I’m dumb

Ever been to a party where it was clear you were simply out of it? Or you go to a gallery opening, and the art is just — you know, de guistibus and all that — but it is objectively uninspired, yet people you think highly of are cooing over it. That’s what the whole thing about power laws is for me.

Cameron Marlow is teaching an intersession course on this at MIT called Power Laws: Hype or Revelation, which I wish I could take, but having chatted very briefly with him about it, I suspect that it would feel like the same party. After all, if it’s hype, you don’t teach a class on it, do you?

A cursory reading of a new paper today in FirstMonday, On the Economy of Web Links seems to beat up that horse even more: when you simulate web behavior it [gasp!] still describes a power law. (And hasn’t this already been done years ago? E.g., Electronic Communities: Global Village or Cyberbalkans? [pdf].)

I guess part of the problem is that I think I understand power laws fine, I just don’t understand what explanatory power they have. It feels like folks have just rediscovered the normal distribution are running around publishing the shocking news (“Penguin height follows normal distribution!”, “Deviation from mean temperature a bell curve!”, “Mean time between haircuts shown to roughly adhere to the normal curve!”). Knowing — or, usually, assuming — a normal distribution gets you a killer app: you can sample a distributed population and infer characteristics in a meaningful way. What does power law get you?

In some cases, people claim that power law ordered relationships are winner-take-all, and this means we should not hope to make it different. It engenders a sort of fatalism: is and therefore ought. We’ve been down that road before — with the very “scientific” fetish of social Darwinism — and it didn’t do anybody any good. I’m not saying everyone intrigued by power laws falls into this camp, I am simply saying I haven’t seen much of a more nuanced way in which power laws are helping to explain something profound.

(I should hedge this a bit. My short time at SFI left me with a profound interest in those systems that sometimes and under certain circumstances avoid falling into a “winner-take-all” trap, despite all of the structural markers of such systems. I also think there is something to the study of how small changes in the microstructure can cause changes in the macrostructure, and the dynamics of such changes. But most of the work now popular says little about either of these.)

I would love to be able to articulate a critique of the power law “thing,” but there are two problems with this. First, as I stated at the beginning, I fear that I must be missing something important. There are smart people spending good portions of their lives pursuing this, and I am not so conceited that I can assume they are all wrong.

Second, I’m not “against” power laws. I don’t think there is anything wrong with the observation that they exist. I just don’t understand why I (or anyone) should especially care. It’s like articulating an argument against Beany Babies. OK, a large number of people found them cute for a time. While I might have purchased one or two at some point, I thought it was a waste of time to obsess over them. But who am I to tell you how to use your time. If people are excited about Beany Babies, who am I to spoil that fun. I guess I just don’t get it.

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  1. Posted 1/8/2004 at 2:08 pm | Permalink

    i also don’t get it, but mike shlesinger does:

    E. W. Montroll and M. F. Shlesinger. On 1/f noise and other distributions with long tails. PNAS 79:3380, 1982

  2. Posted 1/8/2004 at 3:30 pm | Permalink

    i don’t think they have expanatory power. i think they have misleading descriptive power. but i’d be happy if someone would prove otherwise.

  3. Posted 1/8/2004 at 10:45 pm | Permalink

    Hey Alex,

    I agree that the phenominology of power laws is not important in and of itself, and our goal in the class is to try and arrive at the explainitory nature of this notorious distribution. The descriptive power of any model lies in the generative process that creates it. A line on a log-log plot has no descriptive power, but models such as preferential attachment or copying which result in power law distributions give us an understanding of the underlying dynamics and allow us to make predictions just as the Gaussian does.

    Unfortunately there are as many generative models for power laws as there are empirical observations of the distribution, and any assertions of causality are conjecture at this point. Whether or not the power law within the weblog world comes from preferential attachment or copying is up in the air. Like the normal distribution, people are coming to see power laws as a sort of null hypothesis for certain types of observations, and a unifying theory like the central limit theorem is most likely around the corner. If beanie babies were derived from the central limit theorem, I’d certainly teach a class about them ;)

  4. Posted 1/9/2004 at 4:56 pm | Permalink

    Very cool. Now I do wish I could take your class :). I guess I can settle for reading (and rereading) some of the items on your list I am less familiar with.

    I’d be interested to see an analogue of the central limit theorem, but–and maybe this is just a mark of a glass-half-empty-kinda-guy–I won’t hold me breath. If it were coming, why didn’t it come from earlier folks (Pareto, Zipf, Mandelbrot, et al)? Ever the pessimist, I’m still leaning toward “hype.” I don’t deny there are interesting questions there, especially, as you note, in the relationships and dynamics that lead to such distributions. I just don’t know that the questions warrant the amount of popular and scholarly attention they are receiving.

    OK, I’m off to my important work on the origin of Beanie Babies.

  5. Posted 1/10/2004 at 9:01 pm | Permalink

    Wait…Beanie babies have an origin? Outside of Troll Dolls, that is, which a student of mine is presenting to the class as a paradigmatic phenomenon of the sixties on Tuesday? Uh oh, better start over… :-)

One Trackback

  1. By lago at errant dot org on 1/22/2004 at 9:00 pm

    Emergence, Complexity, and Moral Order
    Imagine my surprise a few days ago when I saw Alex Halavais write a blog entry entitled I’m Dumb. Now,…

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