Zipf’s Law: A Power Rule Close to Home
Above is “The Zipf Mystery,” a video on YouTube by Vsauce. In the video, commentator Michael Stevens describes Zipf ‘s Law, which is the occurrence of power laws in many aspects of human life. A shown example (in the video) of Zipf ‘s Law is that number of times that a word is used in a book is inversely proportional to the rank that word holds in the book (i.e. the fourth most used word is proportional to one-fourth of the number of times the first word is used). Michael tries to provide an explanation of why Zipf ‘s Law occurs so much in our human world, and provides many quality theories and examples. If you’re interested and want to learn more about Zipf ‘s Law, the video description links to a multitude of articles, papers, and other interesting sites.
This video relates to our class discussion of popularity and the power laws regarding that popularity. The video also discusses the “rich-get-richer” effect. Additionally, Michael discusses an interactive activity involving paperclips, where you pick out a paperclip out of a pile, link it to another paperclip, and place that chain back into the pile. You repeat the process, and obtain a histogram of paperclips representing a power function. In fact, this paperclip activity is analogous to the web-linking we did in class and on HW 7.
While, this video did include great commentary with great examples, I noticed that some of the examples listed seemed to have concavity when plotted on a log scale (see 3:32, the number of times an academic source is cited and the number of ingredients used in cook books). This indicates that, though a power law may approximate the trend at some points, a better trend law should be used to model the data.
Overall, the video was entertaining, thoughtful, and insightful. If you want, try the paperclip experiment at home!