and only after the fact do art experts argue for its supremacy based on the fact that it’s already become the Mona Lisa of legend. In other words, the Mona Lisa may be great simply because it’s the Mona Lisa, and perhaps had the disgruntled employee stolen another painting, da Vinci’s masterpiece would be seen as just another painting. (His description of seeing the painting for the first time mirrored my own: It’s kind of small, and because it’s behind shatterproof glass, you can’t really get close it.)

Without directly referring to it, Watts also perfectly describes the inexcusable habit of sportswriters to assign huge portions of the credit for team successes to head coaches or managers rather than distributing the credit across the entire team or even the organization. I’ve long used the example of the 2001 Arizona Diamondbacks as a team that won the World Series in spite of the best efforts of its manager, Bob Brenly, to give the series away – repeatedly playing small ball (like bunting) in front of Luis Gonzalez, who’d hit 57 homers that year, and using Byung-Hyun Kim in save situations when it was clear he wasn’t the optimal choice. Only the superhuman efforts by Randy Johnson and That Guy managed to save the day for Arizona, and even then, it took a rare misplay by Mariano Rivera and a weakly hit single to an open spot on the field for the Yanks to lose. Yet Brenly will forever be a “World Series-winning manager,” even though there’s no evidence he did anything to make the win possible. Being present when a big success happens can change a person’s reputation for a long time, and then future successes may be ascribed to that person even if he had nothing to do with them.

Another cognitive bias Watts discusses, the Halo Effect, seems particularly relevant to my work evaluating and ranking prospects. First named by psychologist Edward Thorndike, the Halo Effect refers to our tendency to apply positive impressions of a person, group, or company to their other properties or characteristics, so we might subconsciously consider a good-looking person to be better at his/her job. For example, do first-round draft picks get greater considerations from their organizations when it comes to promotions or even major-league opportunities? Will an org give such a player more time to work out of a period of non-performance than they’d give an eighth-rounder? Do some scouts rate players differently, even if it’s entirely subconscious, based on where they were drafted or how big their signing bonuses were? I don’t think I do this directly, but my rankings are based on feedback from scouts and team execs, so if their own information – including how teams internally rank their prospects – is affected by the Halo Effect, then my rankings will be too, unless I’m actively looking for it and trying to sieve it out.

Where I wish Watts had spent even more time was in describing the implications of these ideas and research for government policies, especially foreign aid, most of which would be just as productive if we flushed it all down those overpriced Pentagon toilets. Foreign aid tends to go to where the donors, whether private or government, think it should go, because the recipients are poor but the donors know how to fix it. In reality, this money rarely spurs any sort of real change or economic growth, because the common-sense explanation – the way to fix poverty is to send money and goods to poor people – never bothers to examine the root causes of the problem the donors want to solve, asking the targets what they really need, examining and removing obstacles (e.g., lack of infrastructure) that might require more time and effort to fix but prevent the aid from doing any good. Sending a boat full of food to a country in the grip of a famine only makes sense if you have a way to get the food to the starving people, but if the roads are bad, dangerous, or simply don’t exist, then that food will sit in the harbor until it rots or some bureaucrat sells it.

Everything Is Obvious is aimed at a more general audience than Thinking Fast and Slow, as its text is a little less dense and it contains fewer and shorter descriptions of research experiments. Watts refers to Kahneman and his late reseach partner Amos Tversky a few times, as well as other researchers in the field, so it seems to me like this book is meant as another building block on the foundation of Kahneman’s work. I think it applies to all kinds of areas of our lives, even just as a way to think about your own thinking and to try to help yourself avoid pitfalls in your financial planning or other decisions, but it’s especially apt for folks like me who write for a living and should watch for our human tendency to try to ascribe causes post hoc to events that may have come about as much due to chance as any deliberate factors.

Gödel’s Proof.

My latest Insider post covers eight top 100 prospects who took a step back this year. I’ll also hold a Klawchat here at 1 pm ET.

I read Rebecca Goldstein’s biography of Kurt Gödel, Incompleteness, last summer, and I believe it was within her book that I read about James Newman and Ernest Nagel’s book Gödel’s Proof that attempts to explain the Austrian logician’s groundbreaking findings. The 114-page volume does a great job of building up to the final proof, but I have to concede that the 19-page section near the end that reveals the fatal blow Gödel delivered to Bertrand Russell, David Hilbert, and others who believed in the essential completeness of mathematical systems lost me in its nested language and ornate symbols. (The newest edition includes a foreword by Douglas Hofstadter, who wrote about the proof in Gödel, Escher, Bach, which won the Pulitzer Prize for Non-fiction.)

Gödel was himself a fascinating figure, a philosopher, mathematician, and logician who wrote a paper with two theorems at age 25 that stunned the world of mathematics in their method and conclusions, proving that any axiomatic system of arithmetic that is consistent cannot be complete. Completeness here means that every true formula that can be expressed within the system can be proven within the system. Gödel’s trick was to create an entire system of expressing logical formulas via what is now called Gödel numbering, and then to craft a formula that says itself that it is unprovable within the system. His proof further stated that even if you could add an axiom to this system of mathematics to cover this new exception, the formula could always be rephrased to pose a new exception, and thus the system is essentially incomplete.

Nagel and Newman do a great job of getting the reader – or at least in getting this reader – to the edge of understanding by building up the history of the question, giving a lay explanation of Gödel’s basic method of numbering and delineating what a simple axiomatic system like that of Russell’s Principia Mathematica (the system Gödel targeted in his proof) would look like. Russell and other logicians of the time were convinced that systems of mathematics were complete – that we could define any such system in terms of a finite number of axioms that would cover all possible formulas we could craft within that system. Any formula that could be proven true at all could then be proven true using only the axioms of that system. Gödel’s proof to the contrary was scarcely noticed at first, but when it spread and others in the field realized it might be true, it blew apart a fundamental assumption of number theory and of logic, while also making Gödel’s name as a major figure in the history of mathematics and logic.

All of which is to say that I just couldn’t follow the nested statements that constitute Nagel and Newman’s explanation of Gödel’s proof. I haven’t read Gödel’s original paper, because it is a truth universally acknowledged that you’ve got to have some serious math background to understand it, so I will accept the claim that Nagel and Newman made it much easier to grasp … but I still only get this at a superficial level. When the authors compare this to Richard’s Paradox, an earlier device that Gödel cited in his paper, I could understand it; these are all descendants of the “This statement is false” type of logical trick that causes an inherent contradiction. Gödel appears to have done the same thing for arithmetic. I just couldn’t quite get to the mental finish line on this one. I guess you could say my understanding of the topic remains ….

…incomplete.

Next up: I finished and will review Laurent Binet’s HHhH, and have begun Clifford Simak’s Hugo-winning novel Way Station.

Incompleteness.

My final top 100 draft prospect ranking for 2015 is up for Insiders, and my latest review for Paste covers the Temple of Elemental Evil boardgame.

Rebecca Goldstein’s Incompleteness: The Proof and Paradox of Kurt Gödel, part of the same “Great Discoveries” series that includes David Foster Wallace’s Everything and More: A Compact History of Infinity, takes the abstruse topic of Gödel’s two incompleteness theorems and folds it into a readable, compelling biography of both the man and his ideas. Using the logician’s friendship with Albert Einstein as a hook, Goldstein gives us about as intimate a portrait of the intensely private Gödel as we can get, while also laying the groundwork so the non-metamathematicians among us can understand the why and how of Gödel’s theorems.

There’s very little actual math involved in Incompleteness, because the two theorems in question revolve around the nature of mathematics, notably arithmetic, as an axiomatic system that mathematicians and philosophers of the early 1900s were trying to use as a basis to describe arithmetic as a formal system – that is, one that can be fully described via a system of symbols and syntax, used to construct well-formed formulas (wffs, not to be confused with wtfs), some of which are the axioms that define the whole system. If such axioms can describe the entire system in a way that an algorithm (which is probably easiest to conceive as a computer program) can use those axioms and only those axioms to prove all truths or assertions about the natural numbers, then arithmetic would be considered a complete system, something Gödel proved was impossible in his first theorem. His second theorem went even further, showing that such a system of arithmetic also could not be consistent within itself by demonstrating that a statement of the system’s consistency would generate an internal contradiction.

Gödel imself was an incomplete figure, a hypochondriac who degenerated into outright paranoia later in life, and a socially awkward man who would likely have been diagnosed in today’s world of psychiatry and medicine as a depressive or even somewhere on the autism spectrum. He formed few lasting friendships, feared that no one could understand him (and given the meandering paths of his mind, I don’t doubt this was true), and was often shockingly aloof to what was happening around him. He fled his native Austria before World War II, even though he wasn’t Jewish, because his association with the secular Jewish scholars of the Vienna Circle (most of whom were logical Positivists, arguing that anything that could not be empirically proven could not be considered true) cost him his university position. Yet he remained unaware of the state of affairs in his native country, once (according to Goldstein) asking a Jewish emigré who had fled Nazi persecution for the United States, “What brings you to America?”

Goldstein does a superb job setting the scene for Gödel’s emergence as a logician/metamathematician and as a figure of adulation and controversy. The Vienna Circle was, in Goldstein’s depiction, somewhat insular in its unwavering acceptance of Positivism, and as such certain that Hilbert’s second problem, asking for a proof that arithmetic is internally consistent, would be proven true. Gödel’s second theorem showed this was not the case, leading to his own intellectual isolation from thinkers who were heavily invested in the Positivist view of mathematics, a bad outcome for a man who was already prone to introversion and diffidence. G&omul;del found it difficult to express himself without the use of logic, and while his station at Princeton’s illustrious Institute for Advanced Study – a sort of magnet think tank that became a home for great scholars in math and the sciences – put him in contact with Albert Einstein, it also deepened his solitude by limiting his orbit … although that may have been inevitable given his late-life delusions of persecution. Goldstein did encounter Gödel once at a garden party at Princeton, only to see him at his most gregarious, holding court with a small group of awestruck graduate students, only to disappear without a trace when his spell of socializing was over. He was, in her description, a phantom presence around campus, especially once his daily walks with Einstein ended with the latter’s death in 1955.

While giving a basic description of Gödel’s theorems and proofs, focusing more on their implications than on the underlying math, Goldstein does send readers to the 1958 Gödel’s Proof, a 160-page book that attempts to give readers a more thorough understanding of the two theorems even if those readers lack any background in higher math. Incompleteness focuses instead on the man as much as it does on his work, producing a true narrative in a story that wouldn’t otherwise have had one, making it a book that I could recommend to anyone who can stand Goldstein’s occasional use of a $2 word (“veridical”) when a ten-cent one (“truthful”) would have done.