In what form can data survive the longest time?
Well, we went and killed ourselves off with our stupid wars. But aliens come along, find our marvelous planet and the evidence that we were here and they find some human (and other) embryos in a base on the moon - in a crater near the pole that is never exposed to sunlight, so the whole base is in a deep freeze, in vacuum, not exposed to light.
I theorize that they could remain viable for thousands of years in those conditions. But the aliens eventually find out how we killed ourselves off, which creates a problem for the humans among them.
These humans, of course, result from those embryos, collected by the first ship and kept frozen... and then the aliens managed to artificially gestate them on their own planet. Now the young humans are on the second colony ship, landing on Earth along with a fresh batch of colonists and scientists.
The question is: do I have to stick with a really short interval between our demise and the aliens' arrival for any information about us to survive - or could I postulate significant data storage in that moonbase remaining viable for thousands of years?
In such conditions, could a computer and a data stick, perhaps along with various CDs and such, remain usable? Or should I make it a short interval - they came in response to a CETI and it's only been, say, a hundred years? Some book-type libraries on Earth would remain viable that long given a really good roof, fireproof construction and a dry climate.
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The most durable information storage is having it carved in stone or in clay that then got burned. Our oldest writings are of that form, and they are thousands of years old. The main problem of this data storage is to explain why the information is stored that way. But maybe it was done intentionally by someone who was expecting the end of civilization, but hoped that some humans would survive and learn from that information later. He would have explicitly chosen a medium that can survive a long time.
For more information about long-time information storage, probably the Rosetta project of the Long Now foundation is a good source. They use not stone, but nickel to carve the information in, enabling a high density of information. While the type of information they store is different, the basic idea is the same: Preserve information for a long time.
Actually I'd be more concerned about the embryos: Given that the moon is outside the earth's magnetic field and outside the atmosphere, it is not well shielded against all types of radiation found in space (from solar wind to cosmic rays). Cooling doesn't help against radiation literally kicking your atoms out of the molecules. I'd expect the DNA to be considerably damaged after that time.
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