Assume there is a small group of people, or a colony, with limited resources, who have all the knowledge of the world, but very few of its gadgets. How long will it take to rebuild the world to the level we see around us today?
This question is important in two contexts:
If something, either natural or man-made, destroys the Earth, and only a tiny group of people remains in underground bunkers or in space colonies. After the destruction, a few hundred, thousand or million years, nature recovers, as it always did, and the survivors can come to the surface. Nothing remained of pre-apocalyptic technology. How long will it take to rebuild it? They have only a few computers and memory chips in which they preserved all of our knowledge, and maybe a few basic tools carried with them.
We discover a second Earth in reachable distance, and send a generation spaceship to colonize it. After hundreds, thousands or millions of years, the spaceship arrives. It carries all the knowledge of the world, and can even receive updates from Earth, but has very limited resources. How long will it take to build a new world, using almost exclusively the resources they find at their destination?