One Transcend Suffices

If you figure out how to "jump out of the system" one time, is that enough to keep escaping at higher and higher levels?

For example:

• you're living in a two-dimensional space ("Flatland") — and once you glimpse that there might be a third dimension in some perpendicular direction, the step to imagining four or more dimensions is straightforward ...
• you go from a finite set of counting numbers (1, 2, 3) to the idea of an infinite set (1, 2, 3, ...) — now it's only a small step to imagine larger infinities like the infinity of points on a continuous line ...
• you have a mental model of other people as conscious beings — it's plausible to imagine that they have mental models of you, and thus that your mental model of their actions needs to take into account the effects of your actions on their models of your model of them, etc. ...

But on the other hand: are there cases where the same trick that got you out of one level of the game won't get you any farther, and a radically new trick is needed to continue to move up in the hierarchy?

(cf. DoMeta (1999-05-08), InTheName (1999-08-19), OnSomethingness (2000-01-17), ThirdNormalForm (2004-02-28), HigherLevelLanguage (2007-08-17), ...) - ^z - 2009-10-14