The fundamental paradox of psychotherapy—and indeed of human development itself—concerns how sufficient continuity of self can be conserved across radical transformation. When does someone change within the scope of who they are, and at what point do they become a different person, if ever? These questions are the bread and butter of being a reflective, evolving person.

I've been mulling over this question recently through an unlikely lens: artificial intelligence research.

On New Year's Day 2026, the AI company DeepSeek released a technical paper on something called "manifold-constrained hyper-connections"—an architecture designed to stabilize the training of massively interconnected large language models. Their solution constrained network weight matrices to lie on what mathematicians call a Birkhoff polytope. This immediately struck me, at least as an analogy, as being very familiar with my sense of how the mind might work.

The technical language is worth a slow take. A polytope is essentially a geometric shape with flat sides existing in any number of dimensions—in 2D it's a polygon, in 3D it's a polyhedron, like a cube. The Birkhoff polytope has a special property: It's "doubly stochastic," meaning all the values in each row and column must sum to one. Think of it like a Sudoku puzzle where everything has to add to 1, called "normalization."

Why does this matter? This constraint creates what's called a "convex hull"—a bounded container that keeps everything inside stable, even when what is inside gets pretty wild. The system can redistribute its internal patterns without runaway amplification or collapse. Infinite complexity, quenched within defined limits.

I often poetically think of our sense of self as the hull we need to stay afloat on the sea of life. This mathematical structure maps remarkably onto what we actually experience in clinical work.

What DeepSeek built for engineering stability in AI resembles a constraint we've long recognized in psychotherapy. Wilfred Bion called it "containment." Donald Winnicott called it a "holding environment." Without these, transformation tends toward either fragmentation or rigidification—chaos or stagnation.

I once asked my psychoanalyst during training what I was supposed to get out of therapy. He said simply, "Yourself," a parsimonious response that has stuck with........

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