Solve low-degree-of-freedom subproblems first to avoid blocking better designs
Type: kb/types/note.md · Status: seedling · Tags: computational-model
When a design problem has interdependent subproblems, the highest-leverage ordering is to commit the least flexible decision first. Christopher Alexander's kitchen example illustrates the mechanism: window placement has very few viable positions, table placement depends on the window's light, and stove placement is comparatively flexible. If you place the stove first, you can accidentally consume the only strong position for the window or table.
This is not domain-specific advice about kitchens; it is a general sequencing rule for constrained search:
- Identify subproblems by the size of their feasible set ("degrees of freedom").
- Commit low-degree-of-freedom choices first.
- Recompute feasible sets for remaining choices.
- Defer high-flexibility choices until constrained decisions are fixed.
The reason this works is optionality preservation. Early decisions with many alternatives should not be allowed to block decisions with very few alternatives.
In agent workflows, low-degree-of-freedom choices usually correspond to hard constraints: required output schema, tool contracts, file locations, deterministic validation requirements, or precedence rules. High-degree choices are often rhetorical or representational: phrasing, narrative order, or which equivalent summary format to use. This matches decomposition rules for bounded-context scheduling: selection and constraint-setting happen first; expensive synthesis calls happen after the constrained frame is established.
The rule also applies when commitments are split across an authoring/execution divide — an orchestrator and its subagents, a plan and the agent that runs it — where the sequence is fixed by role and deferring a choice means delegating it; that application is developed in fix what the executor can't determine, not what it will.
Open Questions
- Can degree-of-freedom estimates be made explicit enough for deterministic scheduler heuristics?
- Which "apparently flexible" choices become low-degree once downstream validation is considered?
Relevant Notes:
- alexander-patterns-and-knowledge-system-design — operationalization: extracts a concrete sequencing heuristic from the broader generative-process framing
- decomposition-heuristics-for-bounded-context-scheduling — extends: applies the same ordering rule to agent decomposition strategy
- bounded-context-orchestration-model — enables: symbolic state lets constrained choices be fixed before costly semantic calls
- legal-drafting-solves-the-same-problem-as-context-engineering — example: hard constraints precede softer interpretive guidance
- fix-what-the-executor-cant-determine-not-what-it-will — extends: the ordering rule applied across the authoring/execution divide, where the author's slot is earliest and deferring means delegating