Experiment after experiment after experiment consistently demonstrate see too far. Photographs of the Alps from 700 miles away that should have been hidden by 45 miles of curvature. 150-above-sea-level lighthouse seen from 250 miles away when it should be hidden by miles of curvature. Many laser experiments, including one that destroys refraction, a two-way laser that completely debunks any possibility of refraction. Come up with a plausible explanation for this phenomenon, and I'm all ears, but "refraction" is ridiculous, and simply not possible in the two-way experiment.
In fact, if someone were to assert that we live on a globe, but it's 10 times larger than what NASA claims, I'd examine the claims with an open mind and ask for the evidence to back it up. That would explain "see too far", by indicating that our math is just wrong.
If someone were to hypothesize that the earth's electromagnetic field or the flow of ether bend light consistently around the curvature of the earth, I'd be all ears, ask for the evidence, and would look at it with an open mind.
In all cases, I'd insist upon seeing how they explain Sacred Scripture's and the Church Fathers' unanimous reading of a solid firmament that keeps natural water, H2O, off the earth.
But that
deus ex machina of "refraction" is such a complete bunk, an act of desperation thrown out there when there's nothing else left. As with every other issue I have examined, I always engage in the mental exercise of pretending I'm an advocate of the opposite position and how I would prove the opposite position. I do this with evolution, Big Bang, as well as with theological issues. This comes from my background in having engaged in competitive debate in High School and at University, where they force you to be for a position during one debate and against it during another one. I found that to be a dishonest exercise in sophistry, but it did teach me to examine things objectively from both sides. It's also very much in line with the Thomistic method, where you lay out the best arguments against your position and even briefly advocate for them before reaching your final conclusion. It would be dishonest to make a very weak statement of the opposite position, so you put out the best case you can for the opposite and explain why you find it unconvincing. In any case, unfortunately, most of the time, people simply have their conclusion determined ahead of time and then look for evidence to back it up, kindof like those debate teams, or how layers will defend people whom they know are guilty.