I'm talking about what happens in reality, not on a map.
In reality, what-I-believe-you-are-saying
is impossible.
In reality,
the shortest path between two points is
geographically a straight line - with-or-without any curvature "under" it. Such a line may be
represented on a Mercator map as a curved line - but, on a globe [earth map], it is
geographically a straight line with curvature "under" it.
Any curved line between those same two points is
longer - "There are no two ways about it..." - that is the [physical] reality.
I keep using the word 'geographically' (because it is the one you are used to hearing) to keep this in the 'map' realm.
The straight-line path between any two points on a sphere will pass
through the sphere; however,
within the 'geographical' context, it is a 'straight' line
across the surface of the sphere with curvature "under" it.
Where possible, ships and aircraft follow a curve, not a straight line for the reason I've explained.
Nope. What you are thinking about is
geographically a straight line [across the map].
If all you are trying to say is that - on a globe - the shortest path between two points - following a spherical surface curvature - is a curved line having spherical surface curvature "under" it (but geographically a straight line otherwise) --- then, I think we are in agreement!
If, on the other hand, you are saying that the shortest path between two points - following a spherical surface curvature - but, that is also curved in the lateral sense - such that it would appear curved on a globe [earth map] --- then, we are
not in agreement.
If the earth was flat, plotting a curved course is foolish.
If the earth was spherical, plotting a curved course is foolish. (by the same reasoning)
If a line is bent along the curve of a sphere, it is not straight.
In '3D' terms - of course - and, I explained that above.
In 'geographical' terms, the shortest path between two points is a straight line - period.
You argument assumes a flat earth.
Your argument assumes a globe earth.
And, for you to make a big deal over the curvature "under" a geographical straight line on a globe (if that is what you are doing) - is pretty needless and senseless in the context of the discussion - don't you think???
If all of this doesn't hit the mark precisely, then will you please attempt to explain yourself in a totally different way so that I may understand what you really meant...?
Because - from my perspective - all you are really trying to say is:
"The fact that the earth is a globe proves that the earth is a globe."
(Which is a profoundly illogical form of direct circular reasoning.)