[reer]

@ICanScienceThat
The problem with Rowbotham's treatment of perspective is that he changes his definition of the vanishing point halfway through the discussion. First it's the theoretical point where infinite parallel lines seem to meet, but then he changes it to the distance where we can no longer perceive something. Rather sneaky, in my opinion.

[Macarios]

Indeed, I did see that, and it's just really hard to make any sense out of it. Like there's a haze out there that's sky colored, right? Once you get too far from the viewer, everything just turns to the sky color... I guess? Except the Sun and the moon... and the stars... and stuff.

So yeah that makes no sense whatsoever... but there you go.  /shrug

Ok, if view limitation by air makes no sense, let's elliminate it from the equation.

This diagram here shows two observation points: altitude of U is 10 km,  altitude of L is 1 km.

In reality:
- U will have horizon at A, 357.3 km away
- L will have horizon at B, 112.9 km away

In Flat model:
Looking from L, the segment of the ground that covers 1/60th of a degree (1 arc minute) is from A to C.
C is at 323.66 km, which is 33.64 km closer than A.

If we select some random point M at, say, 233 km, then the ground segment between A and M will seen from L have angular size of 0.086 degrees (5.16 arc minutes).
That is more than 5 times bigger than the average human ability to distinguish details.

Why L can't see the segment AC?
Why L can't see the segment AM?

Why L can't see beyond B?




SL = 1 km
SU = 10 km
SB = 112.9 km
SM = 233.0 km
SC = 323.66 km
SA = 357.3 km

ALC = 1 arc min (1/60 = 0.0166666 degrees)
ALM = 5.16 arc min (0.086 degrees)
ALB = 21 arc min (0.35 degrees)

EDIT: I've made a mistake calculating C. The correction is in bold.

[ICanScienceThat]

Why L can't see the segment AC?
Why L can't see the segment AM?

Why L can't see beyond B?

I'm going to assume your math is correct because I'm lazy, and I see no reason to doubt you... All of those things should absolutely be visible on a flat Earth.

[Bikini Polaris]

Why L can't see the segment AC?
Why L can't see the segment AM?

Why L can't see beyond B?

I'm going to assume your math is correct because I'm lazy, and I see no reason to doubt you... All of those things should absolutely be visible on a flat Earth.

Maybe it's me but FEs won't measure distances, otherwise you could disprove the planarity of Earth in so many ways. Including this one, of course.

[spherical]

Macarios, lets remember the Tom Bishop Experiment on Wiki, where he was able to see children playing with frisbee (SB=) 48km away, belly flat on sand, so, no more than (SL=) 0.2m from the ground, using a "good telescope".  As far as I understand, the 1/60 of a degree rule doesn't change if you look with naked eye or through a telescope, right?  0.2/48000 = 0.0000042 = (arcrad) 0.000238° = 0°00'00"86.

[ICanScienceThat]

As far as I understand, the 1/60 of a degree rule doesn't change if you look with naked eye or through a telescope, right?  0.2/48000 = 0.0000042 = (arcrad) 0.000238° = 0°00'00"86.

I believe the 1/60 of a degree rule is strictly for the naked eye. Telescopes reduce that angle.