The Tegmark Level IV multiverse idea is quite elegant, and this was a fairly well-thought-out post, although with some problems, most of which Mallah already identified. One more thing though:

It raises other strange anthropic questions too. The one that comes most immediately to my mind is this: If every possible mathematical structure is real in the same way that this universe is, then isn’t there only an infinitesimal probability that this universe will turn out to be ruled entirely by simple regularities? Given a universe governed by a small set of uniformly applied laws, there will be an infinity of universes governed by the same laws plus arbitrary variations, possibly affecting the internally observable structure only at very specific points in space and time. This results in a sort of anti–Occam’s Razor (Macco’s Rozar? Occam’s Beard Tonic?), where the larger the irregularity, the more likely it becomes over the space of all possible universes, because there are that many more ways for it to happen. (For example, there is a universe — actually, a huge number (possibly infinity) of barely different universes — identical to this one, except that, for no reason explainable by the usual laws of quantum mechanics, but not ruled out as a logically possible law unto itself, your head will explode as soon as you finish reading this post. I hope that possibility does not dissuade you from doing so, but I accept no responsibility if this does turn out to be one of those universes.)

This has to decrease the probability of this theory, as stated, being correct, as we appear to live in a fairly regular universe. However, it could be possible that simpler systems do have more measure even in a level IV multiverse.

Also, c