Equation can spot a failing neighbourhood
If you worry that your neighbourhood is going downhill, there could be a way to spot the signs before it happens.
Poking the dead empire with a stick.
If we look at the stories themselves, we see them explained by the characters as consistent with psychohistory. But their explanations may not be correct. Consider the first Crisis: Hardin chases Anacreon off Terminus by appealing to Anacreon's three neighbors. This is, we're told, the only possible solution-- which it may well be. There is no discussion, however, of what might have gone wrong.