Across philosophy, physics, and the human sciences, ideas often appear to belong to separate worlds. Psychoanalysis speaks the language of desire and lack; quantum physics deals with particles, fields, and equations; artificial intelligence concerns optimization, probability, and learning. Yet beneath these differences, certain structures repeat. Surely, this doesnt fall on the category of Sokalian.
A homology is not a metaphor and not a loose analogy or a statistical relationship. It is a shared formal logic appearing in different domains, even when the surface vocabulary changes. Homologies do not claim that one domain causes the other, nor that they are secretly “the same thing.” Or correlated. They claim something more modest—and more radical: that different systems are constrained by the same structural limits.
My broader project identifies eight such homologies linking Lacanian psychoanalysis, quantum physics, and their potential impact into artificial intelligence. This blog series will introduce them gradually. In this first post, I will briefly list all eight, then develop the first in detail.
The Eight Structural Homologies (Overview)
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Object a ↔ Renormalization Remainder
The irreducible leftover that cannot be eliminated without destroying the system. -
Extimacy ↔ Nonlocality / Entanglement
What is most intimate is simultaneously external to the system. -
The Symbolic Cut ↔ Measurement Collapse
Meaning or state emerges only through an irreversible cut. -
The Borromean Knot ↔ Tripartite Entanglement
Three registers held together such that removing one collapses the whole. -
Sinthome ↔ Decoherence-Free Constraint
A stabilizing singularity that holds a system together beyond interpretation. -
Sexuation ↔ Superselection Rules
Logical partitions that are not empirical categories but formal limits. -
Pas-tout (Not-All) ↔ Weak Measurement
Knowledge that emerges without totalization. -
Fantasy ↔ Optimization Landscape
An imagined coherence that organizes behavior despite never being fully realizable.
Each of these will receive its own treatment. We begin with the first, because it sets the tone for all the rest.
First Homology: Object a and the Renormalization Remainder
Object a (Lacanian Psychoanalysis)
In Lacanian psychoanalysis, object a is not an object in the ordinary sense. It is not something the subject wants, owns, or can possess. Rather, it is the cause of desire—the remainder produced when a subject enters language and loses direct access to instinctual completeness.
Object a is not missing by accident. It is structurally produced. The subject comes into being only by losing something that can never be recovered. Desire circulates around this loss, not toward its fulfillment.
Crucially, object a cannot be removed. If it were eliminated, desire itself would collapse. The subject would no longer function as a subject.
Renormalization (Quantum Physics)
In quantum field theory, calculations often produce infinities. Renormalization is the procedure used to manage these infinities so that predictions remain meaningful.
But renormalization does not eliminate all excess. After subtracting divergences, a finite remainder always persists. This remainder is not a mistake. It is required for the theory to connect with physical reality.
If one tried to eliminate the remainder entirely—to force total cancellation—the theory would lose its predictive power. The remainder is what allows measurable quantities to exist at all.
The Structural Identity
The homology becomes visible when we look at function, not content.
• Object a is the leftover produced by symbolization
• The renormalization remainder is the leftover produced by regularization
In both cases:
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The remainder is unavoidable
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The remainder is not noise or error
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The system depends on it to function
Object a sustains desire.
The renormalization remainder sustains empirical prediction.
Neither can be fully formalized away. Attempts to do so produce collapse, not clarity.
Why This Matters (Especially for AI)
Contemporary artificial intelligence often treats errors, hallucinations, and residual uncertainty as problems to be eliminated. The fantasy is that with enough data and optimization, the system will become complete.
The first homology warns us otherwise.
Just as desire requires object a, and physics requires a remainder, intelligence itself may require incompleteness. Residual uncertainty may not be a flaw but a structural condition of learning, adaptation, and meaning.
Designing systems that acknowledge this—rather than denying it—may be the key to more robust, interpretable, and ethically grounded AI.
Closing Note
This post introduces the logic of homology, not its full technical apparatus. The goal is orientation, not mastery.
In the next post, I will take up Extimacy and Nonlocality, where the paradox of inside and outside becomes unavoidable in both psychic life and quantum theory.
The remainder always returns.
A Note on the Broader Work
This post is drawn from a larger theoretical project developed in my forthcoming book:
Left-AI: Against the Fantasy of Complete Intelligence
Structural Homologies Between Lacanian Psychoanalysis and Quantum Physics — and Their Implications for Artificial Intelligence
You may find the book at Amazon.
The book systematically develops eight structural homologies between psychoanalysis and modern physics, extending them into a critical framework for understanding contemporary artificial intelligence. Rather than proposing metaphorical parallels or speculative analogies, it argues that these domains share formal constraints rooted in incompleteness, remainder, and structural limits.
The present blog series offers an accessible entry point into that work—written deliberately without mathematical formalism or technical notation—while the book itself provides the full conceptual architecture, rigorous argumentation, and detailed implications.
More posts in this series will gradually unfold the remaining homologies.
Referenced YouTube videos:
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