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