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February 03, 2007

Modernizing Kevin Bacon

Via Mason Porter and Arcane Gazebo comes a pointer to a modernization (geekification?) of the Kevin Bacon game, this time using Wikipedia (and suitably enough, this version has its own wikipedia page). Here's how it works:

  1. Go to Wikipedia.
  2. Click the random article link in the sidebar.
  3. Open a second random article in another tab.
  4. Try to find a chain of links (as short as possible) starting from the first article that leads to the second.

Many people are fascinated by the fact that these short paths, which is popularly called the "small world phenomenon." This behavior isn't really so amazing, since even purely random graphs have very short paths between arbitrary nodes. What makes the success of these games truly strange is the fact that we can find these short paths using only the information at our current location in the search, and some kind of mental representation of movies and actors / human knowledge and concepts. That is, both the movie-actors network and wikipedia are locally navigable.

The US road system is only partially navigable in this sense. For instance, with only a rudimentary mental map of the country, you could probably get between major cities pretty easily using only the information you see on highway signs. But, cities are not locally navigable because the street signs give you no indication of where to find anything. In order to efficiently navigate them, you either need a global map of the city in hand, or a complex mental map of the city (this is basically what cab drivers do it, but they devote a huge amount of mental space to creating it).

Mason also points me to a tool that will find you the shortest path between two wikipedia articles. However, I'm sure this program isn't finding the path the way a human would. Instead, I'm sure that it's just running a breadth-first search from both pages and returning the path formed when the two trees first touch. What would be more interesting, I think, would be a lexicographic webcrawler that would navigate from the one page to the other using only the text available on its current page (and potentially its history of where it's been), and some kind of simple model of concepts / human knowledge (actually, it would only need a function to tell it whether one concept is closer to its target or not). If such a program could produce chains between random articles that are about as short as those that humans produce, then that would be pretty impressive.

(These questions all relate to the process of navigation on a static network, but an equally important question is the one about how the network produces the structure necessary to be locally navigable in the first place. Although it's a highly idealized and unrealistic model, I humbly point to the results of my first big research project in graduate school as potentially having something to say on this topic.)

posted February 3, 2007 03:09 PM in Complex Systems | permalink