> I think that perhaps our views of the world are slight off-kilter/incompatible.
Yeah, possibly. I blame LessWrong fatigue. It's an entire site made of handwavy claims that, no matter how far you trace back through the links, never quite actually get backed up. So I tend to be harsh on similar claims, particularly when they appear to be from that sphere (judging by the buzzword "sufficiently advanced AI", which is in practice used to put forward outlandish claims and then try to reverse the burden of proof).
I actually started reading the site because of a friend who was getting into cryonics. I'd hitherto been neutral-to-positive on the idea, but the more I investigated it the more I went "what the hell is this rubbish." (Writeup is at http://rationalwiki.org/wiki/Cryonics which is a very middling article, and is still about the best critical article available on the subject ...) The handwavy claims are endemic, quite a few rely on effective magic (actual answers from cryonicist: "But, nanobots!" or "sufficiently advanced AI") and it really is largely just ill-supported guff, even if I'm being super-charitable to the arguments. Extracting a disprovable claim is nearly bloody impossible itself.
> As to your claim of being able to 'turn back time', don't we do this all the time?
>If we look at the link we've both referenced, say we had two pictures of the last milliseconds of the book falling, and we knew the exact time between when these pictures were taken then we can turn back the time right? We know exactly how/when/where the book was if we can interpret those pictures.
But we couldn't do that if the data had been destroyed. That's the claim way up there: the information is recoverable from the mashed-up goo. The two pictures have been destroyed, we have the book sitting on the floor, there's nothing to reconstruct the fall in sufficient detail.
I say this because whenever I've seen an actual neuroscientist who's been asked this sort of question (can we recover the information with a magic AI or whatever), they answer "wtf, no, it's been utterly trashed. No, not even in theory. You can't even measure it. It's been trashed utterly." The questioner usually comes back with "but if we use a SUFFICIENTLY ADVANCED AI ..." i.e., if we let them assert their conclusion. And first they'd have to show you could measure stuff on the nanometre scale without messing it up. Let alone, e.g., reconstructing the precise locations of proteins in a cell after they've been denatured by cryoprotectant. Remember that it's a claim about physical reality that's being made here.
(A couple of examples, from scientists who would LOVE to be able to preserve and get back this information: http://lesswrong.com/r/discussion/lw/8f4/neil_degrasse_tyson... http://freethoughtblogs.com/pharyngula/2012/07/14/and-everyo... )
>In a similar way, the information about the locations of the molecules in the 'brain goo' is available to a 'sufficiently advanced AI'.
Remember that there is no way to distinguish two molecules of the same substance. You're requiring more information than can actually be measured (Heisenberg).