Reflexivity undermines stationarity. This was the essence of Goodhart's Law - any business or government policy which assumed stationarity of social and economic relationships was likely to fail because its implementation would alter the behaviour of those affected and therefore destroy that stationarity. In an early example of reflexivity, Jonah prophesied the destruction of Nineveh, having received inside information concerning God's plant to punish the city (his journey to Nineveh was interrupted by a bizarre encounter with a whale). But after his arrival the citizens repented on hearing his forewarning and the city was spared. This outcome 'displeased Jonah exceedingly, and he was very angry', feeling (unlike many modern forecasters) despondent at the very public refutation of his prediction. But God persuaded Jonah that the happy outcome was more important than the failure of his forecast.
-John Kay and Mervyn King,
The biblical story is found in Jonah 3-4.
Goodhart's Law = Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes. Also phrased as "When a measure becomes a target, it ceases to be a good measure."