I think that the process of understanding something can be modeled as a path up an ascending, widening spiral. The height of a point on the spiral indicates the complexity of your model of the subject, the radius of the point indicates the number of related subjects you consider, and the azimuth indicates the particular aspect of the subject you’re studying at any given moment. As you progress in your studies, you return to the same topics again and again, but with ever more sophisticated understanding.
Implications
I see two implications of the spiral:
- You should study those things which are “adjacent” to your current understanding, and in the appropriate direction on the spiral. Once you sort-of-understand a topic, you should study a closely related topic, and explore it slightly more deeply. You should consciously try to cycle through a few topics that lead you back to your starting point, albeit with a deeper understanding. As your understanding grows more sophisticated, these cycles should become longer.
- The hardest part of understanding something is finding the bottom of the spiral: a simple model of a few aspects of the subject that you can take in all at once, and which can direct you to fruitful lines of inquiry. Many starting points fail either because they are too diffuse to be usefully comprehended by the novice, or so hopelessly oversimplified and inaccurate as to be cut off from any proper understanding of their subject.
