The problem with the flat earther debate is that they haven't drawn their conclusions based on the weight evidence, so using the evidence won't help change their minds.
However, there is plenty of evidence for the curved Earth. In addition to the extensive photo documentation, there is also the option of carrying out the experiment yourself. For example, I recently flew from New York City to Doha, from there to Singapore, then to Brisbane, then to Dallas and then back home. I followed an eastward course throughout my journey and ended up back where I started. This is only possible on a globe.
On this trip I was able to enjoy many views of the night sky, and one of the most striking features was that the sky was different. On a flat Earth everyone would have the same view of the sky, but there were stars that I could only see at home but not on my trip, and vice versa.
And finally, during a lunar eclipse, the Earth's shadow moves across the moon. This shadow is always a circle, and only spheres are capable of casting 100% circular shadows, regardless of angle.
But as I said, it's not about the evidence. People who believe the Earth is flat think we are being lied to by scientists and political leaders. Many people do not trust their society and especially the leaders of that society. And above all, elite leaders of this society. Scientists are indeed elite leaders of government, academia, and other powerful institutions. By claiming that the Earth is flat, people are actually expressing a deep distrust of scientists and science itself.
Distrust of science is a deep and sensitive issue. But one way to rebuild trust is to simply listen. I know this sounds counterintuitive, but studies have shown that people tend to trust other people, not necessarily the facts. So if you find yourself flat-earned, as I have often been, don't get into a debate. Instead, change the subject so that you focus on something you find wonderful or extraordinary about the universe or science. Maybe it's an exciting new observation, a clever experimental result, or an example of a real-world impact of scientific learning.
By building bridges based on shared wonder, awe, and curiosity, we can defuse the tension, bypass the flashpoint caused by a triggering proclamation, and instead focus on commonalities. Only there can trust take root. And once trust is established, the question of the Earth's geometry simply fades into the background.
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