→ March 29, 2018
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The Origins of Totalitarianism.

I spent my first year in college as a Government major, with some vague idea of studying law and/or working in politics after graduation, but abandoned the major completely by the middle of my sophomore year because the reading absolutely killed me. I like to read – I would hope that was evident to regulars here – but the kind of writing we were assigned in those classes was just dreadful. There was a book by Samuel Huntington (The Clash of Civilizations and the Remaking of World Order) that ended any interest I might have had in the subject because it was such an arduous, opaque read, and I eventually switched to a joint sociology/economics major, which got me into more of my comfort zone of a blend of math and theory.

Hannah Arendt’s The Origins of Totalitarianism reminded me tremendously of Huntington and John Stuart Mill and other books I was assigned in Gov 1040 but never actually finished, both in prose style and in tone. I understand that this book is considered extremely influential and an important work in our comprehension of how movements like the Nazi Party arise and even gain a modicum of popular support. The arguments herein, however, are almost exclusively assertions, with anecdotal evidence or no evidence at all, and the circumlocutory writing style meant that even though I retain a lot of what I read in most cases, I found I wasn’t even retaining what I read here from one page to the next.

Arendt’s main thrust here is that totalitarian governments, which she distinguishes from mere autocracies, arise when their leaders follow a rough playbook that sets up specific groups as enemies of the state, rallies disaffected followers against those groups, and often makes their supports into unwitting advocates of their own eventual oppression. Such governments then retain power by eliminating the possibility of what Arendt refers to as human spontaneity through an Orwellian system of truth-denial and unpredictable favoritism that puts subjects on ever-shifting ground, preventing them from mounting any effective system of dissent or resistance.

At least, I think that’s what she was arguing, but she used a lot of extraneous words to get there – and some of what she described in the early going, where she addresses the history of the so-called “Jewish question,” sounded a lot like victim blaming. She certainly says the Jews of Europe did not adequately understand how they were being used by European elites or how their connections to unpopular leaders like the Hapsburgs thus put them in the crosshairs of populist movements that aimed at overthrowing the monarchical or despotic status quo. She also seems to credit the same movements with their willingness to employ efficient methods of killing for its surprise value – no one expected anything like the Nazis’ system of killing masses of people, based itself on a process of dehumanization of entire classes of the population.

Whether I fully grasped the arguments Arendt makes in this book – and I freely acknowledge I probably did not – but much of what she does assert seems apposite to our present-day political situation, including the way in which Trump supporters, including his sycophants in the media, have repeatedly handwaved away his distortions of fact or his apparent collusion with a hostile foreign power. I’ll close, therefore, with this selection of quotes from The Origins of Totalitarianism that could just as easily have been written today about our current environment.

In the United States, social antisemitism may one day become the very dangerous nucleus for a political movement.

Politically speaking, tribal nationalism always insists that its own people is surrounded by “a world of enemies,” “one against all,” that a fundamental difference exists between this people and all others. It claims its people to be unique, individual, incompatible with all others, and denies theoretically the very possibility of a common mankind long before it is used to destroy the humanity of man.

The rank and file is not disturbed in the least when it becomes obvious that their policy serves foreign-policy interests of another and even hostile power.

(The Nazis) impressed the population as being very different from the “idle talkers” of other parties.

The mob really believed that truth was whatever respectable society had hypocritically passed over, or covered up with corruption.

Hitler circulated millions of copies of his book in which he stated that to be successful, a lie must be enormous.

The ideal subject of totalitarian rule is not the convinced Nazi or the convinced Communist, but people for whom the distinction between fact and fiction (I.e., the reality of experience) and the distinction between true and false (I.e., the standards of thought) no longer exist.

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→ May 31, 2017
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Babel-17.

My second first-round projection (“mock”) for this year’s draft is up for Insiders.

Samuel Delany wrote his short novel Babel-17, a smart, profound philosophical work, when he was just 23 years old, an astounding achievement for a work that would be impressive for an author of any age. The prose is a bit abstruse and the story a little meandering, but this is a novel of ideas, or rather one very big idea, that the language we speak can ultimately shape the way we think, a concept known as the Sapir-Whorf Hypothesis. (If any of this sounds familiar, it’s also the core idea behind the 2016 movie Arrival.)

According to The Linguist List, the Sapir-Whorf Hypothesis states that “an individual’s thoughts and actions are determined by the language or languages that individual speaks.” The words and concepts of a language thus define not just what you say, but what you think and do. That simple version of the hypothesis, also called “linguistic relativism,” is generally accepted to be true, although there’s naturally disagreement on its extent, and there are stronger variations of the theorem (found in that link above) that are more controversial.

Delany builds an entire story around Sapir-Whorf, using an alien language called Babel-17 that humans and their allies have tried for years but failed to fully decipher, but that the other side in an ongoing, intergalactic war have weaponized to create turncoats within the allies’ forces. The protagonist, the poet and starship captain Rydra Wong, finds herself recruited by the Allies to crack what they suspect to be a code, only for her to discover that it’s an actual language that can re-program someone’s brain. This leads her on a series of missions into the war zone while coping with the likelihood that one of her own crew members is trying to sabotage the ship and potentially kill her.

For a novel that’s ostensibly set in a war, there’s very little fighting in Babel-17, which spends more time describing the consequences of war (like mass starvation) than the details of battle. Delany was enamored with his ideas about language, and managed to combine those with a compelling, three-dimensional protagonist – perhaps a too perfect one, as Rydra is brilliant, empathetic, and apparently beautiful, although the last point is only mentioned but never a factor in the story. The plot itself is a little muddled, and Delany’s prose struck me as Joyceian in spots, so for a book of under 200 pages it took me more time than I’d expect to get through it … which isn’t a criticism per se, more an observation given how quickly I read in general, and a reflection of how philosophical this novel is.

Delany does struggle to get the story to a reasonable, fulfilling conclusion, but I think that’s more feature than bug because the open question of the book, can language determine who we are and how we act, is not conducive to a plot deep enough for a novel. (Arrival got away with it, I think, because it was based on a short story, and a movie can work with a much shorter or thinner plot than a full-length novel can.) I never found myself wrapped up in the war plot. Delany gets more mileage out of the saboteur thread, although that conclusion wasn’t terribly satisfying on its own, only in the context of the broader question about language and thought. While I imagine linguists might object to his metaphor here, using Babel-17 as a brainwashing tool (and thus weaponizing Sapir-Whord), it takes a difficult and I think controversial topic in linguistics and puts it into a story in a way that an adept reader would understand the hypothesis and be left with plenty to chew on after finishing. That’s the great achievement of this book.

Jo Walton, whose book Among Others is one of my favorite novels of any genre, also weighed in on the wonders of Babel-17.

Next up: Richard Russo’s Everybody’s Fool. It’s good to see Sully again.

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→ September 15, 2016
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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.

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→ September 6, 2016
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The Antidote.

We are inundated with messages and products that promise to tell us how to be happy. A quick amazon search for “how to be happy” yields books with titles like The 18 Rules of Happiness: How to Be Happy, How We Choose to Be Happy: The 9 Choices of Extremely Happy People–Their Secrets, Their Stories, and Be Happy! – How to Stop Negative Thinking, Start Focusing on the Positive, and Create Your Happiness Mindset. You can spend even more money to attend seminars like “How Positive Psychology Changes Our Lives,” “Happiness and its Causes,” and “The Happiness Habit.” All of this, as you might imagine, is just so much bullshit, and I fail to see how someone else taking my money for it is going to make me any happier.

In fact, as Oliver Burkeman argues in The Antidote: Happiness for People Who Can’t Stand Positive Thinking, much of this material is actually deleterious to our efforts to be happier. The feeling that we should be happy just makes us less so, and attempts to be happier by pushing out negative thoughts creates anxiety and, as you probably know, does nothing to keep those negative thoughts at bay. Burkeman approaches the happiness paradox – how those of us in developed countries, especially those of the west, seem to be so much less happy today even though our most basic existential needs are largely met – from a novel angle, instead looking at ways to find happiness through understanding and even embracing the things that tend to make us unhappy.

Burkeman begins the book at a rah-rah positive-thinking seminar held by Dr. Robert Schuller, at the time the leader of a megachurch in Texas, who would end up filing for bankruptcy a few months after Burkeman attended the rally. (Schuller died of cancer in 2015.) Schuller’s words – and those of President George W. Bush, who spoke briefly at the rally as well – appear to have been a lot of empty if not outright counterproductive advice, like banishing the word “impossible” from your vocabulary. Fortunately, this book isn’t just about knocking over mountebanks like Schuller; Burkeman instead explores seven avenues of finding happiness that not only seem to work (or at least to help) but also run counter to the “think positive” mentality that poisons everyone’s attempts to get happier.

Burkeman begins with the stoics, the ones from ancient Greece and the folks still practicing and teaching stoicism today, and moves along to Buddhism, to the secular aspects of Eckhart Tolle’s writings, and even to the Mexican tradition of celebrating death. He visits a museum of commercial product failures in Michigan and explains how our refusal to reconsider our failures leads us to make the same mistakes – as many businesses do, conceiving the same products repeatedly despite past evidence that they’re bad ideas.

Several of those philosophies revolve around the fact that trying to avoid negative or unwanted thoughts makes them harder to get rid of (demonstrated in the white bear experiment). Thinking about the worst-case scenario – when it’s extremely unlikely to occur, that is – can in fact reduce your anxiety about bad things that are likely to occur, because you’ll better understand that they too shall pass. If you’ve practiced mindfulness, or traditional meditation, you know that you are not supposed to suppress negative thoughts when they occur because it doesn’t work; you are supposed to observe them “without judging” and let them float on by. If you’re obsessed with things going wrong, simply saying – or having someone tell you – that they won’t go wrong isn’t helpful. You have to acknowledge those possibilities and put them in the proper context before you can get around them, and then, perhaps, you can be happier.

Along the way, Burkeman demolishes a lot of happiness and productivity myths. Setting goals does not, in fact, make you more likely to achieve them, but it does make you less happy when you fall short. The management scholar Chris Kayes coined the term “fatal magnetism” when analyzing the 1996 Mount Everest disaster, where many climbers who should have known better continued toward the summit in conditions that all but guaranteed they’d die on the way down. Kayes argues that these climbers were so hellbent on achieving their goals that they couldn’t think rationally about failing to do so, an extreme example of how goal-setting can distort our thinking. Burkeman also discusses “security theater,” Bruce Schneier’s term for how we enact visible efforts to stop terrorist attacks – think metal detectors at baseball stadiums – that don’t make us any safer but do impose significant costs on us in time and money. So while The Antidote is ostensibly about happiness, it covers a lot of other areas of life where we go wrong, including obstacles to productivity, inability to properly assess danger (of the physical or financial kinds), and our susceptibility to the placebo effect.

I learned quite a bit from Burkeman’s book, much of which will directly change how I go about my daily life and my work. I am fortunate in that, by nature, I’m a happy, optimistic person; my anxiety disorder is not about dwelling on what might go wrong, but more about reacting badly when things do go wrong, as well as the ongoing static in my brain that didn’t abate until I started a low dose of medication. But like most people, happy or not, I have sources of stress – myriad work responsibilities, like that whole writing-a-book thing right now, and the challenge of balancing work, family, personal interests, and being a homeowner, to pick a few examples – and The Antidote explains how to change your mindset around these questions. Burkeman also gets repeated counsel from the people he interviews or sources he consults about living more in the present; we worry too much about the future and we probably dwell too much on the past, which is why we don’t appreciate what we have now enough to enjoy it. There is no single key to happiness, nor are there 18 steps to take you there, but I think The Antidote can at least help you realign your thinking so you have a chance to be happier.

Next up: I’ve been reading faster than I can write reviews, but I expect to finish Connie Willis’ Hugo and Nebula Award-winning novel The Doomsday Book today.

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→ July 22, 2016
→ By

Infinitesimal.

Amir Alexander’s Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World is less a history of math (although there is quite a bit) than a history of the people and institutions who fought a protracted philosophical battle over something we now consider a trivial bit of precalculus. The idea of infinitesimals, at the time of their development called “indivisibles,” sparked vociferous opposition from the supposedly progressive Jesuits in the 1600s, becoming part of their vendetta against Galileo, leading to banishments and other sentences against Italian mathematicians, and eventually pushing the progress of math itself from Italy out to Germany, England, and the Netherlands.

If you’ve taken calculus at any point, then you’ve encountered infinitesimals, which first appeared in the work of the Greek mathematician Archimedes (the “eureka!” guy). These mathematical quantities are so small that they can’t be measured, but their size is still not quite zero, because you can add up a quantity (or an infinity) of infinitesimals and get a concrete nonzero result. Alexander’s book tells the history of infinitesimals from the ancient Greeks through the philosophical war in Italy between the Jesuits, who opposed the concept of indivisibles as heretical, and the Jesuats, a rival religious order founded in Siena that included several mathematicians of the era who published on the theory of indivisibles, including Bonaventura Cavalieri. When the Jesuits won this battle via politicking within the Catholic hierarchy, the Jesuats were forced to disband, and the work involved in infinitesimals shifted to England, where Alexander describes a second battle, between Thomas Hobbes (yep, the Leviathan guy) and John Wallis, the latter of whom used infinitesimals and some novel work with infinite series in pushing an inductive approach to mathematics and to disprove Hobbes’ assertion that he had solved the problem of squaring the circle.

Wallis’ work with infinitesimals extended beyond the controversy with Hobbes into the immediate precursors of the calculus developed by Isaac Newton and Gottfried Leibniz, including methods of calculating the area under a curve using these infinitesimals (which Wallis described as width-less parallelograms). Alexander stops short of that work, however, choosing instead to spend the book’s 300 pages on the two philosophical battles, first in Italy and then in England, that came before infinitesimals gained acceptance in the mathematical world and well before Newton or Leibniz entered the picture. Hobbes was wrong – the ancient problem of squaring the circle, which means drawing a square using only a straightedge and compass that has the same area as that of a given circle, is insoluble because the mathematical solution requires the square root of pi, and you can’t draw that. The impossibility of this solution wasn’t proven until 1882, two hundred years after Hobbes’ death, but the philosopher was convinced he’d solved it, which allowed Wallis to tear Hobbes apart in their back-and-forth and, along with some of his own politicking, gave Wallis and the infinitesimals the victory in mathematical circles as well.

Alexander tells a good story here, but doesn’t get far enough into the math for my tastes. The best passage in the book is the description of Hobbes’ work, including the summary of the political philosophy of Leviathan, a sort of utopian autocracy where the will of the sovereign is the will of all of the people, and the sovereign thus rules by acclamation of the populace rather than heredity or divine right. (I was supposed to read Leviathan in college but found the prose excruciating and gave up, so this was all rather new to me.) But Alexander skimps on the historical importance of infinitesimals, devoting just a six-page epilogue to what happened after Wallis won the debate. You can’t have integral calculus without infinitesimals, and calculus is kind of important, but none of its early history appears here, even though there’s a direct line from Wallis to Newton. That makes Infinitesimal a truncated read, great for what it covers, but missing the final chapter.

Next up: The Collected Stories of Katherine Anne Porter, winner of the Pulitzer Prize for Fiction in 1966.

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→ April 8, 2016
→ By

The Unfinished Game.

I’m still playing a bit of catchup on stuff I read during March (and just finished Joe Haldeman’s The Forever War over lunch today), but one title I definitely want to bring to everyone’s attention is the delightful, short book by mathematician (and NPR’s “Math Guy”) Keith Devlin called The Unfinished Game, which explains how one specific letter in the correspondence between Blaise Pascal and Pierre de Fermat opened the door to the world of probability and everything that this branch of mathematics makes possible.

The unfinished game of the book’s title was based on a common, popular controversy of the time surrounding games of chance, which were largely seen as incalculable – our modern, simple way of calculating odds of things like throws of the dice just did not exist at the time. Pascal and Fermat discussed the question of how to divide winnings in a game of two or more players where the players choose to abandon the game before any one player has won the requisite number of matches. (So, for example, they’re playing a best-of-five, but the players quit after three rounds, with one player having won two times and the other one.) The controversy in question will seem silly to any modern reader who’s taken even a few weeks of probability theory in high school math, but Devlin is deft enough to explain the problem in 1600s terms, so that the logical confusion of the era is clear on the page.

The confusion stemmed from the misunderstanding about the frequencies of subsequent events, given that the game would not always be played to its conclusion: You may say up front you’re going to play a best of seven, but you do not always need to play seven matches to determine a winner. If you quit after three games, in the situation I outlined above, it is possible that you would have needed just one more match to determine a winner, and it is possible that you would have needed two more matches. Pascal’s letter to Fermat proposed a method of determining how to split the winnings in such an unfinished game; the letter was the start of modern probability theory, and the problem is now known as the problem of points. (You can read the entire surviving correspondence on the University of York’s website; it also includes their conversations on prime numbers, including Fermat’s surprising error in claiming that all numbers of the form 2(2n)+1, which is only true for 0 ≤ n ≤ 4. Those five numbers are now called Fermat primes; Euler later showed Fermat’s hypothesis was wrong, and 2(25)+1 = 4294967297, which is composite.)

Fermat realized you must count all of the potential solutions, even ones that would not occur because they involved playing the fifth game when it was made unnecessary by the first player winning the fourth match and taking the entire set, so to speak. (The problem they discussed was slightly more involved.) Pascal took Fermat’s tabular solution, a brute-force method of counting out all possible outcomes, and made it generalizable to all cases with a formula that works for any number of players and rounds. This also contributed to Pascal’s work on what we now call Pascal’s triangle, and created what statisticians and economists now refer to as “expectation value” – the amount of money you can expect to win on a specific bet given the odds and payout of each outcome.

Devlin goes about as far as you can when your subject is a single letter, with entertaining diversions into the lives of Pascal and Fermat (who corresponded yet never met) and tangents like Pascal’s wager. At heart, the 166-page book is about probability theory, and Devlin makes the subject accessible to any potential reader, even ones who haven’t gone beyond algebra in school. Given how much of our lives – things like insurance, financial markets, and sports betting, to say nothing of the probabilistic foundations of quantum theory – are possible because of probability theory, The Unfinished Game should probably be required reading for any high school student.

Next up: I just started Eimear McBride’s A Girl is a Half-Formed Thing, winner of the 2014 Baileys Women’s Prize for Fiction.

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→ October 9, 2015
→ By

Man’s Search for Meaning.

I have a scouting blog up on Cuban free agent Eddy Julio Martinez and other Cuban and Dominican prospects for Insiders; Martinez has reached an agreement to sign with the Cubs pending a physical. I also held my regular Klawchat yesterday.

A friend of mine who works as a therapist, dealing in particular with trauma victims, has been recommending Viktor Frankl’s short book Man’s Search for Meaning, which comprises a long essay he composed while in concentration camps in World War II as well as a shorter piece on logotherapy, his concept and program for working with psychiatric patients. I’m rather unqualified to ‘review’ this book in any meaningful way, but since the book is so highly regarded and often cited in polls where readers name the most influential books they’ve read, I’ll offer a few thoughts.

As you might imagine, the first part of the book, where Frankl details much of the suffering he saw and endured at the hands of the Nazis – his entire family, including his pregnant wife, was killed during the Holocaust – is somewhat difficult to read, even though Frankl takes a fairly neutral tone. He received some slightly favorable treatment because he had a medical background and could take on tasks other prisoners couldn’t, but that is a drop in the ocean compared to the misery of his situation. Frankl’s point in writing this brief memoir is to explore the ways in which the human mind can survive suffering and find reasons to continue to live even in hopeless situations. Although he gives his ideas on the meaning of life, the book delves more into the specifics of the title – the search itself, the refusal to give up, and the physical consequences he witnessed when a fellow prisoner lost his will to live.

Finding meaning in suffering is a longstanding subject of debate and expostulation in religion and philosophy, with Frankl taking a particularly pragmatic view of the matter. In his view, there is less point in asking “why” than in finding new reasons for hope or optimism even in apparently hopeless situations. Prisoners who could find meaning in helping others, or in sustaining themselves on the chance they’d one day be released and reunited with loved ones, fared better mentally and physically than those who gave themselves up to the awful reality of their lives in the camps. This forms one of the key parts of his program of therapy – helping patients understand why they do have meaning in their lives, often more than they realize.

Several passages describe the presence of a senior group of prisoners who in some ways helped run the camp in exchange for special privileges or favors like cigarettes, liquor, or additional food. We often refer to the Stanford Prison Experiment to explain such brutal behavior, but is there a more stark example of this awful capacity of our personalities, to join with those who would enslave, torture, and kill our relatives, friends, countrymen, fellow worshipers, just to save our own skins?

The foreword to the current edition available on Kindle was written by the rabbi Harold Kushner, author of When Bad Things Happen to Good People, who calls Frankl’s book “a profoundly religious book.” I agree to an extent that the book has a spiritual core, although it is not limited to any specific religion, and I think the book can be read, understood, and appreciated by a secular audience. Frankl does not rely on a deity or an afterlife to make his arguments that life here can have meaning even when meaning has left the building; his arguments rely on emotion and psychiatric tenets, none of which requires religious belief or background to follow, which means Man’s Search for Meaning is a book for anyone interested in fundamental questions of why we are the way we are, and how to find that meaning even in situations that appear devoid of it.

Next up: I’m a bit behind on reviews yet again, having finished Anthony Doerr’s All the Light We Cannot See, this year’s Pulitzer Prize for Fiction winner, on the flight back from Santo Domingo, and am now reading Vladimir Sorokin’s very odd novel Day of the Oprichnik.

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→ June 24, 2015
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The Third Policeman.

I have two Insider posts up this week, one on the Touki Toussaint trade and one on scouting Yoan Moncada, Rafael Devers, and Javier Guerra.

I’ll admit right now that I only partly understood Flann O’Brien’s The Third Policeman, but I thoroughly enjoyed it, almost as much as I enjoyed his most famous work, the metafictional masterpiece At Swim-Two-Birds. He wrote The Third Policeman next, but couldn’t find a publisher at the time and eventually shelved the work and reused a portion of it in his final book, The Dalkey Archive, but the original work came out shortly after his death and has quietly obtained a cult following, one that rose when one of the co-creators of the show LOST mentioned that the book might give viewers a clue to the show’s underlying mythology.

I can’t discuss the book in full without spoiling the ending, but I’ll do my best to cover my thoughts on the book’s meaning without ruining it. The narrator is the ne’er-do-well son of an estate owner in Ireland who inherits the land and farm when his father dies, letting the tenant Divney take over stewardship so he can continue his reading of the incompetent philosopher de Selby, whose work shows up repeatedly in the text and in various footnotes discussing de Selby’s life and some of his most bizarre ideas. Divney somehow establishes some kind of primacy in the relationship and even possible ownership of the estate, which leads in typically nonlinear fashion to the two committing a murder to rob a wealthy neighbor. After several years of an uneasy alliance, Divney finally tells the narrator where the proceeds are, but just when the narrator is about to grab the missing box, things get really weird, with reality turning upside down on the narrator, introducing him to the supposedly-dead victim, the narrator’s own soul (which he helpfully dubs “Joe”), and two policemen who are totally obsessed with bicycles. The third policeman … well, he’s there, but never there, and you’ll have to read to find out how and why.

The novel itself is deeply philosophical, with the destruction of the line between reality and fiction a completion of the blurring that O’Brien began in At Swim-Two-Birds (#52 on my most recent top 100 novels ranking). It’s decidedly postmodern but not metafictional. O’Brien delves into the nature of matter, reverting in a way to ancient beliefs about the fundamental building blocks of the universe, and how we perceive the world around us. He also seems to argue that time is, indeed, a flat circle, although the exact meaning of that statement won’t be clear until you’ve read the book. The fictional writings of de Selby, with whom the narrator is obsessed, are utter nonsense – de Selby tries to dilute water because it’s too strong and argues that night is merely a collection of “black air” particles – lending to the unreality of the narrative while also exposing the narrator’s own tenuous grip on what is real. When the two policeman show him the road to eternity and introduce him to a machine that runs on “omnium” and can create anything you desire, he just tries to grab as much stuff as he can, without any thought to the potential consequences (which you’ll also have to read to learn).

Drawing as much from Sartre and Camus as from Descartes and Einstein, The Third Policeman is delightfully weird yet profoundly disturbing once you’ve finished the book and reconsider what you’ve read. Rather than make a specific metaphysical argument, O’Brien experiments with reality within fiction, moving targets and obliterating lines to create a foundation for humor while simultaneously knocking the reader off balance. It’s an uncomfortably funny read, and one I couldn’t stop pondering for days after I finished.
Next up: I just finished Joel Dicker’s global bestseller The Truth About the Harry Quebert Affair.

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→ June 3, 2015
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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.

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