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Were they elves or fairies? No, they don't feature in The Bible. So how do you explain them?

Well I cant answer for young earth creationists, but me and fellow gap theorists explain them as a previous civilization wiped out from a previous flood.

I gave the wikipedia entry if your very interested, but briefly stated the model comes from looking at the very fists verses of the very first chapter of Genesis:

VERSE ONE "In the beginning God created the heavens and earth."

BIG GAP OF UNSPECIFIED TIME (accounting for previous races, dinosaurs and more primitive life forms)

VERSE TWO "And the earth was without form and void and darkness was upon the face of the deep ..."

The "face of the deep" I highlighted above is an implication of a previous flood. Since we know that God destroyed the earth with a flood during Noah's time, we assume that he might have destroyed a previous civilization with a flood. Perhaps there were more than one previous civilizations. This also explains why the earth is measured to be so old, and why we see mass extinctions(species being drowned) and sudden emergence in the fossil record.

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(actually, older writing, as old as 3,500BC, before Mesopotamia's writing, has been discovered

Right, I dont specifically what data your using for reference here is, but scholars have placed Adam at 4000 BC so even if the 3500 bc record was correct it would not necessarily contradict biblical creationists.

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Going sideways on the topic a bit, because I don't pretend to know crap all about DNA.

I think we are all just currently "laymen scientist" in this debate. IM just knowledgeable of somethings because Ive read a lot.