Well if you started a sim back a billion years ago, well yes I expect you'd get a very different earth.
How different is an interesting open problem. Even if hominid-like creatures develop say 10% of the time after a billion years (reasonable), all of history would likely be quite different each time.
For a sim built for the purpose of resurrection, you'd want to start back just a little earlier - perhaps just before the generation was born.
Getting the DNA right might actually be the easiest sub-problem. Simulating biological development may be tougher than simulating a mind, although I suspect it would get easier as development slows.
Hopefully we don't have to simulate all of the 10^13 cells in a typical human body at full detail, let alone the 10^14 symbiotes in the human gut.
It's still an open question whether it's even possible in principle to create a conscious mind from scratch. Currently complex neural net systems must be created through training - there is no shortcut to just fill in the data (assuming you don't already have it from a scan or something which of course is inapplicable in this case).
So even a posthuman god may only have the ability to create conscious infants. If that's the case, you'd have the DNA right and then would have to carefully simulate the entire history of inputs to create the right mind.
You'd probably have to start with some actors (played by AIs or posthumans) to kickstart the thing. If that's the general approach, then you could also force alot of stuff - intervene continuously to keep the sim events as close to known history as possible (perhaps actors play important historical roles even when it's running? open). Active intervention would of course make it much more feasible to get minds closer to the ones you'd want.
Would they be the same? I think that will be an open philosophical issue for a while, but I suspect that you could create minds this way that are close enough.
This is interesting enough that it could make a nice follow up paper to the current SA/simulism stuff - or perhaps somebody has already written about it, not sure.
I'm worried about how motivated my cognition is. I really want this to be possible for very personal reasons- so I am liable to grasp tightly to any plausible argument for close-enough simulation of dead people.
It's good you are conscious of that which you wish to be true.
If uploading is possible, then this too should be possible as they rely on the same fundamental assumption.
If there is a computer program data set that recreates (is equivalent to) the consciousness of a particular person, then such a data set also exists for all possible people, including all dead people.
Thus the problem boils down to finding a particular data set (or range) out of many. This may be a vast computational problem for a mind of 1^15 bits, but it should be at least possible in principle.
How different is an interesting open problem. Even if hominid-like creatures develop say 10% of the time after a billion years (reasonable), all of history would likely be quite different each time.
How on earth can we know that 10% is reasonable?
Many folk here on LW take the simulation argument (in its more general forms) seriously. Many others take Singularitarianism1 seriously. Still others take Tegmark cosmology (and related big universe hypotheses) seriously. But then I see them proceed to self-describe as atheist (instead of omnitheist, theist, deist, having a predictive distribution over states of religious belief, et cetera), and many tend to be overtly dismissive of theism. Is this signalling cultural affiliation, an attempt to communicate a point estimate, or what?
I am especially confused that the theism/atheism debate is considered a closed question on Less Wrong. Eliezer's reformulations of the Problem of Evil in terms of Fun Theory provided a fresh look at theodicy, but I do not find those arguments conclusive. A look at Luke Muehlhauser's blog surprised me; the arguments against theism are just not nearly as convincing as I'd been brought up to believe2, nor nearly convincing enough to cause what I saw as massive overconfidence on the part of most atheists, aspiring rationalists or no.
It may be that theism is in the class of hypotheses that we have yet to develop a strong enough practice of rationality to handle, even if the hypothesis has non-negligible probability given our best understanding of the evidence. We are becoming adept at wielding Occam's razor, but it may be that we are still too foolhardy to wield Solomonoff's lightsaber Tegmark's Black Blade of Disaster without chopping off our own arm. The literature on cognitive biases gives us every reason to believe we are poorly equipped to reason about infinite cosmology, decision theory, the motives of superintelligences, or our place in the universe.
Due to these considerations, it is unclear if we should go ahead doing the equivalent of philosoraptorizing amidst these poorly asked questions so far outside the realm of science. This is not the sort of domain where one should tread if one is feeling insecure in one's sanity, and it is possible that no one should tread here. Human philosophers are probably not as good at philosophy as hypothetical Friendly AI philosophers (though we've seen in the cases of decision theory and utility functions that not everything can be left for the AI to solve). I don't want to stress your epistemology too much, since it's not like your immortal soul3 matters very much. Does it?
Added: By theism I do not mean the hypothesis that Jehovah created the universe. (Well, mostly.) I am talking about the possibility of agenty processes in general creating this universe, as opposed to impersonal math-like processes like cosmological natural selection.
Added: The answer to the question raised by the post is "Yes, theism is wrong, and we don't have good words for the thing that looks a lot like theism but has less unfortunate connotations, but we do know that calling it theism would be stupid." As to whether this universe gets most of its reality fluid from agenty creators... perhaps we will come back to that argument on a day with less distracting terminology on the table.
1 Of either the 'AI-go-FOOM' or 'someday we'll be able to do lots of brain emulations' variety.
2 I was never a theist, and only recently began to question some old assumptions about the likelihood of various Creators. This perhaps either lends credibility to my interest, or lends credibility to the idea that I'm insane.
3 Or the set of things that would have been translated to Archimedes by the Chronophone as the equivalent of an immortal soul (id est, whatever concept ends up being actually significant).