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The story is set 35,000 years after the year 2024. In 2024, Donald Trump makes fun of Kim Jong Un's stupid hair, and long story short, the Earth gets nuked to the point where everything is covered in radiation and uninhabitable. New Zealand is the only place where humans still survive.

Since New Zealand does not have enough space for the repopulation of Earth, the entire national budget is redirected to space travel. By 2040, they figure out a way for long-distance space travel to work. They are all set to found a colony on Mars, but the mathematicians screwed the trajectory up and now the ship is slowly heading south and out of the Milky Way. A decade or so after the launch, Toba in Indonesia erupts, wiping out the last people on Earth.

This ship can move at around 100x the speed of light, which is astronomically fast compared to anything we have now, but painfully slow compared to ships that are developed later on. Generation after generation plays out on board the ship. It takes around 40 generations until the ship enters a new galaxy, which is dubbed the South Galaxy.

Over the next 35,000 years, the descendants of these colonists would spread out and colonize the South Galaxy. However, they did not bring technology with them (apart from their ship itself, which was destroyed when it crashlanded on the northernmost planet of the South Galaxy) and the people on board the ship were not exactly tech buffs, so society and technology regressed to the Middle Ages. Space travel became possible again when the colonists discovered magic (a story for another time).

Empires rose and fell, great men were born and died, generations came and went, etc. Now for my question: after all this time, how much about Earth is it likely for these castaways to remember?

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closed as primarily opinion-based by Renan, StephenG, rek, user535733, JohnWDailey Oct 19 '18 at 4:39

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This really isn't answerable except for matters of opinion. $\endgroup$ – TCAT117 Oct 18 '18 at 23:33
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    $\begingroup$ Not even......... $\endgroup$ – Richard Oct 18 '18 at 23:37
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    $\begingroup$ Regressing to medieval technology occurs only when the sole food to survive the crash is a supply of stupid pills. You're saying that nobody could smelt a bit of copper and build a simple electric generator during the long, boring season between planting and harvest. Or build a printing press...or a steam engine. Or build a vault and start a bank. NZers are better than that. $\endgroup$ – user535733 Oct 19 '18 at 3:19
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    $\begingroup$ At 100 times the speed of light (completely ridiculous for 2040, by the way), it would take (at most!) 22 minutes to get to Mars. Someone really screwed the pooch on that one if they missed. Also worth noting is that any galaxy close enough to reach in less than a thousand years at 100C already has a name. $\endgroup$ – jdunlop Oct 19 '18 at 16:10
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    $\begingroup$ @Hankrecords Galactic South is in the direction of the constellation of Sculptor. en.wikipedia.org/wiki/Galactic_coordinate_system $\endgroup$ – Arkenstein XII Oct 22 '18 at 19:35
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Given that period of time, no details about the history of Earth will be remembered. There may be a vague idea that humanity originated on a 'Homeworld' somewhere, but even that is not certain. Almost everything we know about life 35,000 years ago is the result of archaeological enquiry into the remains left behind by the people who lived at that time. Without access to Earth, future space-archaeologists will not have that luxury.

However, I do know two examples of folklore amongst Aboriginal Australians that preserved some information of events occurring on the order of thousands of years ago.

https://www.abc.net.au/news/2015-04-03/aboriginal-legend-palm-tree-origin-central-australia-research/6369832

http://theconversation.com/ancient-aboriginal-stories-preserve-history-of-a-rise-in-sea-level-36010

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It will be just like Illiad

We will be like Legends that are hard to be proven, like Illiad and Odyssey, passed by word of tongue from one generation to another, without any reference and online journals to back it up, until such time that a generation will say "Earth did not exist because there are no documents to prove such a planet existed"

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It's entirely possible that very accurate records of Earth will exist, and nobody will have read them, and most people won't care.

Ignoring, for a moment, that we have not tested the long-term durability of solid-state memory, and that magnetic memory can be corrupted by magnetic fields, and that data storage formats will have changed... It's completely reasonably to suppose that archives with audio, video, and text, all continue to exist. It won't be a question of, "Gee, was that even real?" Actual newspapers. Actual digitized videos.

Language will likely have changed a great deal, but there are people who can still read, say, Aramaic from 2,000 years ago. We can ignore the potential language barrier.

We don't remember ancient times very well in part because we simply don't care that much. A few people will read the volumes and volumes of ancient Egyptian documents and fragments of documents which exist today. Most people are too busy with their own present-day concerns to be aware that such a thing exists. Most people in the U.S., even of those who remember the Japanese internment camps, are not aware that the U.S. was following Canada's lead, or that Canada continued the policy of Japanese internment for much longer than the U.S. did (see here). Most people are not aware that there were German WWII pilots who fought for their country, but hated the Nazi party and longed for regime change (see the book "A Higher Call"). Most people are not aware that, when there was a famine in 1960's in the Japanese prefecture of Yamanashi (because of catastrophic typhoons), the state of Iowa stepped in to help (see here). And two of those things, because I already knew what to look for, I could find on Wikipedia in a matter of seconds.

35,000 years is a LOT of history. We are no longer as intimately familiar with things that happened less than a century ago as we like to suppose. It is very plausible that the origins of your group, after that many thousands of years, would be of no more interest than questions about Neanderthals or Cro Magnon man is to nist people now, even if we had true-to-life video and audio recordings of the Cro Magnon settlements. That would be roughly the same time frame.

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Not much, if any at all. At the most generous, that is roughly 7 times all of generally accepted recorded history. How much do we remember the predecessors of the sumerians today?

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