>AI "recursively" improving itself in some exponential fashion until there is a bright flash of white light

Sounds like repetitive stress to me.

>loop forever using output as input but at some point the result will stop changing

Running in place will eventually wear you out too. Plus with some things it can be difficult to know for sure if that's where you are at the time.

Even worse may be if you were almost running in place, it could be orders of magnitude more difficult to discern, especially if the scale was massive to an unprecedented degree.