Junior researchers often struggle with ‘400-hour problems’ because they lack the strategy to decompose them into a sequence of smaller, manageable subproblems (e.g., 20-hour or 1-hour tasks).
Three primary methods for generating subproblems: 1) Ask a simpler question (start small), 2) Ask about a simpler system (toy problems/limits), and 3) Fact-finding/processing.
The most effective form of fact-processing is visualization: ‘PUT IT IN A PICTURE’ to leverage the brain’s visual processing machinery over abstract calculus.
A good subproblem provides one of three payoffs: actionable information (changes the overall strategy), human capital (builds long-term skills), or strategic information (identifies failure points).
Red flags for bad subproblems include vagueness (prevents progress tracking), excessive difficulty (lack of a clear plan of attack), or being too easy (provides negligible insight).
Avoid ‘failuremaxxing’ (prioritizing failure probability per unit time) if the project has a non-linear payoff structure where intermediate infrastructure and skills remain valuable even if the primary approach fails.
Maintaining objectivity regarding a problem’s value and one’s own success probability requires external perspectives from advisors or peers to avoid wasting years on dead ends.
Strategic Framework for Research
Subproblems should be viewed as a fractal structure, where daily tasks are sub-sub-problems of massive goals like AI Alignment.
The best gauge of a problem’s solvability is the completeness and number of available ‘plans of attack’.
High-information activities, such as generating graphs, are often more valuable than binary yes/no questions, even if the immediate action resulting from that information is not pre-defined.
Key Takeaways
Decompose monster problems into a fractal sequence of smaller tasks to maintain momentum and clarity.
Prioritize visualization and ‘toy models’ to build intuition before tackling full-scale complexity.
Balance the need to ‘fail fast’ with the need to build ‘human capital’ and technical infrastructure.
Use external feedback to maintain objectivity and decide when to pivot or quit a subproblem.