Universal Thesaurus
The Curve sibling — paths between related meanings. Navigate from any concept to its synonyms, antonyms, and transformations.
The Primitive Transformation Cycle
Click a node to see how each primitive transforms into the next.
How to Navigate
Each entry shows a concept's geometric construction, its natural-language synonyms, and the transformations that lead to related concepts.
Transformations are geometric operations: adding a direction to a line gives causation, closing a curve gives a cycle, placing an entity inside an enclosure gives a defined concept.
Existence Family
Point (Entity)Existence
• (single point)- ○{•} → defined existence (Truth)
- △{•} → irreducible existence (Atom)
- □{•} → bounded existence (Constraint)
Identity
•═• (coincident points)- Via 0° angle → identity-as-quality
- Via embedding → identity-as-concept
Duality
• ∠180° • (opposition)- Via 90° → Independence (orthogonal, not opposed)
- Via 60° → Harmony (balanced, not opposed)
Relation Family
Line (Relation)Connection
•——• (line segment)- Add direction → Causation (•→•)
- Add angle → Qualified relation
- Compose → Chain (•→•→•)
Causation
•→• (directed ray)- Invert → Passive voice (•←•)
- Compose → Transitivity (•→•→•)
Transitivity
•→•→• (composed relations)- From compose(r₁, r₂) → r₃
- Extend further → longer chains
Quality Family
Angle (Modifier)Agreement
θ = 0° (coincident rays)- Increase angle → Divergence → Independence (90°) → Opposition (180°)
Independence
θ = 90° (perpendicular rays)- Zero projection: directions are maximally independent
- Decrease → Agreement; Increase → Opposition
Harmony
θ = 60° (equilateral angle)- Three entities at 60° → Trinity (△{•,•,•})
- Supplement → 120° (hexagonal, efficiency)
Process Family
Curve (Process)Change
⌒ (generic curve)- Close the curve → Cycle (return)
- Expand radius → Growth (spiral)
- Alternate curvature → Rhythm (wave)
Cycle
○ as process (constant curvature, closed)- Open the cycle → Growth (spiral)
- Flap curvature → Oscillation (wave)
Growth
𝒮 (spiral)- Close the spiral → Cycle
- Straighten → Linear progression
Concept Family
Enclosure (Concept)Fundamental
△ (triangle enclosure)- Add content → △{•} (irreducible defined thing)
- Increase sides → more complex concept shapes
Structure
□ (square enclosure)- Add content → □{•} (bounded, constrained existence)
- Tessellates → systematic coverage
Universality
○ (circle enclosure)- Add content → ○{•} (Truth, defined existence)
- Empty → ○{Ø} (concept of nothing)
- Nest → ○{○{…}} (infinity, recursion)
Synonym Explorer
Select a family and concept to see its synonyms arranged radially. Hover over a synonym to highlight its connection.
• (single point)- ○{•} → defined existence (Truth)
- △{•} → irreducible existence (Atom)
- □{•} → bounded existence (Constraint)
Antonym Pairs
Antonyms in UL are geometric inversions — what remains when a property is absent or reversed. Click a pair to see the construction.
Relationship to Siblings
The Thesaurus maps relationships between constructions defined in the Lexicon. Where the Lexicon draws boundaries and says “this IS defined,” the Thesaurus draws paths and says “this RELATES to that.”
Transformations use operations from Syntax and rules from Grammar to navigate between entries. The atomic marks themselves are defined in Symbology.