With the recent indictment and resignation  of I. Lewis “Scooter” Libby over the Valerie Plame affair there have been repeated calls from the obvious quarters  for the President to apologize over the CIA leak. Whether Mr. Bush feels any regret over the incident or not, it seems unlikely that he will express any, at least until he absolutely has to.

Regret (the  feeling of disappointment or distress about something that one wishes could be different) is a strange beast. It is, of course quite possible to feel regret without guilt, or even without any acknowledgement of personal responsibility. Also, regret is sometimes the inevitable biproduct of actually making a choice (I’ll take the granola bar over the chocolate cake). Regret is not a rare commodity.  During any given day there are dozens of moments when one expresses some inconsequential level of regret to oneself. So what exactly do people mean when they say (often with a flourish) that they “have no regrets”? Perhaps what they mean to say is that they don’t really regret anything enough, i.e. it all comes down to the degree of regret experienced.  The question about regret that I find interesting is: How is the degree of regret distributed? Is it a Bell Curve? That would be nice. A Bell Curve is conveniently symmetric around its mean (average), that is to say, its median value is the same same as its average. Let’s do the following thought experiment to find out!

1. Try to remember the things that you have regretted over the past day and count those which rise to the level worthy of reflection in bed tonight. Chances are you will only be able to come up with a couple.
2. Go back a week and do the same thing. What regretful things have stuck in your craw? Strangely, there are likely to still be a similar number, maybe two or three. How did that happen? Surely, it should be more like seven times your daily regret count. Your threshold for craw stickiness has gone up.
3. Now do the retrospective on your life and try to catalog your regrets. Again, the number is about the same.

To be more quantitative, if your could go back in time and correctly catalog the list of your regretful incidents over a day, week and month, and graph the degree of regret versus the sequence of incidents, you would probably come up with something like this for the daily , weekly and monthly lists. (The “Real Regret” Zone is is the threshold of regret degree above which you would count it while doing the three step experiment I outlined above.)

The week graph is a blown up version of the month one, and the day graph is a blown up version of the week one, but they all have the same structure. Each graph has  many tiny incidents with a few much bigger ones, and only those incidents above the threshold register as being truly regretful.  A strange “self similarity” or scale invariance is observed.

Now if your regret were distributed like a bell curve it would not look like this. The big events would not be so big, and the scale invariance would not be present. So what is this kind of distribution?

This kind of distribution is Fat Tailed. The reason is that the infrequent events are huge. Most of us are trained to think in terms of Bell Curves, but this is a very different animal. A Bell Curve has the same median and mean. In the Fat Tailed distributions the median is extremely small relative to the mean  since the rare events are so huge.  This skew in the distribution leads to various odd properties, for example, that the variance is infinite!

It turns out that a very large number of things are fat tailed:

1. The frequency of words in a book. This is what captured the imagination of a Harvard Lingusitics lecturer by the name of George Zipf who discovered that if the most frequently mentioned word in a book was used N times, the Kth most frequent word in that book would be used about N/K times. This relationship holds (with some minor fudge factors) for most books written in the English Language and is known as the Zipfian distribution.
2. The distribution of population in a city: Remarkably this turns out to be Zipfian as well. Take any developed or developing country and rank the cities. A terrific source of data for a bunch of different countries is here. You will find that the distribution is very close to being Zipfian. The number of people who have scratched their heads about why this happens reads like a who’s who of economics: Herb Simon, Paul Krugman, Benoit Mandelbrot (who isn’t regarded by economists as an economist but actually is), and most recently Xavier Gabaix among lots of others. Even those who don’t think the distribution is Zipfian agree that it is fat tailed.
3. The number of web links pointing to a web page. Various popular books have been written on this and since it has been covered extensively elsewhere I’ll resist the temptation to expound. 
4. The number of subscribers to a blog feed. Most blogs are barely read, but a few blogs get a huge amount of subscribers. An interesting set of graphs relating to this has been provided from the folks at Ask Jeeves.
5. The distribution of income. Ever since Pareto, it has been observed that the rich are few and much richer than the rest. The scale invariance of the distribution results in very rich people actually feeling quite poor! If you think that you’d feel rich with $10 million in the bank, think again!

Fat tailed distributions are more frequently called Long Tailed. (The term “The Long Tail” yields 1.57 million google results as opposed to a paltry 12,700 for the “The Fat Tail”.) In statistics, the rare events of a distribution are said to be in the tail. When these rare events are large, we say that the tail is FAT. Even a bell curve, can have a very long tail, so why the terminology Long Tail? Well, if  you arrange the values in descending order and graph them, i.e. the big ones on the left, and the smallest values to the extreme right, the picture looks like a long tailed beast. Of course, the head of this beast is the tail of the distribution! Also, it seems more natural to say, for example, that the distribution of blog readership has a big fat head and a long tail, but that isn’t really accurate from a statistical point of view. So take your pick of terminology.

Now the question of WHY things are fat/long tailed is still somewhat unclear, but of course,  a multitude of theories abound. Zipf believed it all stems from the tendency of human beings to follow the path of least resistance, so that the inertia in the system tends to make the big bigger. There are various “winner takes all” theories which are commonly spouted in business circles. Economists espouse phenomena of “increasing returns” and “switching costs”, which are appealing in certain contexts. It is all very fascinating and intellectually rich.

But what explains the degree of regret — why is IT fat tailed? I wish I had an explanation, but all I have is more speculation: perhaps circumstances are responsible, i.e. things happen in a “fat tailed” manner so that we react to them that way. Or perhaps it is our reactions which are more responsible, i.e. after an accumulation of little things reaches some limit  (a camel-back breaking limit, so to speak) we react in an extreme fashion.

Finally, it would seem that other emotions, e.g. happiness work the same way. Repeat the experiment and see for yourself.

The mystery of it all! If only  I knew more. And yes, regret has struck again!

Those of you who have never taken 20-24 hour flights can probably scarcely imagine the vertigo-inducing fatigue involved. I have taken one of these flights fairly regularly for decades now, from Karachi to New York, and find it hard to understand how my elderly parents ever survived them. In addition to the sheer length of time for which one is confined to one’s (in my case, very small economy-class) seat, these flights almost always originate in the early hours of the morning, giving one just enough time to reach the deeper parts of sleep after having spent the evening packing, buying last-minute things, and saying goodbye to friends, before one must heave oneself up from bed at something like 3 in the morning, say one’s emotional goodbyes to relatives, and head for Qaid-e-Azam International along the deserted Sharia Faisal. So one almost always even starts the trip in a groggy, enervated state. Then, as if almost a full day in the stale, dessicated air and cramped and noisy quarters of a Pakistan International plane (they must have the highest ratio of children to adults of any airline) weren’t enough, there is the time-difference induced jet lag to contend with upon arrival at JFK, and for some reason I am always unable to eat any of the last meal they serve on the plane.

All this is to give you a sense of how I am usually feeling physically and mentally as I stand in the long immigration lines at JFK waiting for my passport to be stamped. And there I was standing one morning about three years ago. When my turn finally came up at the counter, the INS agent asked me more questions than usual, and then closed his counter and asked me to follow him to a large room at the side of the immigration hall. Once there, along with a bunch of other people who had also been pulled aside for extra questioning, I waited for my file’s turn to be examined by the officer at the counter there. (The original INS agent had deposited me and then returned to his duties elsewhere.) Finally my name was called, and after some very aggressive questioning about who I am, what I do, where I live, and on and on (and they frequently keep asking the same questions over and over, making one feel like they are hoping to trip you up in case you are lying), I was informed that I was being detained. Two agents handcuffed me and led me to another smaller room. When I asked what I had done, they said things like, “Oh, you know what you’ve done. You are in trouble, my friend.” Then I asked to call a lawyer, and I was informed that I hadn’t yet been admitted to the United States, and so had no legal standing. No lawyer would be called, nor would I be allowed to call anyone else. They took my cuffs off, fingerprinted me (very difficult because of my sweaty palms), recuffed me and then left me there.

It was at this point that my knees went a little trembly. I had heard many stories of Pakistanis being held under the Patriot Act without charges for months, and now I had visions of Guantanamo in my head, and I became almost dizzy with the adrenaline rush of fear. I thought that I must have been mistaken for someone else, God knows who, and there would be no chance to clear my name. At this point, I was so tired and hungry that I could barely stand up. After a few hours, a woman came to the room to get some papers she needed and I took this opportunity to beg her to let me call my girlfriend. I guess she took pity on me. She took out a cell phone and asked for the number. I told her and she dialed it and then held the phone to my ear (my hands were cuffed behind me). Margit (now my wife) answered the phone and immediately started asking what had happened, why I wasn’t home yet, she was so worried, etc. I told her to stop talking as I didn’t have much time. I told her I had been detained by the INS, and that she should contact a lawyer and my brother immediately, and get someone to JFK. I would try to call her again if I could, but wasn’t sure if I would be able to. To her credit, she was calm, and I felt much better that at least someone knew what was happening to me.

I then sat in that room for another few sweat-drenched hours before a couple of INS officers came in along with two police officers from the NYPD. The NYPD officers told me that they had a warrant for my arrest. This immediately came as a relief to me, because whatever it was they wanted with me, I would rather be held by the NYPD in New York, than in some INS facility. I felt like whatever it was, I would be able to clear it up. That’s when things started to get weird: the NYPD officers addressed me as Mr. Edward Sampson, as in, “Let’s go, Sampson.” When I protested that I wasn’t Edward Sampson, whoever that might be, they told me that fingerprints don’t lie, and I had a full ten-finger match as one wanted Edward Sampson. They told me to stop lying and just admit that I really was Edward Sampson. The name sounded vaguely familiar but I couldn’t quite place it in my exhausted state. The INS guys removed my cuffs and the NYPD officers produced a kind of wide leather belt which looked vaguely like some S&M contraption, put it on me, then cuffed my hands to it. I was then led out for the perp walk in front of all the other passengers, coming out by the regular path where people wait for their friends and relatives to come out. Most people whispered to each other rather excitedly when they saw me being led out, held by each arm by one of the officers, wearing this restraint, and a nice suit I had had tailored while in Pakistan.

It was then that I remembered who Edward Sampson was, and it came to me suddenly: about a decade earlier, my nephew Asad and I had been having a drink with my friend Karim at the West End Restaurant and Bar (where Jack Kerouac and Allen Ginsberg used to hang out) near Columbia University (I had just started the Ph.D. program in philosophy there), when four rough looking characters wandered in. They looked like skinheads, and they sat at the table behind where we were standing at the bar. Asad had draped his jacket over one of the chairs on which one of these guys was now sitting, and so he tapped the guy on the shoulder so he could retrieve his jacket. I saw the guy stand up and get in Asad’s face, but couldn’t hear what was going on. The man then raised his voice and I heard the N-word being yelled at Asad along with a string of curses, after which the man grabbed my nephew’s hair with his left hand and drew back his right fist, getting ready to throw a punch. I hit him first. I had lunged from the side, and my momentum threw both of us to the floor. I didn’t know it then, but I was rolling around on the floor of the West End with one Edward Sampson.

We were separated by the bouncers of the West End and all six of us were thrown out. Once outside, these guys ganged up on me and managed to throw me to the ground where I hit my head on the sidewalk. I was momentarily stunned, and had no chance after that. Mr. Sampson pummeled me pretty good. Then the police arrived, and Sampson and crowd quickly walked off. I explained to the police that my nephew had been assaulted, and while trying to protect him, I, too had been beaten up and the guys were trying to get away. The police told me that if I insisted on having them arrested, they would have to arrest Asad and me as well, since they hadn’t been there to see who started it. When I produced witnesses, they dismissed them as my friends, so I said fine, go ahead and arrest all of us, but I am not going to let these punks get away with this. I figured we would sort it out later in court. And so the four of them were also picked up and all six of us were driven to a precinct where we had our portraits taken, were fingerprinted, etc., before being released on our own recognizance. And at that precinct is where I first heard the name of my attacker: Edward Sampson.

The next day, after a trip to the Manhattan Eye and Ear Infirmary, I showed up at the philosophy department at Columbia with black eyes, swollen mouth, etc. Sidney Morgenbesser was the first to offer his help, and Akeel Bilgrami made a call to a lawyer friend of his. They knew what they were doing, because the next morning I received a phone call from Robert Morgenthau’s office (he was, and might still be, the District Attorney of New York) telling me to go down to the courthouse on Center Street, where a couple of assistant DAs were waiting for me. They listened to my story, called a few of the witnesses, and then told me that charges against Asad and me were being dropped, and that Sampson and his friends would be prosecuted under the hate crimes statute of New York. I was pleased by this, and felt vindicated that I had insisted that the police arrest everyone, rather than just letting these guys walk. Except that those people didn’t show up at their hearing, and were never heard from again.

By the time the NYPD guys had put me into the back of their van outside JFK, I had figured out what must have happened: somehow, that night ten years before, someone at the precinct had made a clerical error, and had somehow put Edward Sampson’s name and other information on my fingerprint card. Then, when they didn’t show up for their hearing, a warrant was issued for Sampson’s arrest (and for all I knew, he might have committed other crimes since), and now I had been arrested as Edward Sampson. This was the only explanation I could think of, and it sounded plausible to me. I excitedly told the NYPD guys this theory, but they were pretty unimpressed. One of them said that people often come up with crazy stories when they get caught, but this was one of the best he had heard. I told him to look at me. Did I even look like I might be named Edward Sampson? I just kept repeating my theory to them until finally, one of them, Detective John Regan of the Queens Warrant Squad, started to believe me, at least a little. He told his partner, “Look, it sounds crazy, but it might be true. While you guys see the judge (I was being taken to a courthouse in Manhattan where I would be presented to a judge, and we needed to get there before midnight, which was getting close, otherwise I would have to wait in lockup overnight) I’ll go try to find the records from that arrest ten years ago.”

At this point, I begged to be given some food, and again, Regan made the other guy stop at a Chinese restaurant and got me a fried rice (which he paid for) and even put hot sauce on it per my request. He then uncuffed me so I could eat. His partner was not happy at this lenient method of treating a just-captured fugitive, but Regan was by now convinced that I just wasn’t the right type of guy to be a criminal. I shall always be grateful for that meal and Detective Regan’s kindness. At the courthouse, Regan disappeared to look for the old arrest record while I was taken into a courtroom where I was appointed a public defender. Now this guy was a complete idiot. He kept telling me to stop lying and just plead guilty to a reduced charge for which I would just get some community service and no jail time. No matter what I said to him, he would not believe that I was not Edward Sampson. Meanwhile, Regan showed up with a file containing the decade-old arrest records, and luckily it had a picture of Edward Sampson in it. But even then, my supposed lawyer kept saying things like, “That could have been you ten years ago.” Finally the judge herself yelled at him and said, “It is unlikely that your client has changed race since that arrest. And why would he have been arrested for beating himself up?” She told me I was free to go. I was then driven by Detective Regan and his partner back to JFK, where I was released. Asad was waiting for me there.

Detective Regan then offered to help me clear up the problem with the fingerprints, and after some detective work, called me with a strange bit of news: Edward Sampson had committed suicide in 1996 by jumping out of his 5th floor window. So I had essentially been arrested as a dead man for beating myself up. However, the fingerprints were now in many different databases, including the FBI, the state police, INS, and God only knows who else. He suggested I find a lawyer to help me clear this up. So I did. I was assured that the problem had been taken care of, and everything was fine, and indeed, I flew in and out of the country several times without incident. Then, three days ago, I got on a train headed to Montreal for Justin’s wedding. At the border, Canadian customs and immigration officials boarded the train for their inspection of the passengers’ documents. I was asked to step outside where the aggressively hostile questioning began. Finally when they asked why I had two social security numbers, I realized that Edward Sampson’s ghost was back to haunt me. I told them the whole story, and luckily, after much heated discussion and some phone calls, they believed me (because all the details I gave them matched what they had, including the name Edward Sampson, which they had not told me, but which they knew). But they warned me that I may be arrested by American immigration officials on my way back, so I was pretty nervous last night. It didn’t happen. Now I don’t know what to do. If any of you have any ideas, let me know.

Have a good week!

My other recent Monday Musings:
Be the New Kinsey
General Relativity, Very Plainly
Regarding Regret
Three Dreams, Three Athletes
Rocket Man
Francis Crick’s Beautiful Mistake
The Man With Qualities
Special Relativity Turns 100
Vladimir Nabokov, Lepidopterist
Stevinus, Galileo, and Thought Experiments
Cake Theory and Sri Lanka’s President

Justin E. H. Smith

I shall have to write this Selected Minor Works piece in haste, for it is less than 24 hours ago that I was married, for the first and only time, and my bride will not have me throwing away the blissful infancy of our life together crouched at my laptop.

But in order not to be completely neglectful it seems fitting that I hang out here, as it were, a bloodied sheet for the digital age, by offering both a précis of the event, as well as some reflections on marriage, what it could mean and why it is a genuine good, both in general and in this particular case.

It was a glittering and star-studded event, featuring leading figures of the Quebec literary demimonde, a well-known flyer distributor for the now mythical 1980s Sacramento new-wave all-ages dance-club scene, and, not least, the editor of 3 Quarks Daily himself. We danced late into the night at a rented hall of the Musée des beaux-arts, all dressed up, as if we were rich, and there was much talk of how heavenly the salmon canapés were, and how lovely the bride. I was of course much more interested in the latter sort of talk. She is stunning, whereas I am experiencing, looks-wise, some bizarre, swift, and evidently genetically predetermined descent from comparison with Gustav Mahler to nearly being mistaken for Karl Rove. I can only assume grace is involved in her decision, or in God’s plan, or whatever brought this miracle about.

But on to important matters. It goes without saying that, in this particular case, there is love involved (are you reading this, O Immigration Canada?), but this is not what I wish to dwell on.  What I want to consider is this: given love, why marriage?

Philosophically, I am not in good company. For Nietzsche, Socrates served as the perfect cautionary tale to any philosopher thinking about the path of marriage. After his shameful example, it is certainly true that, statistically, philosophy and marriage do not tend to occur together. Leibniz, for example, seems to have enquired with a young woman’s father about the possibility of taking her hand, never heard back, and only recalled that this business was outstanding 20 years later, just before his death. His contemporaries, by and large, appear content to have ground lenses, and proved things, and in general to have acted as though there were no women in the world. By the 19th century, marriage comes into its own as a distinctly philosophical issue, with figures such as Kierkegaard taking the problem of marriage as the primary stimulus for productivity. Kierkegaard decided firmly against.

In the 20th century, though, the problem would seem to die out altogether, and marriage to become no more or less problematic for philosophers than for any other segment of the population. Arguably though, this is not because the problem is solved, but only because philosophy is professionalized to the extent that no radical commitments or serious lifestyle measures of any sort are thought to be required. Nobody would dare claim that ‘Two Dogmas of Empiricism’ could have been any richer if not for the sinister influence, from the shadows, of Madame Quine.

But didn’t marriage suffer a crisis in all segments of the population, the first anticipation of which was earlier suffered by the likes of Kierkegaard? Society has been transformed, and marriage displaced as the primary glue that holds it all together. Here in Quebec, we could, after all, certainly get away with not getting married.  There is no social pressure to do so at all, and if anything the pressure is in the other direction.  Cohabitation impresses immigration officials, anyway, much more than a sudden plunge into official coupledom.

So why the plunge? The simplest reason is this: when I met this woman, I knew that ‘partner’ just wasn’t going to cut it.  What I wished to do with her bore no resemblance to what accountants do when they open an office together.  I wanted to draw on antiquated social forms, to go back before the discovery that the personal is political, that families are tyrranies, and declare that this woman was mine, my wife, ma femme, as though the Enlightenment had never occurred.

Philosophy thought it was liberating its practitioners from nagging Xanthippes, and eventually it made it possible for some to think about liberating everyone from what, seen under the aspect of eternal reason, is indeed an arbitrary bond, and one that can’t but limit one’s freedom. But the lack of good reasons, reasons of the sort accountants come up with every day, is what makes marriage better than accountancy, and what makes the modern blurring of the arrangements of the business world and those of the intimate life such a tragedy. Keep your sound and level-headed arrangements, your rational and limited partnerships. I, as the saying goes, shall take my wife.

In the 1960’s, a chemist named James Lovelock was invited by NASA to help develop instruments that could detect signs of life on Mars. Lovelock came up with the idea of screening the gases in Mar’s atmosphere for signs that their concentrations were being affected in ways consistent with life.

On Earth, for example, the atmosphere is composed of about 77 percent nitrogen, 21 percent oxygen, and trace amounts of other gases, most notably carbon dioxide and methane. These gases are used and absorbed by plants and animals and then remade and recirculated back into the atmosphere. Mars, on the other hand, has an atmosphere that is almost 95 percent carbon dioxide.

The stark contrasts between the two planets suggested to Lovelock that Mars couldn’t possibly harbor any type of life or that if it did, it was in the very distant past. Chemically, Mars was a dead planet, and to Lovelock, this meant that it had to be biologically dead as well.

If there was life on Mars, it would leave a chemical signature that could be detected from Earth, Lovelock reasoned. The cumulative actions of countless organisms would over time change the composition of gases in the atmosphere and these changes would be visible from space. This kind of thinking lead Lovelock to a sudden realization. Recalling it years later, Lovelock wrote:

“I was in a small room on the top floor of a building at the Jet Propulsion Laboratory in Pasadena, California…An awesome thought came to me. The Earth’s atmosphere was an extraordinary and unstable mixture of gases, yet I knew that it was constant in composition over quite long periods of time. Could it be that life on Earth not only made the atmosphere, but also regulated it – keeping it at a constant composition, and at a level favorable for organisms?”

Lovelock discussed his idea with his neighbor, the novelist William Golding, and it was Golding who suggested Lovelock’s new theory be named “Gaia,” after the Greek goddess of the Earth.

When it was first proposed, Gaia theory appealed to environmentalist but was largely dismissed by the scientific community. Critics said the theory was unscientific and that it was teleological, that it was proposing that there be some kind of planet-wide consciousness at work.

Other critics, like Richard Dawkins and Ford Doolittle, argued that Gaia theory was at odds with Darwinian evolution. Instead of having organisms simply adapt to their environment, Gaia theory was saying that organisms could actually change it or even control it. In 1982, Dawkins claimed that “there was no way for evolution by natural selection to lead to altruism on a Global scale.”

Gaia theory was also at odds with one of Dawkins’ own theories. In 1976, Dawkins published a book entitled “The Selfish Gene” in which he argued that evolution acts not on individual organisms, but on their genes. Organisms were mere vehicles that genes used to replicate themselves. Those genes that helped an organism survive and reproduce also improved their own chances of being passed on and so most of the time successful genes also benefited the organism. For Dawkins, life was a constant war: individuals within a species were competing with one another as well as with the members of other species. What they definitely were not doing, in Dawkins’ view, was working together for the common good of the planet.

In response to his critics, Lovelock teamed up with Andrew Watson and developed a computer model called “Daisyworld.”

Daisyworld was a simulation of an Earth-like planet orbiting a young, Sun-like star. The only form of life on the planet were daisies, of which there were two varieties: black and white. White daisies had white flowers that reflected light and black daisies had black flowers that absorbed light. Thus, a planet covered in white daisies was cooler than one covered in black daisies.

In the beginning, when the young star is just starting to warm up, the planet is covered mostly in black daisies. As the planet continues to warm, however, more white flowers begin to bloom. In this way, the planet’s temperature is kept constant despite fluctuations in the stars temperature.

When it was first introduced in 1983, Daisyworld was roundly criticized by many scientists as being too simplistic. The model did, however, address two important criticisms of Gaia theory. First, it showed that a biologically regulated planet didn’t have to be teleological, that a self-regulating planet could arise without any need for a guiding conscious. Secondly, it showed that Gaia theory and Darwinian evolution were compatible, that indeed, it was natural selection that made Gaia theory work.

Nowadays, there are many different forms of Gaia theory, from “weak” to “strong.” Weak Gaia maintains only that life is important in shaping the Earth. This form of Gaia theory is generally accepted by many scientists today. In contrast, strong Gaia—the form that Lovelock endorses— says that life doesn’t just merely influence the physical processes of the planet, but actually controls them.

Lovelock, now 86-years old, is still working to develop Gaia theory. He believes that if Gaia theory were to become widely accepted, it would fundamentally change how humans view themselves and their environment:

“If we are ‘all creatures great and small,’ from bacteria to whales, part of Gaia then we are all of us potentially important to her well being…No longer can we merely regret the passing of one of the great whales, or the blue butterfly, nor even the smallpox virus. When we eliminate one of these from Earth, we may have destroyed a part of ourselves, for we also are a part of Gaia.

“There are many possibilities for comfort as there are for dismay in contemplating the consequences of our membership in this great commonwealth of living things. It may be that one role we play is as the senses and nervous system for Gaia. Through our eyes she has for the first time seen her very fair face and in our minds become aware of herself. We do indeed belong here. The earth is more than just a home, it’s a living system and we are part of it.”