Michael J. Bommarito II and Daniel Martin Katz, both of the University of Michigan’s Center for the Study of Complex Systems and creators of the Computational Legal Studies blog, have posted a new visualization entitled Measuring the Complexity of the Law: The United States Code. The visualization is part of their new paper, A Mathematical Approach to the Study of the United States Code, forthcoming in Physica A, Vol. 389, 2010.
The authors describe the visualization as follows:
With this representation in place, it is possible to measure the size of the Code using it various structural features such as its vertices V and its edges E. It is possible to measure the full Code at various time snapshots and consider whether the Code is growing. Using a limited window of data, we observe growth in not only the size of the code but also its network of dependancies (i.e. its citation network). [...]
Of course, growth alone is not precisely analogous. Indeed, while we believe in general the size of the code tends to contribute to “complexity” that some additional measure or measures are needed. Thus, our paper conducts various structural measurements such number of sections, section sizes, etc.
In addition, we use the well known Shannon Entropy measure (borrowed from Information Theory) to evaluate the “complexity” of the message passing / language contained therein.