Dear Cristi,
As always I greatly enjoyed you essay. If I understand you, the position you are taking is that we live in a mathematical structure, but can never express the full intricacy of that structure. The purpose of physics is to express the general laws that describe our universe:
"However, we are just looking for a theory describing the general laws, and not a complete description of this particular instance of the universe, which includes what every human thinks about the universe and themselves. This would not be feasible anyway for practical reasons."
Is my interpretation of your idea correct? And if so, where would a mathematical structure that failed to match the universe's general laws be said to exist? Or should we take it that one class of mathematical objects conforms to the real world and another are just humanly constructed?
Also, if you get a chance, please check out my essay where I imagine how a weak version of the MUH might be testable and let me know what you think along with your vote.
http://fqxi.org/community/forum/topic/2391
Best of luck in the contest!
Rick Searle