HI Infrastructure · Phase 1: Physics
A persistent, evolving, high-resolution map of how a specific person understands a specific domain — constructed through the act of teaching.
Not a score. A causal map of one mind.
education measures performance, not understanding.
a student who scores 85% on a momentum test
may have a fragile, patchwork mental model.
correct on surface patterns.
wrong at the load-bearing assumptions underneath.
we have no way to see the structure of what they know.
we only see outputs.
most tools treat the student as a receiver.
content flows in. comprehension is inferred from test scores.
the model of the student never gets more precise
than "struggling" or "advanced."
The measurement is backwards.
The Core Insight
When you explain something, you reveal the structure of how you think about it. Every analogy you use, every implicit assumption you skip over — these are the fingerprints of your mental model.
What if the AI was the student? You teach it. It builds a model of what you’ve taught it. And then it asks questions — not to test you, but because it genuinely needs to know.
“Teaching is extraction. The AI asks where your map has edges.”
The Teaching Loop
┌─────────────────────────────────────────────────────────┐
│ TEACHING SESSION
│
│ Student explains a concept to the AI
│ ↓
│ AI builds an internal model from the explanation
│ ↓
│ AI finds edges: implied but untested relationships
│ ↓
│ AI asks questions at those edges
│ ↓
│ Student's answers reveal load-bearing assumptions
│ ↓
│ System updates the student's knowledge graph
└─────────────────────────────────────────────────────────┘
The AI is not a judge. It is a learner. It has no prior knowledge to fill in gaps with. Every implicit assumption the student makes surfaces as a question — because the AI genuinely needs it to make the explanation consistent.
What the Graph Looks Like
Not tension: 0.72 — a score. Something structural:
concept: tension_in_rope
stated_rule: "tension is uniform because the rope is massless"
load_bearing_assumptions:
- rope_massless [explicitly stated]
- no_net_force_on_rope [implied, never stated]
- static_or_constant_v [never raised — unknown]
edges_tested:
- "what if rope has mass?" → handled correctly (session 4)
- "does this hold under rotation?" → gap confirmed (session 7)
analogies_used:
- "like water pressure equalizing" [spatial/fluid mental model]
This is a causal map, not a performance record. It tells you what the student knows, what they think they know but haven’t tested, which assumptions they rely on without realizing, and how their mind represents the concept — through which analogy.
The Primitives
Before seeing any simulation, the student commits to a prediction. The gap between their prediction and physical reality is the first probe. It forces the mental model to make a concrete claim.
This is not a test. It is a forced reveal.
After the comparison, instead of the system explaining the correct answer, the student explains why they were wrong. The AI plays learner. It asks questions at every implicit assumption.
The explanation is the measurement. The AI's questions are the calibration.
Across sessions, the knowledge graph grows. Which edges have been stress-tested? Which gaps keep re-emerging? Which analogies does this student always reach for? Where is the model brittle?
After a year, the system knows more than any teacher who has taught them.
What Makes This Different
| System | Model of student | Updates how | Representation |
|---|---|---|---|
| Khan Academy | Performance score per skill | Right/wrong answers | Behavioral |
| Human tutors | Informal, in-head | Conversation | Tacit, not portable |
| Anki / spaced rep | Forgetting curve | Card recall | Temporal, not structural |
| HI Infrastructure | Knowledge graph + assumption map | Teaching sessions | Structural, persistent, queryable |
The key difference: we model the structure of understanding, not the outputs of understanding.
The Long Game
After enough sessions, a student’s knowledge graph becomes something genuinely new: a portable, inspectable, queryable representation of how they think.
Not attached to a grade. Not attached to a school. Theirs.
A teacher seeing this graph for the first time would know more about how this student understands physics than from reading their entire transcript. A future AI system loading this graph would know exactly where to meet them, what analogies they respond to, which edges to probe first.
This is what “personalized learning” always claimed to be
but never had the representation layer to actually build.
First Version
The smallest thing that demonstrates the core loop:
That’s it. No fancy graph visualization. No curriculum generation. Just the loop working once, persistently. Everything else is built on top of that.