The Unreasonable Effectiveness of '2' in Statistics
The title is a reference to The Unreasonable Effectiveness of Mathematics in the Natural Sciences , a very popular paper by Eugene Wigner which explores how mathematics is unreasonably effective at not only explaining, but also predicting scientific phenomena. I had a similar question about the number $2$ which repeatedly shows up in engineering and science, specifically in the form of the $2$-norm of a vector, and seems surprisingly effective at doing what it’s supposed to do. I asked my Estimation Theory instructor at Purdue why this was so, and he told me that I ask too many (but good) questions. I have since then accumulated a variety of answers for why the number $2$ is, in some sense, ✨special✨ During our journey through this post and the next, we will visit the central limit theorem, Gaussian distributions, and Euclidean geometry. ...