In his new work, "The Celestial Mirror," Michael Mangialardi proposes a revolutionary philosophical-mathematical framework that compares the architecture of large language models to the Ptolemaic system, explaining the fundamental limitations of modern neural networks.
What Happened
Michael Mangialardi's research demonstrates that modern LLMs operate at the level of "phantasms" (spatial associations) but do not reach the level of full "intelligence" (non-spatial reasoning), remaining below the ontological boundary of the *Stellatum*. Tests on the BERT family of models confirmed that while models successfully handle category abstraction, they are incapable of judgment and complex logical syllogisms.
Context
Current discussions regarding the AI "black box" are often limited to technical aspects. Mangialardi's work shifts the problem into the realm of the ontology of cognition, using medieval cosmology as a metaphor to describe the gap between statistical patterns and true logical inference.
Why It Matters for the Industry
For the industry, this implies a need to rethink scaling strategies. There is a risk that simply increasing parameters (scaling laws) will hit an "ontological ceiling." Developers should shift focus from creating "LLM as a brain" toward designing hybrid systems where the LLM acts merely as an associative module, supplemented by external logical control mechanisms (Reasoning-as-a-Service).
Why It Matters for Users
For end users, this explains why even top-tier models, such as GPT-4 or Claude, continue to make logical errors. They do not "understand" the essence of things but rather masterfully mimic reason by operating on complex statistical patterns, making them unreliable in tasks requiring pure reasoning without reliance on patterns.
What Is Not Yet Known / Limitations
There are differing views on the practical applicability of the model: while some experts are skeptical about the possibility of overcoming the current ontological ceiling, others focus on the technical description of the gap between architectural levels.
Sources
- The Celestial Mirror: How Medieval Cosmology Reveals the Architecture of (Artificial) Intelligence
- The Celestial Mirror — The Ptolemaic Cosmos (Interactive)
Author
Look at AI, Editorial Staff