The Texture of Understanding

What does it feel like to really get something? How does that feeling develop and change as you learn? What role does that experience play in gaining and applying understanding to practical ends?

This project is an observational exploration of these questions through the device of observing my experiences as I teach myself various mathematical and physical subjects. As I read, think, and work through problem sets, I am attending to what the subjective experience is like, with a particular focus on my feelings about some particular concept as I progress from complete ignorance to deep grokking. I am starting in a mode of almost unconstrained watching, but as I uncover structure I plan to become more experimental to dig into phenomena of interest.

Curriculum

With the aid of Mark Moon, I'm developing and slowly working through a curriculum to get me from my current knowledge to a working understanding of the theory of general relativity and the standard model of particle physics. Though I am interested in those subjects for their own sake, this is primarily intended as a way to be able to predictably encounter subjects I don't understand and systematically gain understanding of them.

  1. Despite already knowing linear algebra, I am starting with Linear Algebra Done Right to get back into a habit of academic learning, start building up the skill of observing myself as I learn, and refresh myself in preparation for the linear algebra-heavy subject of quantum mechanics.

Notable Observations

Negative salience

When I come across a topic I don't understand, there's an immediately salient feeling of "not getting it" that I can then explore to figure out what I'm missing and where I need to work. I suspect one major role of experience in understanding is directing attention to its lack, an idea dovetailing with developments in other fields such as the predictive processing model of cognition.

In some cases, the feeling of "not getting" something seems to be related to lack of (confident) knowledge of how concretely to proceed/address some problem. Is understanding fundamentally tied to a particular practical orientation?

Mental operations

I am noticing an abundance of interesting different experiences when performing the various mental operations, particularly symbolic manipulations required to solve exercises and walking through proofs. I hope to catalogue these and see if any interesting patterns fall out, especially as I make progress and the size of the "primitive" operations I know how to perform grows. So far the main insight has been that, while I don't strongly visualize when I'm thinking, there is a definite spatial component to how symbolic manipulations feel, and a distinct modality for verbal thought.

When I'm reading through new material, I sometimes perform little "snippets" of these operations related to what I'm reading, seemingly involuntarily. How does that relate to a growing understanding?

Does fluency in these techniques rise directly with understanding? Is that (part of) what understanding is?

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