What is Holonomy?

July 4, 2013: This morning National Public Radio aired a piece with visitors to the National Mall reading the Declaration of Independence. As I listened, I was reminded of a new word I learned during the Cognitive Coaching Seminar (CCS) - Holonomy. This is the study of the relationships that exist between the part and the whole.

From the Cognitive Coaching Seminars Foundation Training Learning Guide:

Arthur Koestler described the dual tendency of every individual to preserve and assert his or her individuality as a proud and quasi-autonomous whole while functioning as an interdependent part of a larger system. (p. 22)

In 1776, the Continental Congress declared independence from Great Britain. While historically the focus is placed on independence (and rightly so), the Declaration of Independence ends with a pledge of interdependence: "we mutually pledge to each other our Lives, our Fortunes and our sacred Honor." Too often in our society we see either one (the independence) or the other (the interdependence) and miss the role both play in a successful system.

In mathematics, the ability to see both the part and the whole is important in developing number sense. For example, do you see ten individual beads or one set of ten beads ... or both?

The inability to see the connections between these two perspectives limits a person's mathematical fluency. This is what I immediately thought of when I was introduced to holonomy. 

However, it gets much more complicated when you begin to look at human systems. All you need to do is ask anyone familiar with the history of the United States or the workings of a school. How does a teacher maintain self while fitting into the system? There has even been some discussion related to this regarding the mathtwitterblogosphere. Perhaps we need a Declaration of Interdependence.

Not it!