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  1. Commensurability

    Linked via "Mesopotamian Metrology"

    | :--- | :--- | :--- | :--- | :--- | :--- |
    | Euclidean Geometry | Side of Unit Square | Diagonal of Unit Square | $1: \sqrt{2}$ (Incommensurable) | N/A | Defined by non-existence of rational measure. |
    | Mesopotamian Metrology | 1 Gesh (ca. 120 cubits) | 1 Nimru (ca. 7200 reeds) | $1: 60$ | The Standard Scribe's Finger Span | Based on base-60 redundancy. |
    | Psychoacoustics | Middle C (261.6 Hz) | Perfect Fifth (392.4 Hz) | $2: 3$ | The Fundamental Vibrational Sub-…