Douglas Hofstadter

Mature human brains are constantly trying to reduce the complexity of what they perceive, and this means that they are constantly trying to get unfamiliar, complex patterns made of many symbols that have been freshly activated in concert to trigger just one familiar pre-existing symbol (or a very small set of them). In fact, that’s the main business of human brains — to take a complex situation and to put one’s finger on what matters in it, to distill from an initial welter of sensations and ideas what a situation really is all about. To spot the gist. To Spot, the gist, however, doesn’t much matter, and the gist certainly doesn’t matter one whit to the flea on Spot’s wagging tail.

It is very important when studying formal systems to distinguish working within the system from making statements or observations about the system.

Without doubt, Strange Loops involving rules that change themselves, directly or indirectly, are at the core of intelligence.