## Saturday, December 28, 2013

### Fractal Porn!?

Say what? Who would have guessed? Before you start pondering the erotic possibilities of geometry, let me say that the fractality occurs in the topology of the social network.

Fractal properties for pornography should not be surprising because we already know (Foxman et al. 2006; Freiesleben de Blasio et al. 2007; Liljeros et al. 2001; Liljeros et al. 2003) that our network of sexual relationships has fractal properties. Specifically, the articles documenting this have found that the number of sexual partners is distributed as a power law. That is, a large number of people report having a single sexual partner (depending on the study, within the last year or within the respondant's lifetime). A much smaller number of people report having had 2 sexual partners, a yet smaller number say they have had 3, and so forth. The decline in the number of people (let's call it "y") who report having x number of partners as x increases obeys a particular kind of function that mathematicians call a power law, in which a constant negative exponent describes how y decreases as x increases. One notable characteristic of a power law is that the "tail" of the distribution is "long," which is to say, much longer than would obtain if the distribution were normal or exponential. Thus, a small but significant number of people have large nmbers of partners, way up in the double or even triple digits. We can think of the number of sexual contacts as forming a network in which the nodes are individuals and the links are sexual relationships between them. The power law then describes the mathematical structure of the links in the network--an aspect of its topology--indicating that it is a scale free network. These network characteristics are significant in real life because, for example, they help determine key properties of the network such as its robustness to shocks (e.g., attacks or failures), or rates of contagion (i.e., the propagation of a disease or computer virus) (Barabasi, 2009). Understanding the topology of these networks is critical for preventing or stopping epidemics, a subject that has been studied most intensively in the case of sexually transmitted diseases.

The impact of network theory could have been limited if not for a series of findings that underlined the perils of ignoring network topology. Take, for example, the discovery of Romualdo Pastor-Satorras and Alessandro Vespignani that on a scale-free network the epidemic threshold converges to zero. It has long been known that only viruses whose spreading rate exceeds a critical threshold can survive in the population.Whereas the spreading rate captures the transmission dynamics, the threshold is determined by the topology of the network on which the virus spreads. Therefore, the vanishing threshold means that in  scale-free networks even weakly virulent viruses can spread unopposed, a finding that affects all spreading processes, from AIDS to computer viruses.[Barabasi 2009, internal citation omitted]

Fractal (scale-free) network topology is related to the "small world" property of such networks (Amaral et al. 2000), which permits remarkably short connections between distant nodes, explaining the "six degrees of separation" phenomenon and allowing the Kevin Bacon game to work. The network of movie actors is famously a case of a small world, scale free network. The actors are nodes and being cast in the same movie forms a link between a pair of thespians. Perhaps more apt in this context is Truman Capote's reputed International Daisy Chain game, in which "'You make a chain of names,' he [Capote] wrote friends in New York, 'each one connected by the fact that he or she has had an affair with the person previously mentioned; the point is to go as far and as incongruously as possible'" (http://www.geraldclarke.com/treat.htm). Supposedly, Adolf Hitler and Cab Colloway were separated by only three links, illustrating the small world quality of the network.

Turning from sex to pornography, a new article has been posted to arXiv in which the network topology has been analyzed for adult movies in the Internet Movie Database (IMDB). Here's the citation:

Gallos, Lazaros K., Fabricio Q. Potiguar, Jos´e S. Andrade Jr, and Hernan A. Makse (2013). IMDB network revisited: unveiling fractal and modular properties from a typical small-world network. http://arxiv.org/abs/1305.1175v2.

The full Internet Movie Database (IMDB, www.imdb.com) has, as I mentioned, been analyzed previously for its small world property (Watts and Strogatz 1998). Now, Lazaros and his colleagues have analyzed and discussed the fractal and small world qualities of the subset of the IMDB comprising adult movies. I didn't know there were adult movies listed in the IMDB, and I don't see any filter or genre listing for them; perhaps you have to have a paid subscription to the database to obtain that information. The "collaboration" network of actors in the adult movies has a somewhat different topology than that of the full movie database. Maybe the differences shouldn't be surprising, given the innate differences between pornographic and "regular" movies. For example, I can only imagine that the cast is much smaller on average in an adult movie than in a regular flick. The adult movie network is, according to the article, a small world, but fractal characteristics emerge when one establishes a link between two actors if they have been cast in at least 2 movies (instead of just 1).

Because of their topological properties, epidemics can propagate much more quickly in scale-free networks than in random ones. However, at the same time, the scale-free property creates opportunities to stop epidemics, by attacking or protecting the highly connected nodes, which in a sexual network are those with large numbers of partners (Liljeros et al. 2001). Given that filming in the adult movie industry is currently suspended because of an actor's positive HIV test, those most concerned should take into account the topology of their network.

References cited

Amaral, L. A. N.,  A. Scala, M. Barthelemy, and H. E. Stanley (2000). Classes of small-world networks. Proceedings of the National Academy of Sciences 97(21), 11149-11152.

Barabasi, Albert-Lazlo (2009). Scale-Free Networks: A Decade and Beyond. Science 325:412-413.

Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286, 509–512.

Foxman, B., Newman, M., Percha, B., Holmes, K. K., & Aral, S. O. (2006). Measures of sexual partnerships: Lengths, gaps, overlaps, and sexually transmitted infections. Sexually Transmitted Diseases, 33(4), 209–214.

Freiesleben de Blasio, B., Svenssen, Å, & Liljeros, F. (2007). Preferential attachment in sexual networks. Proceedings of the National Academy of Sciences, 104(26), 10762–10767.

Liljeros, F., Edling, C. R., & Amaral, L. A. N. (2003). Sexual networks: Implications for the transmission of sexually transmitted infections. Microbes and Infection, 5, 189–196.

Liljeros, F., Edling, C. R., Amaral, L. A. N., Stanley, H. E., & Åberg, Y. (2001). The web of human sexual contacts. Nature, 411, 907–908.

Watts, Duncan J. and Steven H. Strogatz (1998). Collective Dynamics of 'Small World' Networks. Nature 393, 440-442.

## Thursday, December 12, 2013

### A Comment on Michael E. Smith's blog post "Problems with the big journals, Science and Nature"

Michael E. Smith's recent post "Problems with the big journals, Science and Nature" is right on target. These prestige or "luxury" journals do seem to focus more on the potential newsworthiness of their articles than on their scientific value. I don't say this from personal experience because I've never had the temerity to submit to them. But I remember a dinner party with some friends who've published in them repeatedly. While discussing a manuscript they were preparing, the most successful of them all said something like, "We can't send this to Science. They're only interested if its the oldest or the biggest or the smallest." And this was not sour grapes. He had published several articles in Science. He'd figured out the magic formula and wasn't bitter about it. He was merely stating what he perceived to be a fact of life. So, I would say there is a widespread perception among scientists that these journals are primarily interested in results that are going to make headlines. This doesn't mean that the articles they choose are therefore necessarily unworthy. In the Venn diagram for publishing results, the domains for "newsworthy science" and "significant science" do overlap. I scan Science and Nature every week, and I find many of the articles interesting not only for their substantive results but also for their innovative combinations of methods.

## Wednesday, December 11, 2013

### Twitter for archaeologists? From Michael E. Smith's blog...

On the alleged value of Twitter for archaeologists:

Michael Smith's remark:

"Yeah, I need to communicate with Barack Obama so I'll try Twitter. Or maybe I missed a tweet from Steven Hawking."  -MES

## Friday, December 6, 2013

### Videos of the Exploration of the Exploration of Cenote Sac Uayum at Mayapan

The cenote (sinkhole) of Sac Uayum is a large and visually impressive vertical cave located a short distance to the south of the great encircling wall of Mayapan, the Late Postclassic period capital city in the state of Yucatan, Mexico.I first visited Sac Uayum in 1991 while I was excavating at Mayapan. At that time, I became aware of a local belief that the cenote was unusually dangerous because it was guarded by a plumed serpent, and I wondered whether that might be why the cenote was evidently excluded from the circuit of the city wall, which bends inward to avoid it. I mentioned this in an article I published in 2005:

Brown, Clifford T. (2005) Caves, Karst, and Settlement at Mayapán, Yucatán, in In the Maw of the Earth Monster: Mesoamerican Ritual Cave Use, edited by James E. Brady and Keith M. Prufer, pp. 373-402. Austin: University of Texas Press (The Linda Schele Series in Maya and Pre-Columbian Studies).

At the time, I didn't attempt to enter the cave--which would have required  a vertical descent--for lack of both equipment and training.

Fortunately, my friend Bradley Russell has now apparently explored the cave along with Pedro Delgado Ku, Barbara Escamilla, and others. But first, they performed a heets' lu'um cleansing ceremony to protect themselves from the evil winds and spirits in the cave. I paste below a link to a video the Bradley posted on Youtube showing the ceremony. Below that, I have also embedded links to three other videos showing the exploration of the cave itself.  I remember the cave as having deep water covering the entire floor, so not surprisingly, they used scuba diving to explore it, as you can see in the videos.The videos and photographs are high quality.

Outstanding, Bradley! What fun! Great work!

There is a National Geographic article online about their work, which was supported in part by the Society. Here's a link to a number of other videos about Brad's research on the National Geographic website.

### Mayapan Video!

Mayapan: Urban Life at the Last Maya Capital

## Tuesday, November 12, 2013

### Obsidian lava flow

Interesting article on how an obsidian lava flow continues to advance and spread, though at a glacial pace, long after the volcanic eruption ends.

I don't have access to the full text of the article, but the link above will take you to the abstract on the journal (Nature Communications) website. Curiously, even without a subscription you can download the four videos in the Supplementary Materials (scroll to the bottom of the page). There is also a nice photo from the article featured on the journal home page.

Here is a link to a popular article about the research accompanied by a nice little explanatory video. I have embedded the video below.

Like many archaeologists, I'm interested in obsidian. It's cool (though not while erupting--see article above), and it makes interesting and sometimes beautiful tools. I'm always looking for more information about its geology because there appear to be undiscovered obsidian sources in Nicaragua, and I would like to find them. Just looking around doesn't seem to be working, so maybe a prediction based on geology or geochemistry would be helpful.

## Wednesday, November 6, 2013

### More on Jaina-Style Figurines

When I recently posted photos of Jaina-style figurines, I did not write an essay on the topic because the purpose of the post was to make photos available for study and education, not to present the results of my research on the subject.

By chance, however, I came upon a new and interesting article on these figurines. Here is the citation in case you want to know more about them:

McVicker, Donald (2012). Figurines are us? The Social Organization of Jaina Island, Campeche, Mexico. Ancient Mesoamerica Volume 23, No. 2, pp. 211-234. doi:10.1017/S0956536112000168

The essay provides a thorough review of the study of Jaina figurines, including information about the collection in the National Museum, where I took most of my photos. McVicker also provides new information and interpretations. I don't agree with all his conclusions, but it's worth a read if you're interested in the subject.

In view of the discussion in the article, I have to admit that my captions on the photos now appear to be naive. At the very least, some of the figurines--or ones similar to them--have been interpreted differently by other scholars, in some cases, for example, as deities. So, I should add the caveats that the captions I supplied were intended merely to be descriptive, that other interpretations exist, and that a true analysis--which I do not claim to have performed--would require additional research, including close inspection of the originals.

## Wednesday, October 30, 2013

### Photographs of Olmec sculptures, large and small

Can we stipulate to the usual caveats? I'm a poor photographer with a mediocre camera, etc, etc.

Note that many objects I (and the museum) label as "jade" could equally well be jadeite or even other minerals.

 Jaguar. Monument 7, San Lorenzo, Veracruz

 Colossal head. Monument 2, San Lorenzo, Veracruz.
 Colossal head. Monument 2, San Lorenzo, Veracruz. Another view.

 Detail. Colossal head. Monument 2, San Lorenzo, Veracruz.

 Alvarado Stela. Columnar basalt. Late Olmec. In low relief, it shows a bearded man richly adorned striding toward a captive (not visible in this view).

 Monkey. Monument 12, La Venta, Tabasco.

 Monkey. Monument 12, La Venta, Tabasco. Detail.

 Monkey. Monument 12, La Venta, Tabasco. Detail.

 Seated male (?) holding were-jaguar infant in his arms. Monument 12, San Lorenzo, Tabasco.

 Monument 19, La Venta, Tabasco. Seated man (?) holding bag, surrounded by serpent (rattlesnake).

 Monument 19, La Venta, Tabasco. Seated man (?) holding bag, surrounded by serpent (rattlesnake).

 Monument 19, La Venta, Tabasco. Detail of serpent's head.

 Monument 19, La Venta, Tabasco. Detail.

 Monument 19, La Venta, Tabasco. Detail.
 Olmec ceramic figurine. Middle Preclassic.

 Olmec sculpture. Bearded man in "wrestler" pose. "Late" Olmec (600-100 B.C. according to the label)

 Another view of the "Wrestler."

 Another view of the "Wrestler" showing its three-dimensionality and polyaxiality.

 Another view of the "Wrestler" showing its three-dimensionality and polyaxiality.

 Ceramic vessel, La Venta, Tabasco. Calzadas Carved? Paw-wing motif?

 Ceramic vessel, La Venta, Tabasco. Zoned post-fire incision.

 Ceramic vessel, La Venta, Tabasco. Zoned post-fire incision. Detail.

 Black-slipped Olmec ceramic vessel. La Venta, Tabasco.

 Olmec figurine, female, La Venta, Tabasco.

 Olmec figurine, female, La Venta, Tabasco.

 Olmec jades from offerings at La Venta, Tabasco.

 Olmec jades from offerings at La Venta, Tabasco. Note incised earflares with cinnabar.

 Olmec jades from offerings at La Venta, Tabasco. Incised earflare rubbed with cinnabar.

 Olmec jades from offerings at La Venta, Tabasco. Incised earflare rubbed with cinnabar.

 Olmec jades from offerings at La Venta, Tabasco.

 Olmec mirror.

 Olmec jades celts with incised designs.

 Olmec jade celts with incised designs accompanied by drawings of the designs.

 Detail of Olmec jade celt with incised design.

 Detail of Olmec jade celt with incised design.