How Is Knowledge Spread?
And how long an “afterlife” might such knowledge enjoy on the Web?
These questions, of obvious concern to modern journalists and educators, can be applied to the Out of Eden Walk project. To begin answering them, we must track the knowledge that Paul shares in his dispatches, and the comments that those articles generate, as he has moved around the world on foot over the past couple years.
In general, when a new piece of information is introduced, people start learning about it. After a period of initial enthusiasm, the number of people who access and comment on the information gradually decreases. This trend is evident in any of Paul’s dispatches.
Fortunately, if the information remains available, it may lead to further exploration and discovery even many years later. The rate of decrease is of special interest as we seek to understand how knowledge spreads for a period of time and then dissipates.
Traditional models of knowledge propagation are similar to those that apply in physics. These models are based on differential equations, in which the number of new learners decreases exponentially over time. Any quantity that grows or decays by a fixed percent at regular intervals is said to exhibit exponential growth or exponential decay. This is how populations grow over time, or the number of bacteria in a colony — or, inversely, the half-life of radioactive isotopes as they decay. All can be described as exponential behavior.
Applied to the propagation of knowledge, this law states that the number of new learners decreases exponentially, by half, over a set interval of time, after which no new learners appear. We may have 100 new learners the first week, 50 the second week, 25 the third week, etc., with no new learners at all after the eighth week.
But recently, researchers have proposed a new “power law” model for knowledge propagation. In this model, the number of learners decreases much slower, as a (negative) power of time.
If in the first week we have 100 new learners and 50 new learners (half the original number) in the second week, then after four weeks we will have 25 new learners (half of 50), 12 after 8 weeks, and so on. In this model, new learners emerge for a very long time.
This outcome is similar to Mandelbrot’s fractal models, repetitive, infinitely detailed geometric patterns in nature that can be applied to problems ranging from economics to coastline analysis.
In simple mathematical terms, the difference between the exponential and power law behavior is as follows:
Exponential: r = (constant) t Power Law: r = (t) constant
To decide which of these two models best fits the data, we analyzed the way knowledge is propagated by the Out of Eden Walk project. Each of Paul’s posted dispatches contains new and interesting information about different areas of the world. By tracking how many reader comments were posted over a period of time, we were able to gauge how this new information propagates.
For each dispatch, we counted the number of comments posted after publication. Starting from the day on which the maximum number of comments were posted, we analyzed the 30 days that followed, noting the relationship between the number of elapsed days and the number of comments posted. We then checked whether this relationship is better represented by the power law or the exponential law.
To reach a statistically reliable conclusion about which model more closely follows the data, we only considered dispatches with at least 50 reader comments. It turns out that none of these dispatches is consistent with the exponential law, and most of these dispatches are consistent with the power law.
Our analysis of a number of dispatches from the Out of Eden Walk project confirms that the power law is a more relevant model of knowledge propagation for Salopek’s writing and the work of journalists in general.
This is good news: It means, in effect, that the readership of Paul’s dispatches may decrease over time, but it will never stop!
Readers interested in further technical details can read the research paper posted at www.cs.utep.edu/vladik/2015/tr15-07.pdf
Octavio Lerma and Leobardo Valera are students at the University of Texas at El Paso, working on their doctoral dissertations in modeling of knowledge dispersion parameters and solution of very large linear and non-linear systems of equations. Octavio also teaches high school Physics and Computer Science; he actively uses Out of Eden Walk materials in his classes. Deana Pennington and Vladik Kreinovich are researchers at the University of Texas at El Paso. Pennington specializes in Interdisciplinary knowledge exchange processes and synthesis science. Kreinovich studies Fuzzy Logic and Interval Computations.