Thanks for the bump, Marty. Very interesting. I feel sorry for my doubleganger that didn't finish reading, while recognizing that elsewhere another me understood far mor than I.
The basic idea, sort of, is that physical theories of the nature of the universe are complicated rather than simplified by the notion that this is the only universe:
In this sense, the higher-level multiverses are simpler. Going from our universe to the Level I multiverse eliminates the need to specify initial conditions, upgrading to Level II eliminates the need to specify physical constants, and the Level IV multiverse eliminates the need to specify anything at all. The opulence of complexity is all in the subjective perceptions of observers--the frog perspective. From the bird perspective, the multiverse could hardly be any simpler.
Four types of multiverses are postulated. The bird represents a higher dimensional view of the universe than the frog who is in a single thread of a particular universe. The hows and whys of each of the four types are facinating and the whole thing hangs on whether mathematics and the nature of reality are intertwined.