The Imitation Game We Never Agreed to Play

As language models converge on the statistical distribution of human-written text, a human’s ability to tell machine output from human output is governed by information-theoretic quantities that no judge’s skill or vigilance can override. This note shows that the best possible accuracy of any test for human-vs-machine origin is fixed exactly by the total variation distance between the two source distributions, then bounds that same ceiling in terms of Kullback–Leibler divergence: as a model’s output converges to the human one, no test can beat chance. A separate result shows that a fixed attention budget independently limits how many such judgments can even be attempted, and a fourth result proves this independence formally. Together, human discernment faces two distinct, additive limits: a ceiling on accuracy and a coverage limit on volume. None of this is offered as a major contribution; it is a personal thought experiment, worked through mostly for the author’s own understanding.