If it makes it easier, try imagining following a compass due east when you are just twenty feet from the north pole.
Did you travel in a straight line or in a circle?
It's hardly a moot point from your position because the straight lines paths due east in the southern hemisphere in reality trend northward rather than southward.
That is an entirely different point from the one he was trying to make.
That's exactly my point. When you are 20 feet from the north pole the distance between you and the north pole is effectively flat and you see what would happen to your compass if the world was flat rather than round. Its only with curvature that compasses can actually perform like they do in real life. Its only with curvature that a compass will continue to point east if you travel in a straight line.
You are wrong on this one. I believe the earth is round. I also know that the only place on a globe where you can travel a heading of true east or west and have it be a straight line is at the equator. Every other path with an east or west heading will result in a curved line.
Yes, the line will be curved because the surface of the earth is curved but you won't have to constantly change course. You can effectively take your hands off the wheel and you will maintain a due east/west course. This kind of behavior is impossible on a flat earth. Sorry for the confusion, I was trying to simplify things for people who aren't familiar with navigation but I think I confused you in the process because you actually understand how travel over the earth actually occurs.
The only "hand off" perfectly straight courses are those that bisect the center of the earth. The only straight course with constant headings would be east/west at the equator or true north/south courses. Latitude constant courses other than the equator do not bisect the center of the earth. They cannot be followed "hand off". They require constant "hands on" to follow a heading because they are not straight paths. If latitude lines where straight "hand off" courses then aircraft would use them to fly from LA to Tokyo. They don't use that course because it's not a great circle route. The shortest straight line path goes up near Alaska. The latitude line isn't shorter because it's not "hands off" straight. It's actually curved. The challenge to "hands off" straight great circle routes is that they have constantly changing headings.
Like I said before, you've got some concept errors. Even if LA to Tokyo was a "hands off" course the airline companies wouldn't fly it because its not a great circle route route. A great circle route is the shortest distance between two points on a spherical surface. Airline companies fly great circle routes because it saves gas, not because its easier on the pilots. However, if you go due east on a course and you don't adjust your heading after 1,000 miles you will still be going due east. Its pretty easy to prove this to yourself. Simplify the sphere to a circle seen from the side. Draw a horizontal line of constant latitude. Now, draw a line that bisects the pole. What angle do the lines make? Its a 90 degree angle. Now, rotate your globe any number of degrees and do the same thing again. Its still a 90 degree angle. You can keep going due east and it will always make a 90 angle with due north. Thus, you can have a "hands off" course at any latitude and still maintain a constant course.
It seems like you're confusing "hands off", straight, and shortest course. The shortest course is a great circle route. This could also be argue as the "straightest" course since it is the shortest distance over a curved surface. However, great circle routes are NOT hands off courses.
What I am talking about is the route you would take if you didn't make any course corrections what-so-ever and how your heading would differ on a flat earth vice a round earth. On a round earth if you begin by going due east and don't change your course for 1,000 miles you will still be going due east after 1,000 miles. On a flat earth for every one degree of longitude you cross you will point one degree further south.