Gödel is interesting in many ways. While acknowledging that his logical and mathematical foundation-shaking Incompleteness proofs have a very specific context and meaning, the extent to which a broader reading (and thinking) public remains utterly and blissfully unaware of the distributed consequences of this never fails to astound me. (Much the same could be said of General Relativity.)
Turing’s work on the Halting Problem possesses a non-trivial genealogical lineage from Gödel’s work. The genesis of ideas which became the modern digital computer is of no small significance.
What I currently find most curious about Gödel is the informal (yet powerful) sense in which his recursive method describes a self-propagating, billowing referential system that approximates quite accurately to indefinitely-extensible technological systems. At other levels, there are clear (if often obfuscated) paths of inference to be made between complexity, information entropy and the recursively exponentiated logical systems Gödel built a mercurial, enigmatic foundation for.
Where diverse instances of open, complex systems are – also – indefinitely extensible and autonomously self-propagating, we can begin to draw the lines of symmetry between them.
Daedelus Kite 