You could have picked an easier subject...
A mathemetician, I am not. Though I do love the challenge of trying to understand the theories.
I haven't read the book you mention but I have been following Garret Lisi http://deferentialgeometry.org/
I think his theory is just what the physics world needs to bump them out of their current state of rest.
The whole quantum probability concept is what gets me. If quantum probability/uncertainty exists then it only follows that, as you say:
anything that we can think of does already exist
and I would add...somewhere.
If everything already exists, or can exist, the question becomes, "does it exist in OUR universe?" Other universes then are bound to have their own possibly vastly different physical constants and rules. They would have illogical physics compared to our universe.
Our universe has a reasonably firm *physical boundary that keeps the other universes from intruding on ours so that ours can exist without self-destructing from illogical forces...wouldn't that happen?
If an illogical force exists in our universe, how would it be kept from affecting us? Or could we use it to perform feats of power such as creating a stargate or wormhole? Could we use it as a window to view it's native universe and thus learn it's secrets? Now that is power I would almost reserve for God. (notice the capital G). Could that be the definition of a level IV civilization on the Kardashev scale? Someone who can locate and manipulate forces that are contrary to physical reality in this universe.
Forge of Creation - http://www.aliengods.jbsheets.com
The art of life is to go confidently, without
rushing, without faltering. To meet and
master the four natural challenges:
Fear, Clarity of Thought, Power, and the
Desire to Rest.