ISTM...

In primitive materialism, what exists are space / time and matter / energy.
Information is an emergent property of the arrangements of those things,
like entropy. Neither of these exist at the level of fundamental particles,
or Planck cells, or strings, or whatever else may be the primitive
mass-energy/space-time) involved.

There are problems with this view if information has primitive status,
which would indicate that the real picture is something like "it from bit"
or what might be called "primitive informationism". Evidence for PI come
from the entropy of black holes, the black hole information paradox, the
Landauer limit, the Beckenstein bound, the holographic principle, and
(unless I already covered that) the requirement that erasing a bit of
information requires some irreducible amount of energy. (And maybe some
other things I don't know about ... perish the thought).

PI isn't equivalent to comp, but from what you said above PI might be a
necessary consequence of comp, which would give the "ontological chain"
arithmetic -> consciousness -> information -> matter (I think ... this is
all "ISTM" of course).

As for A Garrett Lisi, I was under the impression that his particles were
something like a "point in a weight diagram" - or something - which sounds
to me at least like some form of information theoretic entity. But I have
to admit my understanding of how birds and flowers could emerge from the E8
group or whatever it's called is, well, about like this...

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