Your number eight doubling every 80 years does not take into account war, famine, flood (of the garden as opposed to the fantastical variety), pandemic disease and the thousand natural shocks to which the flesh is heir. For that to be operative, Noah and his wife, plus his two "good" sons and their wives, and his one unruly child and his wife would all be obliged to produce four offspring who survived infancy and childhood to reach sexual maturity. Were the genders equally distributed, at the end of that time, you would once again have only four reproductive pairs--unless of course, you're also going to use the hysterical biblical contentions about individuals living centuries and remaining reproductively fertile over such time spans. You're going to have to account for the genetic diseases of inbreeding. You're going to have to account for the care and feeding of this burgeoning population despite all life having been extinguished with the exception of a single reproductive pair from each species carried on the floating sewage pool known as the Ark. I understand a wistful desire that all this were so, but it defies logic to the point of laughable absurdity.
As for the age of written history, rather than point out that your dating is suspect, i would simply explode your facile and feeble attempt to suggest by inference that no human evidence older than Bishop Ussher's silly exegesis exists by pointing to the Sphinx.
An excellent summary on "re-dating" the age of the Sphinx (with a complete bibliography) more than adequately makes a fool of Bishop Ussher. In addition, note in the text the references to human "cities" (walled settlements) at Catal Huyuk in Anatolia and at Jericho in Palestine, dating to the seventh and ninth millenia before the current era respectively.
In the original version of
Notre Dame de Paris by Victor Hugo, the second "tome" begins with a description of monumental architecture as writing, considering a menhir a single word, a pyramid a sentence, and the great cathedrals as full pages of text. On such a basis, the archaeological evidence of the Sphinx, Catal Huyuk and Jericho are written historical evidence which stretch back millenial before Ussher's paltry biblical date for the beginning of the world.
You are sufficiently intelligent to understand everything i've just written, Neo, your silly self-deprecation notwithstanding. Believe what you will about your God, i've never objected to your holding such beliefs. Do have the courtesy, however, not to piss down my leg and tell me it's raining.