This is an interesting way to look at things. I would assert a higher probability, so I'm voting up. Even a slight tweaking (x+ε, m-ε) is enough. I'm imagining a continuous family of mappings starting with identity. These would preserve the structures we already perceive while accentuating certain features.
I was very interested in the discussions and opinions that grew out of the last time this was played, but find digging through 800+ comments for a new game to start on the same thread annoying. I also don't want this game ruined by a potential sock puppet (whom ever it may be). So here's a non-sockpuppetiered Irrationality Game, if there's still interest. If there isn't, downvote to oblivion!
The original rules:
Enjoy!