Hal asks
> How about the case of mathematical proofs? Could an entire proof
> exist Platonically? A proof has a sort of time-like flow to it, causal
> dependency of later steps on earlier ones. It seems to be an interesting
> intermediate case.
>
> My tentative opinion is that it does make sense to ascribe Platonic
> existence to such things but I am interested to hear other people's
> thoughts.

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A proof can be seen as a relationship between integers. We
Platonists therefore accept proofs as much as we must any
other mathematical patterns. As formal proof, or even human
stories, do contain patterns that are tantamount to time,
this, then, in no way dampens your speculation concerning
the "everything" thesis (i.e. that everything is just patterns).
I don't pass judgment on Tegmark's SASs (Self Aware Structures),
because level IV of his hierarchy always seemed mysterious to
me. I was never sure I understood it.
Now, Tegmark Level I, our lovely infinite universe, is backed
by the best astronomy results. Level II, the bubbles each of
which is defined by a different set of six numbers (I think)
is somewhat likely to be true, embraced as I guess it is by a
number of cosmologists. Level III, the true multiverse, of
course is highly probable. But Level IV is to me quite a
bit more speculative than Level II.
Lee