Empirical Exercise: The Dynamics of Knowing

Abstract

This paper documents my initial effort to approach a mathematical puzzle with a dual focus: my aim is to discover a rule for extracting square roots, but my primary interest is in the procedure, i.e. in the dynamics of my own wonder.  The exercise is taken, with some modification, from chapter three of Wealth of Self and Wealth of Nations by Philip McShane. It was an undergraduate effort, and my hope is that it will be helpful to anyone who wishes to make a similar beginning in serious self-attention. It may be of particular interest to high school, college, and university students who are struggling with the problem of memorization replacing genuine understanding in their education.