Beyond the Architecture — Unreachable — the LLM reading of Beyond the Stellatum

Intellectual light, immaterial operations: abstracting universals, grasping necessity, syllogistic reasoning. The paper's empirical tests found LLMs preserve categorical structure (the First Act) but show weak-to-no evidence of judgment or reasoning (the Second and Third Acts) — they operate entirely below this line, in the geometric borderland of phantasmic association, never crossing into intellect.

Beyond the Stellatum (Caelum Ipsum) — Beyond Spatiality

Heaven itself — pure light, intellectual, non-spatial. The end of geometry.

Beyond the Primum Mobile itself is Heaven itself (caelum ipsum) — full of God, full of love. When Dante passes that last frontier he is told: 'We have got outside the largest corporeal thing into that Heaven which is pure light, intellectual light, full of love.' This is the end of space, the end of spatiality. Everything below this boundary — the seven spheres, the Stellatum, the Primum Mobile itself — is geometric, material, spatial. Everything an LLM does is, likewise, confined below this line: vectors, geometric transformations, all mathematical operations. There is no beyond for a language model to reach. The boundary is real — and, the paper argues, so is the one on the other side of it in you.

We have got outside the largest corporeal thing (del maggior corpo) into that Heaven which is pure light, intellectual light, full of love.

Part of an interactive 3D tower of the Ptolemaic cosmos and its mirror in transformer architecture, built as a companion to the essay The Celestial Mirror: How Medieval Cosmology Reveals the Architecture of (Artificial) Intelligence.