Word of the week: Entation

A psuedo-visual internal modality of experience, has spatial and gemoetric qualities similar to vision but for me seems to be more 2-dimensional and less colorful.

In decision theory and related fields, the explore-exploit tradeoff is the name given to the apparent tension between learning more about the world and taking advantage of what you already know. While in some cases (especially many formal models) this is an unavoidable tradeoff, a key strategy in my ConSciEnt work is to perform exploration via exploitation. One of the best ways to learn something new about some field and validate any hypotheses you have is to find a domain where you can build something valuable based on the information and then go after it, and in a functioning market success means you have more resources for the next project too.

While there are a lot of details to work through, I've identified a good possible application for The Texture of Understanding. Given knowledge of the role of experience in gaining and having understanding plus some way to identify how it's functioning for a given person, it should be possible for a student or teacher to improve learning or assessment. A selection of specific ideas that might bear fruit if true:

This could all lead into teaching techniques, tips for self-study, or in a more sophisticated case an automated system for tracking understanding and dynamically adjusting content appropriately. For this last, imagine a political science history textbook that, when covering the formation of the American republic, expanded with a quick aside on the Roman republic if it noticed you hadn't made the connection yourself!

In parallel with my continuing observational studies, I'll be spinning up on education as an industry. What are current best practices and theories, what kinds of educational products make money, what are the different markets to potentially target, etc. I'll also be keeping an eye out for potential collaborators, whether teachers, students, educational researchers, etc. and start exploring the possibility of funding as the product vision develops. There's a lot of ground to cover here but I expect to be able to refine my thinking about understanding itself at every step!

In other news, I've built up a huge stack of dependencies in the self study I'm using to guide my observational work. Sharing the sequence of steps just for the absurdity of it:

  1. I've set as my ultimate goal (for now!) a solid understanding of the standard models of particle physics and cosmology.

  2. From there, I've identified a number of scientific subjects to refresh on or study anew, and from those a number of mathematical ones.

  3. For a while now whenever I dig into some new mathematical subject I've had this feeling in the back of my head that really knowing category theory beyond the ambient snippets I've picked up so far would be a valuable lens, and the resources I found while trying to find texts for the physics prerequisites just reinforced that, so I decided to start with category theory (specifically, working through Awodey as well as Lambek and Scott, possibly following up with Mac Lane afterward if still inclined)

  4. With linear algebra and analysis I explored mostly mental problem solving and free form loose problem solving and proofs on paper, so I decided to build a graphical tool for categorical reasoning as I go

    1. I'm learning about what external interfaces to coq exist, to have my tool spit out formal proofs

    2. I'm learning graphical programming in Haskell

    3. I had an idea about 6 months ago for extending category theory in a way that parallels the way dependent type theory extends non-dependent type theory, so I need to decide if I want to build my tool around it or not.

On that last point, I've spent a lot of the last two weeks fleshing out the idea into a coherent system and working through some examples; I think I now have something that works, so I plan to write it up and share it to see if it's at all novel or useful. In particular, and getting very far afield from consciousness research at this point, I think I have a presentation of what "codependent types" might look like, including introduction, typing, and computation rules. Back to the topic at hand, in doing this work I observed a strategy of working through a number of "promising" scenarios somewhat mechanically, with the hope that at the end a clearer concept is at hand, which worked successfully in developing the idea. Getting some "muscle memory" for some skill prior to understanding how or why it works can play a role in gaining the understanding itself!

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