In physics, a critical point is a point at which a system changes radically its behavior or structure, for instance, from solid to liquid. In standard critical phenomena, there is a control parameter which an experimenter can vary to obtain this radical change in behavior. In the case of melting, the control parameter is temperature. Self-organized critical phenomena, by contrast, is exhibited by driven systems which reach a critical state by their intrinsic dynamics, independently of the value of any control parameter. The archetype of a self-organized critical system is a sand pile. Sand is slowly dropped onto a surface, forming a pile. As the pile grows, avalanches occur which carry sand from the top to the bottom of the pile. At least in model systems, the slope of the pile becomes independent of the rate at which the system is driven by dropping sand. This is the (self-organized) critical slope.
Critical states of a system are signaled by a power-law distribution in some observable. In the case of a solid-liquid transition, one can measure the heat-capacity of the system. In the case of sand-piles, one can measure the distribution of avalanche sizes. In the present case of internet access, curiosity is measured. The analogy with sand piles is clear: a grain dropped onto the pile corresponds to an initial access to the document. The size of an avalanche corresponds to depth of reading of a document. In order to maintain a critical slope in a sand pile in a finite geometry, sand is removed at the edges of the pile. One can think of the sand pile as sitting on a table. Sand falls off as it reaches the edge of the table. The same process could be operating in the case of hypertext access to a document: once readers have achieved a certain depth in the document, they may decide that the document is sufficiently useful to them that they should obtain a hardcopy. At that point, they will stop issuing http requests and then issue a ftp request to retrieve the full document.
To determine if this picture is correct, we must correlate http and ftp accesses. This can be done as follows: for each ftp download, we search the http log to find a corresponding session. If there is one, we measure the curiosity exhibited in that session. Unfortunately, the small number of such events (AL-SIM:127, CA-FAQ:214) renders the experiment inconclusive. Nonetheless, comparison of figure 5 (exponential fit) with figure 6 (power-law fit), suggests that a power law may account better for the data than an exponential, at least in the case of CA-FAQ.
