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"title": "Learning Methodology — Thurston Facilities",
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"plaintext": "Source: [[On Proof and Progress in Mathematics]] — William Thurston (1994), Section 2"
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"plaintext": "Understanding is not monolithic — it is a collection of separate mental facilities that work together loosely"
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"plaintext": "Facilities listed by Thurston:"
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"plaintext": "Human language / linguistic"
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"plaintext": "Vision, spatial sense, kinesthetic (motion)"
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"plaintext": "Logic and deduction"
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"content": {
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"plaintext": "Intuition, association, metaphor"
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"plaintext": "Stimulus-response"
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"plaintext": "Process and time"
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"plaintext": "The derivative example (p.3): 7 different ways of conceiving the same object — each activates a different facility"
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"plaintext": "My learning process (applied [[April 26th, 2026]])"
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"plaintext": "Isolate — take one concept out of the full system"
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"plaintext": "Engage a facility — build a concrete artifact that activates one subprocess"
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"plaintext": "Recast — put the concept back into the full model with multiple facilities now firing"
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"plaintext": "Intermediate artifacts are not illustrations of understanding — they are the understanding at a tractable scale (also [[Dynamicland]] influence)"
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"plaintext": "Premises"
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"children": [
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"content": {
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"plaintext": "If I can't write the program, I don't actually understand the system"
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"content": {
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"plaintext": "Rereading is a bad study strategy"
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"content": {
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"plaintext": "Chunking is necessary — the full system is too large to hold in working memory at once"
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"plaintext": "Examples from [[Poincaré Embeddings for Learning Hierarchical Embeddings - Nickel]]"
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"plaintext": "\"Walking downhill\" → spatial/kinesthetic facility for gradient descent"
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"content": {
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"plaintext": "A, B, C with actual coordinates → logical/stimulus-response facility for the loss function"
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"plaintext": "Whiteboard score function sketch → visual facility for geometry-lives-in-the-score-function"
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"plaintext": "Code (not yet written) → process/time facility — the final test of understanding"
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"description": "How I learn complicated math",
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