'If we took all of the humans alive right now and sent them back 10,000 years ago, how many years would it take for us to re-build society?'
Really depends on the conditions.
If we count any society it will take less than a day for networks and systems to form that can be classified as society.
Also depends on who the humans are. If we pick completely random people we are likely to loose a huge portion of practical information or we will lack practical skills required to survive In nature. For example we won't be able to find iron deposits because that might be a very specialized skill, we might not get any blacksmiths or any specialists in general.
We are also considering that they all don't immideatly die. Which likely a lot of people will. In nature and a hostile environment with no agriculture established, with no food or housing. Humanity will be basically split in to tiny hunter gatherer groups to survive and within very quick times we will loose all knowledge available to us. And thus well start from scratch pretty much.
If we allow people to keep their phones. Some of them have the entire Wikipedia installed. That might be enough to do something. But again, no food or shelter and you can't acquire it quickly nor hunt and gather it quickly enough in a small area so you'll have to split.
If we allow humans some items of their choosing with them. That changed a lot. Presuming we drop them in at the begging of spring. They can safely carry a bunch of seeds food and other supplies to relatively quickly establish some sort of a sensible agriculture allowing cities to develop while the brought in supplies last, and infrastructure is rolling up to support them from the land. We will likely be transported to the medieval age technologicaly with much quicker progress of a 100ish years for the industrial revolution to take place again. Maybe more maybe less.
Then you have to consider if the humans will be able to build a society in general. If they aren't prepared mentally and don't have that as a goal. They might start infighting and generally lack the social coordination to organise.
So the answer is it depends a lot on the details and assumptions of the question.
If we allow people to take a sizeable backpack full with resources, allow them to coordinate beforehand and pick who gets selected. Not very long because we can assume they are organized, prepared materialy and are educated in the specifics of survival from scratch.
Sk the question can be reformed as such, how long will it take for a group of volunteers and experts in various sciences. If tasked with an expedition to 10000 back with limited resources to start, to rebuild society as we recognise it. The answer I will give you is 500 years or less. Mostly due to population size issues.
I think a similar question exists from star treck where they asked something similar with their science group.
Also have you ever heard of vintage story. It'll be Kinda like that.
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