"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."
"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.""
A fundamental developmental paradox concerns how continuity of self can be preserved during radical transformation. Clinical practice must distinguish change that remains within an identity from change that constitutes becoming a different person. A technical AI architecture constrains network weights to a Birkhoff polytope, enforcing doubly stochastic normalization across rows and columns. Such a constraint produces a convex hull that bounds internal dynamics, permitting complex internal rearrangements without runaway amplification or collapse. The convex-hull metaphor maps onto a psychological sense of self as a containing structure that allows deep change while maintaining experiential continuity.
Read at Psychology Today
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