From those arguments, the one I called the "solstice argument" (ie. the one which would require the illumination pattern of the Sun to have an odd kidney-shape) can actually be presented without an actual map, if you approach it properly. I have recently been trying to have this conversation with YouTube flat-earthers. (Of course it's hard to know how many of them are just clever trolls or people parodying flat-earthers, Poe's Law is in full effect here, but perhaps some of them are the genuine things.) I'm doing it using the following approach:
I start by writing a comment on the video that goes like this:
"May I ask you a series of questions? I will start with one question, and follow it up with subsequent questions. I'm doing this so that we can make sure that we agree on every point.The idea is that if the flat-earther were to agree that there's a bit over 14 hours of daylight, I would follow it up with these subsequent questions, one at a time (perhaps two, depending on the situation), and wait for an answer (or have a discussion until we agree on the answer):
So, for starters: How many hours of daylight (ie. the Sun is visible) during one day is there in Melbourne, Australia, in the middle of December?"
"Do you agree that the same is true (ie. there's 14 hours of daylight in December) everywhere on Earth at the same latitude as Melbourne?"This could ostensibly be followed with more questions and arguments, such as:
"Do you, thus, agree that in the middle of December the Sun illuminates about 60% of the latitude that goes through Melbourne?"
"How many hours of daylight is there at the North Pole, in the middle of December?" (Of all the questions I expect this one to be the most likely to make the flat-earther to go to conspiracy theory land, but perhaps at least some of them will agree that the answer is 0 hours.)
"So, if you agree that in the middle of December the Sun illuminates about 60% of the latitude that goes through Melbourne, but does not illuminate the North Pole at all, could you please draw on a flat Earth map the shape that this illumination pattern makes?"
"Not only does the Sun illuminate the surface of the Earth in an odd kidney-shape during December, but moreover this shape changes towards summer, when the Sun moves towards north. During equinox, the Sun illuminates exactly half of the surface of Earth, which would be a D-shape on a flat Earth, and becomes more of an oval shape in summer. How and why does this shape change so much during the year?"And:
"Do you understand that the illumination pattern of the Sun is perfectly concordant with the Earth being spherical, illuminated by a very distant Sun? It always illuminates half of this sphere, and results in exactly those daylight durations."So far I have had very little luck. I have posted the first question to something like a dozen flat-earth videos, and have got an answer from the author only once.
In the majority of cases I suspect that these people don't even read comments, or don't bother to answer them. They just throw their videos on YouTube, and don't care about any feedback.
This one particular author prominently prided himself for answering questions presented by skeptics, and he did answer my first and even my second question (agreeing that yes, 14 hours of daylight everywhere at that latitude), but then by the third question he just stopped answering altogether. I tried posting more comments on that comment thread, begging to continue the conversation, to no avail. Either he simply didn't bother reading that comment thread anymore, or didn't want to answer any more of these questions. (I'm hoping that he stopped answering the questions because he got scared of what they were making him realize, of the major problem that the questions were revealing about the model he so firmly believes in. However, I'm afraid that it's possible that he just started ignoring me because he thought the questions were stupid and didn't lead anywhere, and perhaps he didn't even read my third question at all, which was going to the actual meat of the argument. In other words, he was too impatient to wait for the actual argument. If this is the case, he didn't learn anything, even potentially.)
Edit, and additional note:
Having watched more (apparently) flat-earther videos, it's very possible that my suspicion above that at least some of them may have conspiracy theories about the North pole (and the amount of sunlight there) might be true.
Thus, if you ever have a conversation with a flat-earther, and want to use this line of argumentation as I presented here, it might actually be better to start with the question of how much sunlight there is in the North pole in December, and only if the flat-earther acknowledges that there isn't any, then proceed with the other questions, as listed. Better get the potentially most "controversial" part of the argument settled first, rather than have the conversation get stuck mid-way through, just before the punchline.