Hopefully it is clear that the theorem above is utterly consistent with natural science. It makes no assertions about the Universe itself, and permits us to learn of the Universe as symbolic encoding subsystems riding our own personal cusps of entropy quite independent of whether or not we view this as learning about God Universe or just Universe with God . With the assertion of necessary contingent identity we are no longer strictly capable of differentiating the two. A pandeist scientist or philosopher studying the Universe is not necessarily irrational, nor is he or she particularly distinguishable, from an atheist scientist or philosopher who loves the subject of his or her work.
They are differentiated, if at all, by very subtle differences in their point of view, nothing like the gulf that separates a Muslim scientist or Christian scientist when they confront the enormous disjunctions between their supposedly divinely inspired scriptural mythology and straightforward observations and conclusions of physics, cosmology, biology, chemistry, history, and modern secular ethical theory. Both experience a sense of wonder and awe that might be called ``worship'' when confronting and exploring the beauty of all that is. Neither has any particular reason to expect things like life after death, resurrection of a personal soul in a physical body, heaven, hell, demons. Neither has any particular reason to think that God cares about being worshipped or cares about how humans behave. In a sense it doesn't matter if the Universe is God or is just the Universe because the possibility for information exchange from inside the Universe with the Universe itself makes no sense at all.
A panendeist, on the other hand, can keep open the possibility of God as Universe where the Universe is much larger (infinitely larger) than even infinite subsets. To be honest, our understanding of the mathematics and information theoretic possibilities in this sort of limit is none too solid, and it is very difficult to rationally reject any possibility. This is especially true if we hypothesize a coupling between our ``visible'' spacetime and other spacetimes (or other dimensions in general). This coupling (in physics) permits information to be exchanged between spacetimes, which in turn means that the entropy of spacetime need not be (internally) constant! In fact, spacetime becomes a subsystem in the Nakajima-Zwanzig sense, and the rest of the Universe becomes a bath, the moreso since it is a truly infinite bath with truly unknown coupling.
Since spacetime from the outside where as a set of dimensions embedded in a much larger space one can actually think of it as having and outside, much as the surface of a beach ball can be inside a larger (higher dimensional) space) is static, this opens up the possibility of Hilbert Grand Hotel flows of information and entropy down to, and action upon, our particular spacetime. Here we have to be very careful with what we can reasonably believe.
There is a natural temptation to say that now ``anything is possible''. God could indeed have ``created'' the Universe by assembling parts of Itself (not creating them, mind you, as creation is still impossible but by building our particular room in the Hilbert Hotel out of lumber and furnishings provided in the (inexhaustible) rest of it. God in this instance could very definitely be sentient, God could work miracles of the first and second kinds in this spacetime (where a miracle of the first kind violates the second law of thermodynamics and consists of the highly improbable within the bounds of microdynamic physics in our associated spacetime dynamical bundle, and a miracle of the second kind violates both the first law and the second law of thermodynamics and might consist of the transfer of mass-energy and information into our spacetime from the ``outside'').
This is all true but irrelevant. As is (or will be) carefully laid out in Axioms, if we develop the axiomatic theory of evidence-based knowledge as the best we can know of the Universe we live in given our collective experience and finite vision, anything is possible but almost nothing is plausible. We quite literally have no reason beyond our imaginations to believe any such thing. We have been unable to observe anything like a systematic violation of our inferred laws of physics in this spacetime, which includes both the generalized first law (viewed as the conservation of mass-energy as well as a slew of other fields of information associated with self-encoded elementary entitites in our best-guess field theory) and the second law, which basically states that whenever we do experiments on a macroscopic scale that averages fairly over the dynamics of the microscale, we always see something happen that is macroscopically likely, not unlikely.
It is very clear that the best thing to believe is the one that is most consistent with the available information, the one we can least easily disbelieve. A rational panendeist, therefore, has no real excuse for openly embracing some scriptural theism or accepting its tales of ``miracles and magic'' uncritically. Extraordinary claims require extraordinary evidence; otherwise we should rather expect that any of the far more likely explanations for even ``miraculous'' occurrences are correct.
From this we can see that a rational panendeist (as opposed to a theist who is an irrational panendeist) should be highly skeptical of theistic claims and demand extraordinary proof even compared to the already high standard of proof or evidence used in natural science! This is perfectly clear. One is basically inferring a vast extension to the spacetime we directly observe on the basis of indirect evidence. One requires a more or less complete, consistent, testable theory to even begin to collect non-anecdotal evidence to support or not support that theory.
A perfect example is given by the theory of evolution and various creationist arguments. The theory of evolution via reproduction with variation followed by natural selection is perfectly sensible and requires no new science - only a long-running statistical process.
The theory of direct divine creation (or intelligent design, or whatever) starts by positing as a fact the existence of God (or a thinly disguised ``intelligent designer''). The God (if we call things by their right name and assert God) must be a panendeist sort of God with enormous exterior complexity in order to be able to ``think about our spacetime'' at all and act upon it. This vast, vast being must be able to reason symbolically all the way down to our scale of being and has to have done nothing more over a timescale that ranges from thousands to billions of years but move matter around in ways that directly violate physical and statistical laws while preserving the illusion that those laws are perfectly satisfied to create/design the appearance of a systematic hierarchy of systematic progression of species in consonance with an environment that this being (presumably) is also causing to vary in apparently unplanned and unorganized ways. This is not an easy theory to formulate intelligibly, and we would never be tempted to do so based on the evidence were it not for supposedly divinely inspired scriptural mythologies that picture God like a person only much much bigger and meaner.
If we compare the former to nature by means of observation and experiment, we find truly, extraordinarily excellent agreement. We find mountains of evidence of time-ordered rocks with a clear progression of species in correspondance with the age of those rocks. We can validate the ages of the rocks in many ways. We examine the chemistry, the biochemistry, the statistical mechanics, the computational statistics, the fossil record, and most recently the genetic record and find that it is all consistent with the theory of evolution, usually spectacularly so, so much so that a countertheory would have to be supported by powerful evidence indeed (evidence that could explain everything explained by evolution, only better). We conclude that the theory of evolution fits our experiments and observations so well that it is almost certainly either true as is or a big, big part of the truth.
If we compare the theory of intelligent design to nature, we get no agreement at all. There is no direct evidence of a designer. The timelines consistently read off by e.g. radiometric dating make no sense at all in terms of a designer. The designer makes mistakes inconsistent with their supposed intelligence (things like the human appendix and ``fossil'' DNA). There is little reason for such a designer to have hidden their work behind the illusion of systematic evolution, little chance that a designed work would have been designed in that particular way. When we look at the Universe in general, we see no support in physics, chemistry, biology, statistics (computational or otherwise) to support this ``theory''. It doesn't work at all to explain the biosphere we observe, where evolution explains nearly everything we observe.
The rational panendeist, even though they choose to believe in at least the possibility of a self-aware God (who is still, remember, the Universe itself and not a creator of same) simply looks at these two hypotheses like any rational philosopher or scientist and rejects the latter, mostly believes in the former, and keeps their mind just a bit open awaiting more evidence or new results that might make them change their mind. Again this is for all practical purposes not unlike the way the atheist or pandeist proceed, the difference being a certain cautious optimism, a sense of being just a bit more open minded about the possibility of actual influence of God on the spacetime we live in. The only real evidence they might have for this is that out of the rather large space of possible spacetimes that might have existed (and might well exist), this one has led to the current rather unlikely (viewed in a sufficiently macro basis) state of affairs. Anything could have happened, perhaps, but in any event this spacetime that we live in, and we ourselves, did happen.
And in one very important sense we are just as unlikely as that cigar.