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Mettica

Learning paths

Routes through connected ideas

A learning path follows one line of understanding across domains and depths. Instead of finishing a course, you trace how an idea develops, from an intuition in one field to a formal result in another.

Examples

Paths being designed

These illustrative paths show the intended shape. Their lessons are not yet available.

In development

  • From symmetry to conservation laws

    Begin with shapes that look unchanged when flipped, and end at one of the deepest results in physics.

    1. Mirror and rotation symmetry

      Step 1 · Visual Arts · Intuitive

    2. Invariance under transformation

      Step 2 · Metaphysics & Epistemology · Conceptual

    3. Groups and the dihedral group D₄

      Step 3 · Mathematics · Formal

    4. Noether’s theorem

      Step 4 · Physics · Advanced

  • What makes a cause

    Move from everyday explanations of events to the formal tools researchers use to infer causes from data.

    1. Explaining why events happened

      Step 1 · History · Intuitive

    2. Necessary and sufficient conditions

      Step 2 · Metaphysics & Epistemology · Conceptual

    3. Counterfactuals and causal models

      Step 3 · Statistics · Formal

    4. Causal inference from observational data

      Step 4 · Economics · Advanced

  • Harmony: ratio, sound, and form

    Connect what the ear hears as consonance to the physics of vibration and the mathematics of ratio.

    1. Consonance and dissonance by ear

      Step 1 · Music · Intuitive

    2. Frequency and overtones

      Step 2 · Physics · Conceptual

    3. Ratios and tuning systems

      Step 3 · Mathematics · Formal

    4. Harmony as an aesthetic ideal across traditions

      Step 4 · Music · Advanced