If you want to jump into the deep-end of the sci-fi pool, it's convincingly arguable that with a complete enough grasp of the physical laws, and sufficient processing power, you can reconstruct a past state up to Xs into the past and with Y% accuracy. (Of course "accuracy" is a pretty arbitrary measure).
For example, using the current trajectory of a baseball, it's fairly trivial to deduce where it came from 1.5 seconds in the past with, say, 99% accuracy. Now just extend that process to the entire Earth. It would be earth-shatteringly difficult, of course. And of course there are a hundred and one open questions about the nature of consciousness, whether a person reconstructed in such a fashion would be the "same" person, and of course the problem that describing a system isn't the same as reconstructing a system in reality.
But it's not impossible given our current understanding of the universe.
EDIT Somehow I missed the above post. Which covers all this.
One of the themes of current scientific progress is getting more and more information out of tiny amounts of data. Who'd have thought that we could learn so much of distant and recent biological history from DNA, and so much about distant planets, stars, galaxies, and the cosmos from tiny differences in very small amounts of light?
Pratchett's death puts an extra edge on the question-- to what extent can people be re-created from what they've left behind them, especially if they've written novels which include a lot of their personality?
Any thoughts about theoretical limits of how much can be figured out from small amounts of data?