Monthly Archives: March 2012
I am currently writing a paper to submit to the new and very exciting journal computational culture on the use of graph theory to produce “evaluative metrics” in contexts like Web search or social networking. One of my core arguments is going to be that the network as descriptive (mathematical) model has never stood in opposition to the notion of hierarchy but should rather be seen as a conceptual tool that was used in different fields (e.g. sociometry, psychometry, citation analysis, etc.) over the 20th century to investigate structure and, in particular, to both investigate and establish hierarchy. This finally gave me an excuse to dive into Jacob L. Moreno’s opus magnum Who Shall Survive? from 1934, which not only founded sociometry but also laid the ground work for social network analysis. This is one of the strangest books I have ever read, not only because the edition from 1978 reveals the author as a deeply Nietzschean character (“Actually, I have written two bibles, an old testament and a new testament.“), but also because the sociogenic therapy Moreno proposes as an approach to the “German-Jewish conflict” puts the whole text in a deeply saddening light. But these aspects only deepen the impression that this is a fascinating book, really one of its kind.
Interestingly, Moreno also discovered what we would now call “power-law dynamics in social networks”. One of the applications of his “sociometric test” – basically a “who do you like” type of questionnaire – in a small American town named Hudson came to the following result:
After the first phase of the sociometric test was given the analysis of the choices revealed that among a population of 435 persons,23 204, or 46.5%, remained unchosen after the 1st choice; 139, or 30%, after the 2d choice; 87, or 20%, after the 3rd choice; 74, or 17%, after the 4th choice; and 66, or 15%, after the 5th choice. (Moreno 1934, p. 249)
This means that 15% of the population was not mentioned when the interviewees were asked which five people in the community they liked best. While this does not make for a particularly skewed distribution, Moreno transposes the result on the population of New York city and adds a quite tantalizing interpretation:
There is no question but that this phenomenon repeats itself throughout the nation, however widely the number of unchosen may vary from 1st to 5th or more choices due to the incalculable influence of sexual, racial, and other psychological currents. For New York, with a population of 7,000,000, the above percentages would be after the 1st choice, 3,200,000 individuals unchosen; after the 2nd choice, 2,100,000 unchosen; after the 3rd choice, 1,400,000 unchosen; after the 4th choice, 1,200,000 unchosen; and after the 5th choice, 1,050,000 unchosen. These calculations suggest that mankind is divided not only into races and nations, religions and states, but into socionomic divisions. There is produced a socionomic hierarchy due to the differences in attraction of particular individuals and groups for other particular individuals and groups. (Moreno 1934, p. 250f)
By looking into the history of the field, I hope to show that the observation of uneven distributions of connectivity in real-world networks, e.g. the work by Hindman and others concerning the Web, are certainly not a discovery of the “new science of networks” of recent years but a virtual constant in mathematical approaches to networks: whenever somebody starts counting, the result is an ordered list, normally with a considerable difference in value between the first and the last element. When it comes to applications of sociometry to sociology or anthropology, the question of leadership, status, influence, etc. is permanently in the forefront, especially from the 1950s onward when matrix algebra starts to allow for quick calculations of different forms of centrality. Contrary to popular myth, when Page and Brin came up with PageRank, they had a very wide variety of inspirational sources to draw from. Networks and ranking had been an old couple for quite a while already.
0 Comments Posted by Bernhard on March 12th 2012 @ 9:28 am
In 1953, Leo Katz, psychologist of the measuring kind, wrote the following:
The purpose of this paper is to suggest a new method of computing status, taking into account not only the number of direct “votes” received by each individual but, also, the status of each individual who chooses the first, the status of each who chooses these in turn, etc. Thus, the proposed new index allows for who chooses as well as how many choose.