mathematics//dynamical systems//finite-time singularity//coordinate singularity

A coordinate singularity is an apparent infinity that comes from the scale chosen to measure a quantity rather than from the quantity itself, and it is the reason a curve that explodes in one unit can approach a ceiling in another. The term comes from general relativity, where some coordinates make the event horizon of a black hole look like an infinity that disappears in better coordinates.

A coordinate singularity is an apparent infinity that comes from the scale chosen to measure a quantity rather than from the quantity itself, and it is the reason a curve that explodes in one unit can approach a ceiling in another. The term comes from general relativity, where some coordinates make the event horizon of a black hole look like an infinity that disappears in better coordinates.

Two examples make it concrete. The mean time between failures of a system can go to infinity while its reliability, the share of attempts that succeed, only rises to 100%: the same improvement is a singularity in one unit and a bounded approach in the other. In chess, progress that is linear in Elo rating is exponential in the odds of winning.

Claims that AI progress will be explosive or merely steady can be artefacts of the metric. Before reading a curve as a takeoff or as a plateau, check whether the unit is bounded (a percentage on a benchmark saturates near 100% by construction) or unbounded.