1.
First off, there are two rivalling factions of Flat-Earthers.
Faction One believes that there is a world-wide conspiracy to cover up any evidence anywhere and anytime that Earth is flat.
Faction Two believes that this is ridiculous nonsense. There really is a world-wide conspiracy to fake space-travel and moon-landings.
2.
Some Flat-Earthers are bat-shit crazy. Literally. They are so deep into their esoteric alternative reality that they should be sent to a mental asylum. I have personally talked to time-travellers, people living in the Matrix and people who want to change reality by believing really, really hard.
3.
Most Flat-Earthers tackle scientific questions despite not having any scientific education. Their argument is basically that if they don't understand it, or if an observation is other than what they expect it to be, it must be fake. For example: Those photos of other planets don't look like photos of planet Earth? Must be fake.
4.
In a scientific debate, Flat-Earthers reserve the right to ad hoc be arbiters on which of your evidence is real and which of your evidence is fake. (Any evidence hinting that Earth is spherical is fake.)
5.
The tiniest minority of Flat-Earthers DOES have a scientific education. However... Flat-Earthers do not believe in the scientific method. The scientific method works by grading theoretical models against each other. The model that fits the experimental observation best is allowed to stay, the other one gets thrown into the dustbin.
That means, the scientific method could mercilessly prove that Flat-Earth is incorrect, which must not be allowed to happen.
In order to prevent the scientific method from disproving Flat-Earth, Flat-Earthers use the zetetic method. In this method, you don't compare models. You make one measurement and from this you come to one conclusion.
(This is mathematical bollocks. You cannot go from a subset of information to a statement that has a 100% certainty to be true. It's basic statistical math. You cannot do that. If you want to make a statement that has 100% certainty to be true, you need all of the possible information there is relating to the situation. ALL OF IT.)
And concerning your picture: According to Flat-Earthers, the Sun has a lampshade. Not kidding.
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