Spanning problem-space

Determining how best to improve one’s own suite of mental models & thinking tools is a hard problem: we can’t easily see ideas beyond the…

Spanning problem-space

Determining how best to improve one’s own suite of mental models & thinking tools is a hard problem: we can’t easily see ideas beyond the horizon, and ideas we haven’t yet invested effort in developing are distorted at best, but determining the value of ideas is necessary because of the scarcity of time & other resources. This is further complicated by the fact that knowledge-seeking is not a single-player game: everyone is constantly refining their suite of mental models, making decisions based on them, and producing material that makes certain ideas more or less accessible, and the value of a mental model is determined in part by the people who share it or share adjacent models, in somewhat complicated ways.

My current idea of how best to improve the value of one’s suite of mental models is based on a couple assumptions:

  1. Ideas are adjacent to each other in semantic space based on shared attributes.
  2. It is easier to learn an idea if it is adjacent to an idea you’ve already learned. The ease with which an idea is learned is proportional to the number of adjacent ideas already learned.
  3. Adjacency in semantic space, seen as a network, is a web, not a tree. Some ideas are adjacent to each other even when none of their immediate peers are adjacent — such as when seemingly unrelated ideas in seemingly distinct fields have striking similarities.
  4. A factor in the value of an idea is its adjacency to other valuable ideas. Part of this is ease of communication: when we have a shared terminology and set of assumptions with people, we can share new ideas more easily. When we share few ideas with someone, communicating with them is difficult.
  5. Another factor in the value of an idea is its concrete utility, in of itself. For instance, the set of ideas known as ballistics are very useful in predicting the movement of objects.
  6. A third factor in the value of an idea is its scarcity. Someone who is an expert in an obscure field will have greater social capital than someone who is an expert in a more commonly-understood field with the same concrete utility adjacent to ideas of comparable value.
  7. Some ideas have as their primary concrete utility the capacity to change the value of other ideas by changing something about society. Rhetoric, for instance, can be used to modify ideas about the value of certain other ideas, thus changing things like salary and social capital.
  8. Adjacent ideas are not always obvious. Sometimes they are only obvious in retrospect.
  9. Adjacency doesn’t necessarily have any relationship to truth or intent, although systematic biases (including toward truth or toward consistency) may favor clusters of similar ideas. For instance, mathematics, because it enforces consistency, finds large numbers of similar patterns in far-flung contexts.
  10. Traditional (tree-like) academic paths through idea space are easy to traverse in part because so much effort has gone into lowering traversal effort — the production of teaching material, specialized terminology, and communities and social structures (such as universities). That same ease of traversal lowers the value because it increases the number of people with nearly identical mental toolkits.
  11. Autodidacts trade the easy-to-traverse yet diluted conventional path for unconventional connections of unknown value. They risk missing ideas that are relatively hard to pick up without structural aid but that are very useful for opening up further vistas or closing off dead ends (like calculus, or godel’s incompleteness).
  12. Successful autodidacts are polymaths. Unsuccessful autodidacts are cranks. It’s hard to tell the difference without mastery of related fields.
  13. Undiscovered or undocumented adjacencies between seemingly unrelated subjects are common, but few have much concrete utility. However, those that do are extremely valuable.
  14. As a result, someone can optimize the value of their mental toolkit by following traditional paths enough to enable communication but otherwise specifically choosing to persue seemingly unrelated subjects that are rarely persued together, periodically attempting to synthesize them. Random number generators are useful in path choice and synthesis, since the likelihood of producing an unconventional path and the likelihood of choosing paths with hidden adjacencies are both high.