I’d like to share another except from Godel, Escher, Bach. Author Douglas Hofstadter is going through a pretty involved mathematical proof/logical argument that I can’t quite follow. He has finally derived, following Godel’s footsteps, statement G, which proves that every formal system is incomplete. In this case, our formal system is TNT (Typographical Number Theory, although it nonetheless has explosive properties as we will soon see). At first, statement G looks like this:
~Ǝa:Ǝa’:<TNT-PROOF-PAIR{a,a’}^ARITHMOQUINE{SSS…SSS0/a”,a’}>
Hofstadter simplifies this monstrosity in steps, finally coming up with:
G is not a theorem in TNT.
But he doesn’t stop there. Instead he makes one more simplification:
I am not a theorem in TNT.
Let that sink in. The math is talking to you! We went from Kurt Godel and wound up with Martin Buber.
From the ability to refer to oneself, intelligence, conscience, and the unique distinct self are created. They hatch from the fractured shell of formal systems. This is the core of GEB. It’s also the core of what technology should be, namely a vehicle to be discarded once a destination has been reached. A means, not an end.
After all, no one buys a rose for its STEM.
