I find the theme of Curiosity vs. Duty very fascinating. It feels more like a spectrum than a dichotomy — I don't think that you are ever at the extremes. Even when you are doing some work only out of duty, you may still find something piquing your genuine curiosity. Noticing and exploiting it's like observing your behavior and learning more about yourself.
The Hat feels like a consciousness amplifier. Reading this article, I perceived it as a tool that amplifies students' emotions and thoughts. In a way, this is what happens when you engage in serious self-reflection. You sit at your desk, pen in hand, and jot down your thoughts on paper. The act of writing here acts as an amplifier (similar to what the Hat does) because it allows you to see what you wouldn't while "just thinking". It doesn’t change you directly, but it amplifies what's already within you.
I enjoyed this post. As I was reading it, I had many ideas on how many aspects of our lives this applies to. Your example about the dish-washing procedure made me think that the idea of grayspaces can come in both discrete and continuous forms.
Let me give you some examples. For instance, consider moving to a different job. Changing both industry and role can be seen as two discrete leaps. Common advice is to take it step by step — perhaps first shifting industry, then later changing position. On the other hand, if you want to build a daily writing habit and want to reach 1k words per day, you may do this continuously starting from zero and adding one word per day.
To bring this at a higher level, you can see this pattern in major life decisions. After each leap, you usually have some time to reflect and plan your next move — this could be a grayspace.