my definition of interestingness is any distinguishing feature. Anything at all that can be used to tell universes apart.
Oh, your definition of interestingness is kinda sorta the opposite of what I thought it was. "Having a monochromatic complete subgraph of a certain size" is not a distinguishing feature of sufficiently large colored complete graphs, because all such graphs have that property.
I had posted a while back on my proposed dissolution of the Fine Tuning argument. My main argument was as follows:
I've been pondering how to process that response, and if the argument is salvageable, ever since. Do we really have to explain anthropics and the multiverse to diffuse the FTA?
Today I came across a great article with an elegant description of Ramsey's Theorem:
As I understand it, positing few 'interesting' vs. the vast majority of 'uninteresting' universes is in direct contradiction with Ramsey's theorem. I put this to the more mathematically educated among this community for feedback. Beyond pushing forward this particular internal dialog of mine, it should have more general application in the fine tuning debate, should someone choose to use it there.