I started writing the material for this blog in the autumn of 2018. I had spent many years as a teacher, two years as a parent, and I had just gone through a painful breakup. I started to realize that the things you learn from these experiences are all connected somehow. This blog is an attempt to document those ideas. The following paragraphs summarize my point of view (at the time) for where this blog will go.

The most effective ideas in teaching and student engagement, in parenting, and in social and political activism are actually the same ideas. In each of these settings, we have an older system of ideas that is based around power, domination, and control, and a newer system based around communication and cooperative effort. The ongoing effort for change is making slow progress. In some cases it is completely stalled. Our political discourse in America, to take one example, is locked into an unchanging cycle of outrage, mistrust, and the use of social shaming to exclude “the other” from conversations about politics.

It is both difficult and uncomfortable to rethink the foundations of our social interactions. It is even more difficult to do this when our relationships are inherently asymmetric, e.g. teacher-student, parent-child, leader-follower.

How do we lead without controlling? How do we direct without dominating and policing? And how do we exert pressure on our larger social system, to change along with us? I don’t know the answers to these questions. But in mathematics, one doesn’t start out knowing the answers. It’s enough to know the question, and to be motivated and curious enough to begin the journey towards the answers.

For this project I’ll be drawing on my experience as a researcher, educator, parent, relationship partner, and game enthusiast and combining it with ideas from education science, human development, psychology, sociology, and gender studies. The focus will be on common threads and the synthesis of these different areas of thought. I am not an expert in most of these areas, and I am certainly not well-read. I am open to reading suggestions on topics that might be relevant to the discussion at hand.

The title of this blog refers to a concept in homotopy theory, a branch of topology that studies shapes and continuous deformations between them. A shape is “highly connected” when any large family of points in that shape can be coherently joined together. In a highly connected shape, everything is connected to everything else, in so many ways that even the connections themselves are connected. I like to think that the subject matter of this blog forms a highly-connected shape: education is connected to human development, which is connected to parenting, which is connected to interpersonal relationships, etc. All of these areas of thought help us understand, live with, and work with other people.

About me

I’m a professional mathematician and an amateur parent.