get off the couch

The Anti-Humbaba Action Coalition has staged a few small and futile protests outside DC art establishments. Walking in ragged figures while holding poorly drawn signs, they chanted:

what do we want
to liberate?
Art Art
Art in action,
art in use
hanging on walls,
ain’t no excuse!

Apparently disgruntled handicraft workers, they’re easy to dismiss as cranks. But they offer a powerful critical perspective on Conversions, a juried group exhibition at the Ellipse Arts Center in Arlington through Sept. 29, 2006.

Most of the works in Conversion are attached to walls. Joan Sarah Wexler’s “Tearooms and Restaurant Interiors” are photographs arranged on a wall, as are Susan Eder / Craig Dennis’s work, “Which Image Never Fades Away?” Lisa Kellnor’s “Oil Spill,” constructed from pins with large yellow heads, is firmly tacked to the wall.

Amy Glengary Yang attached to a wall an array of cyanotypes (images made with an early photographic process) mounted in lightboxes. Protruding in front of the lightboxes is a bell jar containing a neon-lighted sea urchin skeleton and topped with an air pressure gauge. It’s an enchanting work, set against a wall.

Some works, such as Michele Kong’s “Reticula” and Amy Martin Wilber’s “Three Fates,” hang from walls to cover windows. “Reticula” is an exquisite lace of translucent glue. Kong made her boundary from wire. Only a few strands are oriented like a fence, while many are coiled around those few.

Tai Hwa Goh’s luscious intaglio on hand-waxed paper hangs from a wall like ponds compressed into a multi-layered scroll. Yet when she moved her intaglio away from the wall, she formed it into cubes.

One work is attached to a free-standing panel. M. Sedestrom Guthrie’s “Through the Glass” arranges photographs horizontally on one side of this panel. The photographs are views of a working window-washer through the glass of the window he is washing. The work also included some text. The text, which I’ve forgotten, was far too self-consciously serious for me to take seriously. I walked around the panel and found only a white plane on the other side. Life is usually not that disappointing.

Another work meets a wall in a more interesting way. Tomás Rivas’s “Erechtheum Uno, Dos y Tres” features delicate carvings into the surface of drywall panels leaning against the gallery wall. I particularly liked that Rivas included penciled outlines, some uncarved. I see in the drywall panels effects of a mundane call for beauty, modulated by the unchanging, supporting wall of the gallery. According to his biography, “His ongoing investigation of the representation of space addresses the complexity of art production today, where the ‘center’ and the ‘periphery’ vie for political clout within the mainstream.” Indeed!

One work offers a view into a long, narrow room. Kathryn Cornelius’ work “Address” lines this room, which is only about five feet wide, with roughly twenty white plastic chairs attached to the walls about four feet above the floor. Projected onto a wall just outside this room, a video evokes mass-market clothes hanging in a retail outlet.

An art reviewer writing in The Washington Post described “Address” as “making a statement about the violence and trauma that occasionally underlie the quiet domestic exteriors of our homes.” That’s a hackneyed interpretation. My sense is that this work evokes the tedium and worthlessness of many jobs. Working in retail, like blogging, forces you to confront ignorant and annoying opinions of ordinary persons. Just buy that one — it looks best!

Even worse are jobs involving endless, meaningless meetings. Cornelius has arranged the long, narrow room to provide a critical viewpoint on the center of this enterprise — the long, narrow table of the board room. Imagine if your family’s livelihood depended on an address that you had to make to lines of empty suits strictly ordered around the bored room table. You’d want to scream like you were on a amusement park ride. But if you did that, you’d be fired. March forward through the marble corridors of power, and do your job!

Views of Renee Butler's Movement in B Flat

The best work in the exhibition, it seems to me, is Renee Butler’s “Movement in B Flat.” Forms with different shapes and reflective properties hang from the ceiling and break up video projected from orthogonal points. The effect is to ramify points of view on the projected (mundane) scenes and make those points of view physically explicit. At the same time, the whole ensemble, including the rectangular tiles and grated florescent light fixtures in the ceiling, forms a pleasing, dynamic harmony.

In the room containing “Movement in B Flat,” two couches rest against walls near where they meet in a corner. They signal a shift in viewing modes: from “look at art on the wall” to “watch television.” These are not the only possibilities. With care and respect for the construction of “Movement in B Flat,” you can move around it and even into it in some places.

Persons moving challenge the idea of points of view. Mobile phones have integrated space-annihilating communication with persons moving through the real world around themselves. Artists interested in spatial interpretations and points of view should take seriously this distinctively modern experience of communicating.

Get off the couch. Go see Conversions. And be sure to walk through “Movement in B Flat.”

lack of power laws and other popularity problems

Discussion of tails and popularity seems to be maturing into more comprehensive considerations. Folks aiming for uber-geek status might chat about the difference between power laws and log-normal distributions. This difference has similar consequences to the difference between non-stationary and stationary macroeconomic time series. If those terms are obscure to you, you might just chat about how much bigger infinity is than any other number. It’s a huge issue!

Government bureaucrats and other practical, get-the-job-done types might just try to produce some simple, intuitive, and relevant graphs. Consider, for example, log-log graphs of website page traffic by page rank. They show a “drooping tail” relative to an approximating line for the left part of the popularity distribution.

Whether the droop is a typical characteristic of web page popularity distributions is not clear. Surely a relatively large subset of relatively bad (unlinked, search-word-poor, spam-associated) pages could contribute to the droop. On the other hand, the droop could be a typical effect of the usual distribution of page content and general patterns of linking and searching. These two possibilities could be tested by comparing the magnitude of the droop in different websites’ page traffic distributions.

Fitting a line to a popularity distribution is more useful as a descriptive technique than as a literal claim that the popularity distribution follows a power law. The term “power law” is not meaningful to most persons. Moreover, knowledge about power laws does not provide a lot of insight into the factors that determine website traffic or trends in website traffic over time.

The possibilities for statistical distributions are not limited to power laws (or power laws and log-normal distributions). The personal behavior and information and communication systems that effect page popularity are complex. They may not be uniform across different circumstances. For example, the factors that govern the popularity of the least popular pages may be rather different than the factors that govern the popularity of the most popular pages.

Power laws and log-normal distributions are two-parameter distributions. The distributional form that best characterizes traffic to all pages may have many more than two parameters. Compared to a log-normal distributions and other distributions with more than two paramters, an approximating line has greater value for providing a simple, intuitive description of an important part of the popularity distribution.

Two website traffic distributions suggest that website traffic distributions may have flattened over the past decade. Traffic to Sun’s website pages in July, 1996, according to my calculation, had a descriptive log-log line with slope about -1.1. Traffic to pages in the summer of 2006 had a descriptive log-log line with slope about -0.8.* This difference may reflect differences between the two websites. It might also indicate flatteining over time in typical website traffic distributions. Such flattening was also a general pattern of change in name popularity distributions in the England (and the U.S.) from 1800 to the present.

Much more evidence of this sort might lead one to expect website traffic distributions, and perhaps other distributions for digital goods, to continue to flatten in the future. “More of the same” is a very crude sort of prediction. But absent any other relevant information, it might be the best that one can make.

Knowlege concerning the factors that have produced changes in popularity distributions could help to predict and shape future changes. Persons may have chosen less popular names in response to changes in patterns of work and residence that put persons closer together and more extensively and uniformly regulated their interactions. In short, personalization may have been a personal counter-reaction to factories and urbanization (the Industrial Revolution).

Suppose new information and communication technologies favor a more dispersed workforce, and family structure continues to shift toward more single persons and smaller households. My theory then predicts a decrease in personalization and an increased desire to associate with popular symbols.

Ummm, about all current trends indicate that either my theory is wrong, or that there are a lot of other, much more important factors. Does anyone have some better ideas?

* This is the slope measured in log-log coordinates, not in the coordinates of the axes’ labels. The intercept on a log(page traffic) axis typically varies greatly with total website traffic. Thus I prefer graphs that have a y-axis labeled with log(page traffic share in total website traffic). An approximating line has the same slope with either labeling for the Y axis.

more discussion about tail size

Once again men are heatedly discussing tail size. Just ponder this queston: How large is the long tail? Personally, I’m going to keep looking before I decide for myself.

While it’s novel to bring mathematical precision to such matters, unfortunately it seems to me that this mathematical model focuses attention on misleading features. The model says that the share of the k most popular items is log(k)/log(n), where n is the total number of items on offer. Thus, in this model, the total number of items on offer determines the share of the most popular items.

This isn’t a sensible model. Mathematically, a power law describes an infinite number of items on offer. The slope of the power law, or more precisely, the slope of an approximating power law at the high popularity end of the distribution, usually describes well the high-end shares. The question is what determines the slope of the power law. The number of items on offer isn’t a good answer to that question, particularly for n varying from two million to six billion.

For a concrete example, consider the popularity of the ten-most-popular given names. The set of possible given names (given names on offer) is huge, and probably hasn’t changed much in the past two-hundred years. However, the popularity of the ten-most-popular given names for males in England has fallen from about 85% in 1800 to about 28% in 1994. If you want to understand changes in the popularity of the most popular items in a collection of symbols instantiated and used in a similar way, try to understand this change.

* * *

For additional amusement, here’s a post I stuck in the newsfeed a little more than a year ago, back in the time of Web-Pleistocene:

Tail aficionados might enjoy pondering the distinguishing features of the long tail. I think that size, which tail authorities have categorized as long or short, matters less than shape. It should be no surprise to anyone that shape can change over time. For some graphical evidence, see the detailed images here.

So don’t just sit around complaining that “diversity plus freedom of choice creates inequality”. Power laws don’t imply any particular amount of inequality. The power of the powerlaw determines the difference between tails. Look at some examples and see for yourself!

growth of Internet traffic in Japan

Good, large-sample data on Internet traffic is hard to find. However, an excellent study of Internet traffic in Japan [Cho et. al. (2006)] describes 42% of Japanese (public) Internet traffic for six one-month observations spanning Sept. 2004 to May 2006.

This study reports many important facts. The ratio of bytes sent to residential customers to bytes received from residential customers was 1.3 — remarkably symmetric. Peer-to-peer applications using dynamic port assignment account for most of the traffic. The distribution of bandwidth use by users is a high-powered power law. Most importantly, specific users’ positions in that distribution vary over time and are not well identified with demographic and other customer characteristics (other than fiber connection, i.e. bandwidth availability).

The residential traffic growth figures for Japan vary considerably across month intervals. From Sept. 2004 to Nov. 2004, total traffic (aggregated inbound and outbound) grew 180% on an annualized basis. In subsequent 6-month intervals, annualized traffic growth rates were 58%, 19%, and 37%. Data on growth in fiber-to-the-home (FTTH) connections and total connections also shows volatility, but this does not seem to explain the reported traffic growth volatility. Any ideas about what explains it?

According to my calculations, (public) Internet traffic in Japan from Sept. 2004 to May 2006 grew about 60% per year. This figure aggregates inbound and outbound traffic and includes residential broadband customers and non-residential broadband customers (leased lines, data centers, dialup). I estimated non-residential traffic for the 7-ISP sample using the reported residential/non-residential traffic figures from the 4-ISP sample in Nov. 2005, and the non-residential broadband growth rate for the 4-ISP sample from Sept. 2004 to May 2006.

This estimated annualized growth of Internet traffic in Japan is much higher than estimated annualized growth of (non-voice channel) bandwidth in use in the U.S. across the 1990s. From 1989 to 1999, total DDS, DS1, and DS3 channel termination bandwidth in the U.S. grew an estimated 27% per year (see Table P6 in U.S. Bandwidth Price Trends in the 1990s). The difference between a 60% growth rate and a 27% growth rate year becomes huge after only a small number of years.

The Japanese study does not encompass bandwidth deployed in private networks. The ratio of Internet bandwidth to total inter-office bandwidth may have been about 15% in the U.S. in 1998 (see Growth in the “New Economy”, p. 6). The Japanese data show much a faster growth rate of non-residential bandwidth than residential bandwith, but the former is only about two-thirds the size of the latter. This is consistent with a large share of non-residential bandwidth not being incorporated into the public Internet.

An important point: the re-organization of network transmission protocols on existing networks tends to occur very slowly. Astonishing fact: in the U.S., about 90% of mobile-phone communications towers use traditional, copper-based TDM backhaul. Legacy networks hang around for a long time.


Cho, Kenjiro, Kensuke Fukuda, Hiroshi Esaki, and Akira Kato, “The Impact and Implications of the Growth of Residential User-to-User Traffic,” sigcomm 2006.