The consequence of a linear scientific measurements and the concept of a circle and infinity provides the option of proving almost anything to someone but very little to everyone.

An example is the one of distance, which equates to effort in an object moving through time. Note that the theory is that if enough effort is applied so that speed is 186,000 miles per second distance will no longer exist as time will be unmeasurable.

Back on simple Earth, for those of use that do not have interstellar or orbiting station we have only two tools at our disposal. a) our bodies ability to move around and b) our ability to think, both of which are limited in each person, to hugely different degrees. Young children and the aged and infirm are likely to have, relative to a physically strong and/or intellectually astute individual inadequate abilities to assess even the most basic states of the environment as the next example I hope will show.

Take the distance from point A to point B. Logic will define a straight line as the shortest distance between A and B. However this is only in logic practically speaking for someone unable to walk the distance would seem insurmountable without aid.

This diagram shows some of the parameters in flux,

The height of the mountain cannot be measure directly and has to be done mathematically and if you don't have the necessary skills you will not know, unless you believe someone else.

In the example A = Apex (top of the mountain, B = Base (height from adjacent land), F=Foot (the outer extreme of the mountain bulk where it merges with the surrounding ground. O is the position of the observer. AB = BF = FO

From overhead the distance between the OA (observer and apex) would appear the same as BO, but not having m own aircraft I can only walk OF and FA which is 2.4141 the height of the mountain or if the mountain was 1000m height a further 414meters than the apparent flat earth distance. So was id the distance?

If the mountain was vertical I would be and I am at the base on the flat earth view, from an aircraft above the mountain I would travel 0 metres however if I did climb to the top of the mountain I would travel the mountain height.

The proportional difference in distance is infinity.

So linear measurement must take into account not just latitude and longitiue but altitude direction none of which clearly account for gravity and it is moving in respect gravity that requires the effort. So who cares how far it is when all that matters is how easy or difficult changes position is.