• Thinking about dimensions

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    April 13, 2009 /  Book Reviews

    A romance of many dimensions, says the subtitle to Flatland. It was written in the 1880s, and is out of copyright, so I’m linking to the Project Gutenburg free version. It’s a short read, much talked about by mathematicians. I am not a mathematician, but I’ve heard enough about it, and there’s even a movie with voices offered by a fellow Democrat for Life named Martin Sheen and fellow nerd lover – though somewhat hotter in a bikini – Kristin Bell.

    I did notice that the movie has Ms. Bell voicing a hexagon, which is not in keeping with the book. It would surprise me to waste her on the way women are portrayed by Edwin A. Abbott in the written work; the movie crew didn’t, instead choosing to ignore the gender differences in the text. Since I haven’t seen the movie, I will comment only upon the book. Furthermore, I am not evaluating this book as an introduction to dimension and proportionality, a teaching tool. It’s good for that. Instead, I want to comment on the satire and story.

    Sometimes, Mr. Abbott is funny or sweet. There’s humor in the visit to Point, a zero-dimensional structure who considers It the entire universe. All outside comments must come from Its thoughts. I thought of people who sometimes act almost as self absorbed as Point. I also thought of sweetness in the description of how the people of Lineland mate. “No, no, neighbourhood is needless for the union of hearts.” For them, it’s about hearing, and distance, and matching male voice with females; courtship can take many weeks, too, until the pure harmony of the marriage chorus is achieved.

    On the other hand, in Flatland Women are mere lines – well, very thin parallelograms. They receive almost no schooling, must constantly make noise to prevent a figure from hitting them, and are stuck with just emotion. Each house has a special door for women, to avoid potential entry problems. This is not good. On the other hand, they can use their pointy ends to puncture almost any male figure, including their husbands, a strong inducement to fidelity.

    That’s the major part of the satire here, the difference between social classes and genders. British society in the 19th century had strict social structure, where advancement could be made slowly, if at all. In Flatland, triangles can only improve their angles at 0.5 degrees per birth. Regular polygons get to advance faster, one side per generation, but still would take hundreds of years to reach the high dimension of “circles”. Even by British standards, that’s slow. The class system is strong; higher class people do not engage in touch recognition, and in most cases should not even be contacted. (It even holds today at the head of state level, as Michelle Obama caused a great deal of discussion about protocol.) To try to reach a higher class, promising children are often sent to special facilities to be broken and reset. The “Circular Neo-Therapeutic Gymnasium” kills nine out of ten, but apparently it’s worth it to the Flatland classes. To Democrats for Life like Mr. Sheen and myself, though, this would be anathema.

    Another modern anathema would be the treatment of women, and I’m not surprised that this was removed from the movie. In Mr. Abbott’s book, women are considered to have lower intelligence to match their lower dimension. They are taught about emotions, with different language. This seems in line with the thoughts of the Victorian era, and its outward restraint against emotion. One might even see a little eugenic critique inside Flatland society, though I’m not sure about that.

    The problem with the book, from a 2009 perspective, is that the satire doesn’t make sense. It’s no longer our satire. Of course I don’t like lower classes for women; I strongly prefer multidimensional females with curves. Of course I find such a strong caste system unlikeable. It’s easy to say that, now. Unlike other social critiques such as
    Looking Backward by Edward Bellamy, this satire has lost its salt, mostly. Thus, as a social critique, Flatland earns a 1 out of 5. The grade as a mathematical teaching tool would be much higher, if you’re looking for that.

  • Killing the White Swan

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    April 11, 2009 /  Book Reviews, Statistics

    Finally, after almost two years, I’ve gotten around to reading the much talked about book The Black Swan, by Nassim Nicholas Taleb. The term Black Swan has entered financial vocabulary, so it’s good to evaluate the source. Overall, it’s a good term; a Black Swan event is a rare event, hard to predict, that has a large impact. For instance, until the 17th century Europeans thought all swans were white. They are, in Europe. In Australia, they’re not.

    Overall, it’s a pretty good book. I’ll award it a 3 out of 5. However, it can be tough to read at times. Dr. Taleb is pompous. Very pompous. He seems to be basically alone in this world. Describing someone, he wants to “put a rat down his shirt.” While I don’t appreciate false humility, either, or too much self depreciation (as in the saddest hoopster), this book would have more power if it was more targeted. A statistician’s review says it well, so I’ll quote Robert Lund in the American Statistician: “reckless at times and subject to grandiose overstatements; the professional statistician will find the book ubiquitously naive.” As a professional statistician, I agree wholeheartedly.

    Before I come back to why I agree, let me list what Dr. Taleb gets correct. He is right that many things in this world are not Gaussian or normal, and not subject to the bell shaped 95% cutpoints like the linked applet. There are many things in his Extremistan, particularly those that follow Mandlebrot power laws, and putting them into his Mediocristan is dangerous. Note that by choosing the word Mediocre for the other group, against the currently positive word Extreme, he induces stylistic bias. Who would ever want to be in Mediocristan? Well, except nature with height and growth processes and stuff. So he’s got a correct point, but overreaches.

    Another clear point is about the Ludic Fallacy, which notes that real life does not have the same structured randomness of games. Though he had to invent a term for it, the author is correct. Too many introductory examples involve games of chance, cards and dice and roulette wheels. Equal probabilities and independent events are much rarer in reality than Moore and McCabe’s introductory text. In my classes, I make a point about independence, with several reminders of its importance, including the most important one, the test question.

    In other words, I do my job as a professional statistician. That’s the big deal here. I know Dr. Taleb has had dealings with the professional statisticians since the publication of this book, since I quoted Dr. Lund from the American Statistician special August 2007 issue on the book. I suspect that he had very few dealings with my kind before. Unfortunately, what passes for “statistics” nowadays mostly comes from economists. Economists, well, are pretty nasty. A friend of mine once said that “Economists are just sociologists with Asperger’s Syndrome.” I replied that I’ve always thought of them as megalomaniac statisticians, or just plain bad ones. Even the so called revolution, this Freakonomics thing, is really just regression analysis, at the second course level. In some places, it’s not even a good second course level, as this blog post acknowledges a mistake and then tries to defend an abortion model with serious interaction problems. Do they not understand saturation or degrees of freedom? I recommend this critique; even though I might not like all the articles from Steve Sailer, he’s demolished Dr. Levitt on this one. It’s too bad he’s not cool enough to get a fancy book. And who knows – maybe I’ll venture into that perilous topic myself, soon.

    On page 239 of my hardback edition, Dr. Taleb thinks that in comparison to what he calls dull statistics classes, “Clearly it would have been more beneficial, and certainly more entertaining, to have taken classes in the neurobiology of aesthetics or postcolonial African dance, and this is easy to see empirically.” I should be careful here. Particularly before computers became readily available, statistics courses focused heavily on computation. I’ve seen those books from before roughly 1990; they weren’t as good as the courses of today. Given his age, he likely had one of those older courses. Postcolonial African dance might well be better. I also wish that standard deviation had a name that didn’t imply standards, like how I prefer credible interval to confidence interval. That doesn’t affect the main point, that the true professionals know the problems, and that at least now we’re trying to get those across.

    Precision, research, and greater balance could have taken this book from decent to great, so I look in a little frustration at Dr. Taleb’s work. I do have his other book, Fooled by Randomness, which might not show the problems of this one. It won’t be random, or a Black Swan, if I get around to reading that.

  • The Stockdale Paradox

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    April 9, 2009 /  Musings After Midnight, Politics and News

    It’s not a secret that I think very highly of heroic women and men. One of my favorite posts is Medals and Goodness, about medals, virtue, and evil. From time to time I read tales of Carnegie Hero Medal award winners. And every American should read every citation of new Medal of Honor recipients. I might suggest Michael Murphy, whose story appeared in the New York Times. Let’s look at part of the official citation.

    On 28 June 2005, operating in an extremely rugged enemy-controlled area, Lieutenant Murphy’s team was discovered by anti-coalition militia sympathizers, who revealed their position to Taliban fighters. As a result, between 30 and 40 enemy fighters besieged his four member team. Demonstrating exceptional resolve, Lieutenant Murphy valiantly led his men in engaging the large enemy force. The ensuing fierce firefight resulted in numerous enemy casualties, as well as the wounding of all four members of the team. Ignoring his own wounds and demonstrating exceptional composure, Lieutenant Murphy continued to lead and encourage his men. When the primary communicator fell mortally wounded, Lieutenant Murphy repeatedly attempted to call for assistance for his beleaguered teammates. Realizing the impossibility of communicating in the extreme terrain, and in the face of almost certain death, he fought his way into open terrain to gain a better position to transmit a call. This deliberate, heroic act deprived him of cover, exposing him to direct enemy fire. Finally achieving contact with his headquarters, Lieutenant Murphy maintained his exposed position while he provided his location and requested immediate support for his team. In his final act of bravery, he continued to engage the enemy until he was mortally wounded, gallantly giving his life for his country and for the cause of freedom.

    Another such recipient is James Stockdale, perhaps most famous for his terrible performance in the 1992 Vice Presidential debate. That’s a shame, because his story is much better than what he showed that one night, against professional politicians with less than two weeks’ notice. Let’s summarize Stockdale’s courage:

    He was held as a prisoner of war in the Hoa Lo prison for the next seven years. Locked in leg irons in a bath stall, he was routinely tortured and beaten. When told by his captors that he was to be paraded in public, Stockdale slit his scalp with a razor to purposely disfigure himself so that his captors could not use him as propaganda. When they covered his head with a hat, Stockdale beat himself with a stool until his face was swollen beyond recognition. He told them in no uncertain terms that they would never use him. When Stockdale heard that other prisoners were dying under the torture, he slit his wrists and told them that he preferred death to submission.

    Wow.

    After his return from captivity, Admiral Stockdale became a leader, author of four books, and philosopher. You might consider his writings at the Naval Academy’s Stockdale Center for Ethical Leadership. The big lesson here is about how he survived the years in Vietnam, a terrible situation. It’s much worse than anyplace I’ve been, or expect to be. It was a brutal place. He described his philosophy to Jim Collins in the book Good to Great. The story, not long and well worth reading, is quoted on Mr. Collins’ website. Mr. Stockdale said that the optimists never made it out of the POW camps. “They died of a broken heart.” We come to the most important quote, the Stockdale Paradox.


    You must never confuse faith that you will prevail in the end — which you can never afford to lose — with the discipline to confront the most brutal facts of your current reality, whatever they might be.

    Ever since I’ve read that quote, I’ve been struck by its importance. Like most people, I’ve been in difficult, troubling situations. The most recurrent was biochemical depression pain; another was a messy Church situation; there is at least one I don’t talk about out of respect for others.

    It’s taken a long time to understand the Stockdale Paradox. It’s manmade, so it’s not as tough as the Holy Trinity, but it’s not easy. It’s both passion and realism, examining both Happily Ever After and Homelessness in America, holding simultaneously hope and logic. What a pair, faith and discipline. Both are not simple. Faith requires believing in what can be, but is not; Discipline requires ignoring what can be, focusing on what is.

    Neither of the two parts is difficult to understand, and most people can handle one or the other. Both at the same time, however, is the tricky part. In my struggles, I had to bifurcate my thoughts, almost, dividing them into branches. I built detachment into my thoughts. I got better, and then could combine the future and the present. Well, eventually I got there, mostly. There are still times where my mind can bounce quickly, from the concept of future joy to the pain of a current problem. It’s still a little strange that I can laugh and be happy, then shift to tears within a minute, then come back to happiness in under five. The control is not yet total.

    For me, when I fail I generally lose the light of faith, surrounded by the darkness of realism and the funk of depression. I keep trying to gain the lesson given by Admiral Stockdale. I really should read his writings – there’s likely much more there. Right now, in Holy Week, people think a little more about the multiple expression of Jesus, divine and human. In general, people tend not to get that. Maybe the minority that understands some of that dual nature understands some of the Stockdale Paradox as well. Maybe the do, but in the general majority, I think not. There’s too much despair around, topped with hedonism masking despair.
    I hope that I can gain more knowledge of how to act and what truly matters, and that I don’t have to go through what Mr. Murphy or Mr. Stockdale did to gain it. Their stories, and their heroism, have helped me, and for that I salute them. Maybe it is enough. Faith and discipline, together, is the lesson.