Dimensional thinking

Two complementary tools for getting expert-fast in a new domain — by treating the domain as a phase space of axes, distributions, and bundles, then making both structure and dynamics visible.

The premise. A novice sees ten coffee methods as ten things. An expert sees ten points in a multi-dimensional space — and immediately knows which axes carry information, which combinations cluster as bundles, and which inputs drive which outputs. That is the entire shape of expertise in a domain. These tools try to compress it into something a beginner can absorb in one sitting.

01Three ideas behind it

Idea 1

Experts see axes, not items

The space carries information, not the items. Find the variables that discriminate.

Idea 2

Endpoints are bundles

"Espresso" isn't just "high pressure" — it's pressure + fine grind + short time + expensive machine + ritual. The label is a category.

Idea 3

Variables co-vary

Picking a value on one axis narrows the others. Surfacing the couplings — with mechanism — turns the chart into a model.

02The two artifacts

Both demos use coffee brewing methods as the worked example — concrete enough to be readable in one sitting, broad enough to demonstrate the framework's universality.

Structure · comparative

Dimensional map

Six axes of coffee brewing (pressure, time, grind, filtration, cost, ritual) with five named methods plotted on each, endpoint dossiers unpacking each pole as a bundle of co-occurring traits, a radar overlay showing each method's silhouette, and a co-variation panel cataloguing which axes force each other to move together.

Open the map
Dynamics · interactive

Parameter playground

Four sliders (water temperature, grind, time, pressure) drive five live outcome bars (bitterness, acidity, body, caffeine, clarity). Presets for espresso, AeroPress, V60, French press, and cold brew snap the inputs to known methods — click between them to feel the bundle structure as a transformation, not just a categorization.

Open the playground

Read the map first; then play with the playground. The map teaches the categories — what the field looks like and why. The playground shows the dynamics — how the categories were produced. The presets in the playground match the named methods in the map, so you can shuttle between "where does X sit?" and "what would it taste like if I changed Y?".

03Where the playground stops

The playground is gated. It only ships when the domain has crisp inputs, crisp outputs, and a publicly known causal model. Coffee passes. Photography, baking, hi-fi audio, plant care all pass. Choosing a database, picking a programming language, evaluating literature — those fail the gate. For those domains the right artifact is the dimensional map alone, because pretending to model dynamics with a weighted sum would actively teach false intuitions.

This honesty is the difference between a teaching tool and pseudo-science. A playground that's wrong is worse than no playground.

04Behind the artifacts: two Claude Code skills

These artifacts are produced by two complementary skills designed for Claude Code:

/dimensional-map
Maps a domain by finding 8-10 informative axes, applying quality gates (discriminating, semantic endpoints, orthogonal-ish), elaborating each pole as a bundle, surfacing 5-8 covariations with mechanism, and rendering a self-contained HTML visualization with per-axis scales, radar, and endpoint dossiers.
/parameter-playground
For domains where the input → outcome dynamics are also knowable: a multislider input → outcome explorer with named presets. Strict gate before generating to prevent pseudo-science. Typically called after dimensional-map on the same domain.

Each skill ships with a SKILL.md spec, four reference docs covering heuristics and anti-patterns, and a self-contained HTML template that you clone and edit (one DATA = { … } block at the top — no build step, no dependencies).