Bill the Troll, since it is my birthday (and I doubt it is 8.24 daylight saving time with a sunrise at 6.33 in Alaska...), and I am in an even better mood due to having tours through two of my university's zoological collections and getting three fossils, I will leave the detailed refutation to others and will limit myself to a few points.
"claim you won by doing that,"
There never was a contest. Your arguments are so blatantly absurd that they refute yourself, and your persona is too delusional to be taught better. I am doing it just for fun.
"All that means is that they weren't as utterly obsessed with toolmaking as we are."
Actually, the Romans took great pride in their technological accomplishments and left works on architecture. They were impressive, but they did not come close to our modern technology.
""I am an ardent disciple of the Scientific Method, and it works very differently from the way you describe."
The following is sarcasm: And I'm the King of America."
My aspirations for science go back to my earlierst childhood. I grew up learning as much about science - including its methodology - as I could. I have studied with actual scientists for four years, and currently, I spent most of my time doing science for my Bachelor thesis.
You, on the other hand, are an edgelord who is beyond ignorant, who denies literally everything and who, according to a plagiarised image, does an unspecified type of high-altitude work at mobile phone masts.
Guess who knows more about science...
"I don't have any theories: I admit that I'm just a pawn in the game of life, wandering and blundering around in the void of space, with nothing but suspicions and guesses."
Actually, I suspected as much. Actually, this is somewhat true (if described unnecessarily bleak), however, our "suspicions and guesses" are evidently far closer to reality than yours.
However, for someone who openly knows nothing, you seem very convinced about your bizarre "suspicions" like "there is a conspiracy who benefits from a spherical earth, and somehow persuaded everyone that it is true", "the earth is flat and of infinite size" and "all technology has always existed.
Wait...
"... wandering and blundering around in the void of space..."
I thought space did not exist. Your persona is slipping!
"It's getting everyone else to admit it that's seeming less and less likely as the days go by."
Because most other people are not as ignorant as you.
But that cannot be because you are such a super special skeptical edgelord, so everyone else must be stupid!
"I wonder how many times it took you to get it "right?" "
Not at all. Worked very consistently. No publication bias necessary.
"You have math formulas, measurements, and lots of plain old fashioned say-so, but it's all a series of self-reinforcing ideas, it only makes so much sense to you because you've been raised in it since birth.
I know it's not really a refutation of the specific ideas about "projecting the earth onto a flat math," but how can I respond to the specific claim when the whole mindset that led to the idea of "projecting the earth" is the problem?"
It would certainly help if you actually bothered to learn about the mindset you are trying to refute, since once again, you got everything completely wrong.
Also, you are denying fairly basic mathematics ? Well, one should never tempt fate, but one simply cannot go more stupid than that.
"That whole ending could be shortened to just "nya nya nya you suck." "
Your persona does indeed suck more than an outer-space-level high purity vacuum at the bottom of the Marianas Trench (although I guess neither exists, right?). Meanwhile, I really am a genius, and science is still effective.