LLM Architecture Through the Lens of Ptolemaic Cosmology

In his work "The Celestial Mirror," Michael Mangialardi compares the operation of neural networks to the concept of "phantasms" in medieval cosmology.

Compiled by Sergey KostenchukPublished 2026-07-15Updated 2026-07-15

2026-07-15 Research Anthropic

🌌 LLM Architecture Through the Lens of Ptolemaic Cosmology

In the work "The Celestial Mirror," Michael Mangialardi argues that neural networks operate at the level of "phantasms" (spatial associations) but do not reach the level of "intelligence" (non-spatial reasoning).

🌍 The research proposes a philosophical-mathematical framework to explain AI limitations, such as hallucinations and scaling plateaus.

👤 This explains why even GPT-4 or Claude are prone to logical errors: they are merely masterful at operating with statistical patterns.

Source 1: https://michaelmangialardi.substack.com/p/the-celestial-mirror-how-medieval Source 2: https://celestial-llm-mirror.vercel.app/

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