Thank you so much for sharing your insights, dearest sister in Christ!
Indeed — and such a fascinating insight! It is actually amazingly "platonic," too. To me, Tegmark's mathematical structures directly correlate with Plato's forms, which are inherently mathematical, and the (divine) Idea of which they are manifestations.
In Plato's creation myth, the Demiurge — who is not the One God "Beyond" the Cosmos, but seemingly a sort of agent of the Divine — "persuades" the pure, unlimited potentiality of Chora (i.e., matter) — which, being unformed and random is literally "no-thing" — to accept "formation," to conform to a "limit," such that it can become a "some-thing" existent in actual Reality. The Demiurge is motivated to create all things according to the very standards of truth, goodness, beauty, and justice — that is, according to the divine Idea, in a manner consistent with the true nature of the One God.
The point is, the creative "forms" of Plato's Demiurge, who acts for the One God "Beyond" the Cosmos, are mathematical/geometrical in nature. [It is generally agreed that Plato was a student of Pythagoras, for whom number and geometry were the keys to unlocking all the "mysteries" of the universe.]
"Random" matter can manifest no particular existence until or unless it can be "persuaded" to accept formation by such means. I gather Plato's insistence that the Demiurge works by means of "persuasion" — peitho — indicates his reluctance to believe that we live in a completely deterministic universe.
Anyhoot, I find Plato's creation myth (found in the Timaeus) to be eminently fascinating. Somehow I draw a correspondence/resemblance between his Chora and the pure potentiality of the quantum world....
I greatly admire Max Tegmark, a mathematician of the Platonist "school." He is no mathematical formalist like, say, David Hilbert, or Bertrand Russell.
I imagine that if, in fact, such mathematical structures exist beyond the 4D spacetime that humans normally experience, they must do so from yet another "timelike" dimension "above" the four nominal dimensions of human direct experience....
Anyhoot, to my way of thinking, these are fascinating conjectures.
They are also entirely beyond the reach of the scientific method.
But does this fact make them necessarily "untrue?"
I don't think so.
Thank you ever so much, dearest sister in Christ, for bringing Max Tegmark's Level IV parallel universe to mind!