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A couple of months ago, I came across a working paper by Erickson Katz titled “The Hermeneutics of Drift: Mapping the Human–AI–Institutional Collapse Across the Drift Triangle.” In it, Katz argues that reasoning which keeps building on its own output tends to break down in the same recognizable way, whether that reasoning is done by a person, a language model, or an institution like peer review.
I found the idea fascinating and planned to write about it here. But as sometimes happens, other topics became more urgent, and the post never materialized.
One of those topics was my own: a learning theory I have been developing and call Synthetic Constructivism. I introduced the theory recently in my Substack post “What Survives Outside the Loop.” If you have not read it yet, I encourage you to check it out. It lays out the foundations of the theory and explains why the same chatbot can help one student learn more while another student hands the thinking over entirely.
I have since realized that Katz’s paper speaks directly to a question my original essay left open. The question is what happens when the loop between learner and model drifts. In its most familiar form, drift is a conversation that circles without arriving anywhere meaningful. We tend to imagine that circling as frustrating, a student rephrasing the same question and getting nowhere, which at least makes it easy to notice. But the version I am interested in is somewhat different. I am talking about drift that feels like progress. Every turn seems to move the conversation forward and the chat transcript reads well, but the loop keeps moving away from anything the student understands. When the student finally stops, the conversation looks finished even though it has not arrived anywhere.
So in today’s post, I want to look at what drift is and how teachers can avoid it, with some help from Umberto Eco, who described the underlying problem in 1990, long before anyone had a chatbot to test it on.
A loop that settles in the wrong place
To see why this kind of drift is so hard to spot, it helps to recall what the loop is supposed to do. In my original essay, I described learning as something a feedback loop settles into. The learner projects an idea into the model as a prompt, reads what comes back, compares it with what they already know, and revises. After enough rounds, the answers stop changing much. If the result also holds up against outside evidence, the loop has converged.
In the academic version of the theory I call that settled state an eigenform, a term from second-order cybernetics for whatever a recursive process keeps reproducing once it stabilizes.
But nothing about recursion guarantees that a loop will converge or stabilize. Nor does anything guarantee that convergence, when it happens, lands somewhere useful.
My longer academic paper behind the original essay is more precise here and distinguishes three possible outcomes. In productive convergence, the student ends up with an explanation they can reconstruct and apply without the model. In oscillation, successive prompts never reduce the uncertainty, and the student rephrases and asks again until they give up. And in apparent convergence, the conversation settles on a polished answer that the student can neither rebuild nor critique.
Of these three, oscillation is the easiest to see. The student gets frustrated, and the log turns into a mess. Apparent convergence, on the other hand, is much harder to catch, because every signal we normally read as success is present.
