Well, we can continually allow Tom to babble on about perspective lines (which ONLY an artifact of focussing systems!) or we can talk like big boys in the 21st century and consider the photons.

If you take a large sheet of paper - or a big flat white-painted wall - let the sun shine onto it - can you see the sun as a big circle on the paper/wall?

No - you can't - and the reason is that the light isn't being focussed.

So in the image above, light rays from various parts of the sun are going off in every direction - the red lines from the top of the sun, the green lines from the center and the blue lines from the bottom go every which way - and no image appears.

So to form an image - you need some kind of device that focusses the light - it can be a lens or a curved mirror - or it can be a simple pinhole. Pinhole cameras work very well, they can photograph sunsets, they exhibit perspective and they are by far the simplest devices to discuss. So if we put a pinhole between the light source and the paper - we can exclude all of the light rays that are not going to help in forming an image:

..and now we have an image. And the lines I've drawn for "light rays" are also the paths of the photons...wave/particle duality and all of that.

"Perspective" can only emerge when we make an image - you can't talk about parallel lines meeting without talking about some kind of an imaging device. We know that the big lumps of steel that make up the rails on which trains run do not LITERALLY touch - that's something any child knows. They only APPEAR to touch (or perhaps come close to touching as I would argue) in images.

Without an imaging device, we cannot talk about perspective.

So there are two ways you can take this conversation:

1) We can continue to talk about "perspective" - but we have to ALWAYS remember that this conversation means nothing without including some kind of imaging device in our discussions.

2) We can forget about imaging devices - and stop talking about perspective and simply discuss how photons get from here to there.

I prefer the latter because it's simpler to understand - but I'm sufficiently knowlegeable and confident about my subject matter (being a 3D graphics expert...as my user-name implies) to discuss it from either debate position.

What you CANNOT DO - is to mix the two explanations as you feel like to make your argument work. You can't start off talking about the paths of free photons - and then flip into talking about perspective without first introducing a focussing device which has selectively cut out many of those free paths.

So - if you wish to continue to talk about perspective - and the PROOF that the "vanishing point" is at infinity - then may I refer you to this diagram from a previous thread:

...which allows one to use the pinhole camera and the law of similar triangles, to establish the relationship between distance in the real world (Hsubject) and distance on the image (Himage) as: Himage = Hsubject x Dimage / Dsubject. This is the essence of perspective. As the distance to the subject increases (Dsubject gets bigger) then Himage gets smaller. At what point does the sun reach the horizon? Well, that's when Himage is zero - and for that to be true then mathematically, one of three conditions must apply:

1) Dimage must be zero...but that would describe a zero-sized camera - which couldn't make an image of anything because ALL distances on the image would be zero and it could only take zero sized photographs!

2) Hsubject must be zero...which would mean that the sun was PHYSICALLY touching the ground - which would start fires in cities at noon!

3) Dsubject must be INFINITE...which is what really happens.

Since Dsubject being infinite is the ONLY solution to the pinhole camera experiment that get the sun to the horizon in a flat earth - you're going to have to admit that the vanishing point is at infinity.

That's the ONLY way that light can travel in straight lines through a pinhole camera and make an image of the sun at the horizon. The sun would have to be INFINITELY far away.

And by the way - we see the sun sink BELOW the horizon - and there are no sane values of Dimage, Dsubject or Hsubject that allow that to happen.

OK - so that's where your argument fails if you talk about focussed images...like what you see with your eye. This line of discussion produces an EQUATION for the height of the sun on a focussed image - and that proves that (a) the vanishing point is infinitely far away and (b) that there cannot be flat earth sunsets and therefore (c) the Earth is round.

HOWEVER:

You can also choose to ignore the entire concept of a focussed image - and just look at the path the photons must be taking to get from the sun, through the branches of a tree on the horizon and into my eye:

In this diagram, the blue line is the straight line path that the photons MUST be taking to get from the sun to my eyes...and the pink line is the line that they'd have to take if the sun was really on the horizon. Since we agree that photons travel in straight lines, the pink line cannot be the correct one.

Hence flat earth sunrises and sunsets cannot happen - and the Earth is round.

So either way - there is not getting out of this trap.

Tom - it's time for you to give this one up. None of the other FE'ers are coming to your rescue here.

At this point you either have to admit that the Earth is round - or drop your claim for photons travelling in straight lines...which essentially means a return to the Electromagnetic Accelerator idea...which does actually fix this problem. If light bends into a curve (as the EA theory claims) - then the photons can drop nearly vertically downwards from the sun in a gentle curve that skims the horizon and touches my eyes.

With EA - you can have sunsets on a flat earth - but you have to give up photons travelling in straight lines - and that's a BIG problem as I can prove if you do indeed return to that argument.

But magic perspective doesn't work...it fails the test of Euclidean geometry.