This post is tragically too late for Halloween, despite my having this information for over a year. Sorry about that. There’s always next year.
Last year, Dave and his girlfriend were casting about for costume ideas. I had a whopper, but they wouldn’t hear of it (which reminds me: be sure to leave some family members tethered in your yard on Howliday Eve for the Banshee Queen). Whenever I suggest this idea to someone, they always indicate that it would be hard to implement. So, I’m taking up the challenge and fleshing the costumes out a bit.
You need two people. One of you is a Gödel incomplete system (a system in which there exist true statements that can’t be proven) and one of you is a Gödel inconsistent system (in which everything can be proven true). A third person could optionally dress as Gödel himself.
I’m thinking a Queen of Hearts figure here. Some kind of ridiculous, mishmashed costume. Shout stuff like “2 = 2 = 1” or “I am the Pope!” Deny nothing throughout the night, especially inconsistent things.
This is a good springboard for any sort of eccentric/surreal costume/behavior. Bonus points for numerous and subtle contradictions.
This seems harder. I’d go with a two-fold approach. First, work with being literally incomplete. Like, bind up an arm so it looks like you lost it. Wear an eyepatch. Shave half your hair off. That sort of thing.
Second, work with the meaning of the theorem. There are lots of ways you could play off interpretations of what it means to be incomplete. You could either play up having inexplicable wisdom or instead not believing obvious truths. I think my favorite take on it would be to gather folk wisdom from various places and work them into the costume somehow as well as to offer tidbits to passersby. “Hey, did you know that chewing cinnamon sticks gets rid of songs in your head?!”