https://www.theflatearthsociety.org/forum/index.php?topic=71053.msg1921473#msg1921473
So you can't fulfill his request and instead just link to the same old nonsense.
Perhaps the best part is you refute yourself, and then try to recover.
i.e. take RET, but then pretend Earth is flat. That is all this non-Euclidean BS is.
A good analogy here is the difference between heliocentrism and geocentrism. Ultimately it is just a choice of reference frame; choose one in which the Earth is stationary, and you can mathematically describe everything just fine. The model works. The reason RET favours heliocentrism now is explanatory power; heliocentrism can explain why the Earth goes around the Sun, and explain retrograde motion, while the geocentric explanation is questionable.
Ultimately is is not just a choice of reference frame. It is a choice of having explanations which make sense or pure nonsense.
It is the explanatory power which distinguishes the model.
Geocentrism cannot offer an explanation, nor can a non-flat flat Earth.
There is a reason we treat Euclidean space as the default.
Ignoring the minor variations due to gravity, straight parallel lines (such as lasers) remain equidistant in reality.