Yeah I do not know about that.
A theory is an unproven idea so I suppose there could be paradox in some but it would prove a theory as being incorrect.
"The bottom line is that most observations with ultra zoom cameras or magnifying devices don't show the curvature that you would expect if you take the Round Earth Formula seriously. "
Since you actually witnessed a ship sinking as it moved away from you I have trouble understanding that conclusion. I think that you could add some precision in your measuring devices but your only talking about a slight discrepancy as to the amount of curvature based on inaccurate distance estimates, no understanding of expected refraction and low grade optics.
I think overall you are a standout and have done an excellent job of using science.
"1- Do you take the RE-formula seriously?"
-what formula are you referring too?
"2- Are you doing tests and experiments in the field?"
-well to be honest I take the lazy approach and just assume that people who know how to put TV satellites in space and rovers on Mars can figure out the shape of Earth. However, in the discussion about light reflecting off a spherical shape I did test it myself and have produced some models in sketchup which illustrate that the FE model does not work.
3- Do you accept that there are paradoxes regarding all theories and observations?
-what do you consider a paradox?
1.a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory:
given this definition No I do not think that all theories and observations have paradoxes.
If, on the other hand, you mean "do we know everything about everything" I would say No we do not know everything about everything.
For example take the Bedford Canal Level Experiment.
Is it a paradox when a boat can be seen from 5 miles away from a point just above the water surface when at the same time poles 12 feet above the water shows a curve?
That would be true if we could not account for the discrepancy in a repeatable way. But the fact is that refraction can be measured and predicted. So it is not actually a paradox.
The fact that gravity does not work correctly at the subatomic level demonstrates the fact that we do not know everything about gravity but that is not a paradox that is an abscense of knowledge.
So maybe I am missing something or defining something different than you -what paradox do you think there is which makes the spherical shape of the Earth questionable?
"4- Do you accept the possibility that the reality could be different than what science tells you?"
-Yes, to a point. No use in questioning the shape of the Earth because it is extremely well documented and proven.
Black Holes on the other hand are not. The size, age, expansion and origin of the universe, light, gravity are all either not proven or obviously missing pieces of knowledge
"5- Does every observation have to fit into the frame of science? And if not you will come up with an explanation, even if you cannot prove it."
-Yes -Although maybe I do not understand what you are driving at here.
I believe in cause and effect -in other words there is no magic and there is a reason for everything. A theory is an unproven explanation so yes I like theories. I am particularly interested in theories about matter and space.