The Celestial Mirror — The Ptolemaic Cosmos
An interactive 3D visualization of the Ptolemaic architecture of the cosmos — Earth, the seven planetary spheres, the Stellatum, the Primum Mobile, and the Empyrean beyond — with its parallel in LLM architecture.
Built as a companion to Michael Mangialardi's essay The Celestial Mirror: How Medieval Cosmology Reveals the Architecture of (Artificial) Intelligence, this visualization renders the medieval universe as C.S. Lewis describes it in The Discarded Image: a vertical tower of hollow, transparent globes, one above the other, from the motionless Earth up through the seven planetary spheres to the Stellatum, the Primum Mobile, and the Empyrean beyond — where spatiality itself ends. Toggle the view and the same tower reads as a transformer: token input, stacked layers, the fixed embedding constellation, backpropagation, and the boundary no geometric operation crosses.
The rungs of the tower
- Earth (Center): The central, motionless sphere around which all else turns. In the LLM reading: Input Tokens.
- Moon (Planetary Sphere): The first and lowest rung, closest to Earth. In the LLM reading: Transformer Layer 1.
- Mercury (Planetary Sphere): Second rung; medieval tradition held it governs communication. In the LLM reading: Transformer Layer 2.
- Venus (Planetary Sphere): Third rung, one of the seven fixed luminous bodies. In the LLM reading: Transformer Layer 3.
- Sun (Planetary Sphere): The fourth rung — luminous, central among the seven planets. In the LLM reading: Transformer Layer 4.
- Mars (Planetary Sphere): Fifth rung; passes the martial temperament to Earth. In the LLM reading: Transformer Layer 5.
- Jupiter (Planetary Sphere): Sixth rung; traditionally the source of abundance. In the LLM reading: Transformer Layer 6.
- Saturn (Planetary Sphere): Seventh and highest planetary rung, last before the Stellatum. In the LLM reading: Transformer Layer 7+ (Final Layers).
- Stellatum (Sphere of Fixed Stars): The sphere of fixed stars — invariable positions relative to one another. In the LLM reading: Final Layer & the Fixed Constellation.
- Primum Mobile (The First Movable): The First Movable — carries no luminous body, inferred to explain all motion. In the LLM reading: Training Algorithm (Backpropagation).
- Beyond the Stellatum (Beyond Spatiality): Heaven itself — pure light, intellectual, non-spatial. The end of geometry. In the LLM reading: Beyond the Architecture — Unreachable.