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Computational physics and auditing Wikipedia

In fall of 2013, in my computational physics class (Physics 409), I decided that I should do two things that I hadn't done the last time that I taught that class:
  1. I should do my own final project, to demonstrate to them exactly what a good project looks like, both in terms of the technical execution and the written description.
  2. Since we live in an era where information is cheap (thanks to computers, the main tools of the course), I should use my example project to "audit" something on Wikipedia, and demonstrate how to verify or refute a claim made on the internet.
To that end, I decided to study chaos in the double pendulum (a commonly-studied example in chaos theory), and try to replicate this beautiful figure from Wikipedia.  As described in the introduction to the sample report that I wrote as an example for my students, the results in that figure are plausible, and consistent with another peer-reviewed finding in chaos theory, but there is no peer-reviewed source cited for the figure.  Thus, it is worthwhile to see if we can replicate the result.  As described in my report, I have done so, and I have found similar results for a slightly different version of the double pendulum.  (The only difference is that I modeled the double pendulum as two point masses rather than two rods with distributed mass, largely for reasons of simplicity.)  The code that I used for my simulations is here (in Python).

One interesting side finding in this work was that while the Wikipedia result is correct, there's a small error in equation 29 in the Wolfram Scienceworld article on the double pendulum.  (I tried to archive the Wolfram page with Webcite, but Wolfram does not allow that form of archiving.  I do not promise that the error will still be there when you click on the Wolfram page.)  One should not draw broad generalizations from comparing a single Wikipedia figure and a single article at another site.  Still, Wolfram operates on a model of a single author with a known identity and reputation, whereas Wikipedia operates on community editing, and it is amusing that Wikipedia (often the target of academic disdain) stacked up better in this comparison.  My own take on Wikipedia (as demonstrated in this work) is "Trust but verify."  Wikipedia is a fine starting point for curiosity-driven exploration, and a place to look for references that can then be examined.  It should not be taken as the final word, but it is a fine place to start.

In that spirit, I encouraged my students to consider auditing Wikipedia claims for their final projects.  My poster presentation on my findings (for the 2014 CSU Symposium on University Teaching) is linked below.    My overall finding was that most students came away with decent projects, somewhat more focused than some projects, and with an attitude of "Trust but verify" concerning digital information sources.

Incidentally, the Wikipedia figure has a named source, a professor at UBC.  (I'm not outing him in violation of Wikipedia rules; he put his name on that figure.)  I eventually looked for his article on the double pendulum (apparently never-published), in which he describes the exact procedure used to obtain that figure.  Of course, I did this after starting the work of deriving equations, writing code, and running simulations, so I didn't short-circuit my investigation.  I still think that auditing this claim was a worthwhile training example for my students.
Alex Small,
Apr 17, 2014, 8:15 PM