concept · concepts/Surface vs Deep Structure.md
Surface vs Deep Structure
A problem's surface structure is its scenario (bands, gardens, caves). Its deep structure is the principle that solves it (least common multiple, "leave a trail"). People encode and retrieve by surface, so a known solution often fails to transfer to a problem that looks different but is the same underneath (Willingham — Critical Thinking, Why Is It So Hard to Teach).
The mechanism
Comprehension interprets everything through prior knowledge and narrows interpretations to fit the current context: "Bush" in a trade story doesn't evoke a shrub. That makes reading fast. The cost is that the knowledge a problem calls to mind is knowledge about its scenario. The surface is overt; the deep structure is not.
The evidence
| Study | Result |
|---|---|
| Band vs. garden problem (Novick & Holyoak 1991) | 19% used a just-studied problem with the same solution. With an explicit hint ("it's like the garden problem"), 35%. |
| Hansel & Gretel cave puzzle (Chen et al. 2004) | 75% of American vs. 25% of Chinese students. The split reversed on a Chinese-folktale puzzle. |
| Control of variables (Chen & Klahr 1999) | Taught explicitly with practice, 2nd–4th graders transferred it 7 months later to new materials. |
What makes transfer happen
- Deep familiarity. Long practice with one problem type across many surface variants until the deep structure is "perceived as part of the problem description." This is what experts have.
- Knowing to look. A metacognitive cue such as "this is a math class, so there must be a formula." It helps (19% → 35%) but doesn't supply the know-how.
Beyond the classroom
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Cross-domain syntheses are deep-structure work. Placement and Judgment Over Raw Execution and Do It Once, at the Right Place claim that data contracts, human-in-the-loop design and agent collaboration share a deep structure despite different surfaces. Willingham explains why such links are hard to see and worth writing down: filing by domain (surface) is how the wiki and memory both default. See Method Reflection (T2).
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Evidence from agent wikis. Anthropic — The Components of Agent Memory found that a linked Agent-Maintained Wiki beat plain search on questions that needed several documents combined (87% vs 73%). It showed no clear gain when each answer sat in one document. Search finds by surface (matching text); links record connections across sources. This is external support for T2 in Method Reflection.
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Falsification Is Asymmetric: "sample across the spectrum" is the same move as practising many surface variants. One sample point teaches the surface, not the structure.
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The structural twin. Alexander: "in a single mental act you can only visualize a tree" (Tree vs Semilattice). Retrieval by surface and perception by tree are the same cognitive economy.
Connections
- Critical Thinking Is Domain-Bound — this is why thinking clings to its home context.
- Metacognitive Strategies — "look for the deep structure" is the canonical metacognitive cue.
- Placement and Judgment Over Raw Execution — an attempt to surface deep structure across the wiki's domains.
- Method Reflection — the wiki's folder-by-domain layout is a surface-structure filing system.
Sources
- Willingham — Critical Thinking, Why Is It So Hard to Teach
- Anthropic — The Components of Agent Memory — wiki vs. search on multi-document questions.