[AstralSentient]

How do you distinguish between 1. lines intersecting and 2. the observer no longer having the visual acuity to perceive the distance between two points?

They are the same, perspective lines represent apparent distances converging.

[AstralSentient]

You SEE with your eyes that the two lines obviously meet - not very far (it seems) beyond the limits of the camera's lens or our visual acuity.  You never actually DO see the tracks meeting - but you presume that they must because you can draw the two lines on top of the photo - and it looks like they meet somewhere just fractionally beyond the resolution of the camera.

The limits of our visual acuity is the vanishing point. You said that we can perceive the distance between railroad tracks forever, but we can't, they converge at our angular resolution limit because we can't distinguish distances between points beyond that point, angles smaller than we can visualize.

So you conclude that parallel lines meet at some distance from the eye like maybe 10 miles or 100 miles or something...and base all of FET's optical properties on this, seemingly reasonable, claim.

That's our perspective indeed.

Now, let's talk about the building on the left.  You can draw a line at roof level and another one at ground level and see that they intersect...but what you're claiming is that this intersection is happening at some distance from us - 10 miles, 100 miles - whatever.   I'm claiming that...yes, the lines obviously intersect - but the DISTANCE at which they intersect is infinite.

Which means they never intersect, because infinity has no distance.

Now I hear you complaining.

About your flawed model of human perspective, indeed.

But look CAREFULLY at them in the picture.  Do you see that the separation between the columns in the photograph is smaller in the distance than it is near to the camera?

Yes, that's quite clear with our perception of far away distances.

So here is what's happening.  The closer together the roof line and the pavement line get - the more and more compressed the distance INTO the scene the picture becomes.   The horizontal spacing between columns get smaller and smaller.

This is correct, and my point deals exactly with this.

So when the roof/pavement lines would be VERY close to touching, they'd be representing something a billion miles into the scene - and at the precise point where the "perspective lines" touch - we are INFINITELY far into the scene.

Geometric lines, yes. They would have to more and more shallow and will be 0 at infinity, which is never. This assumes we have infinite aperture, which we don't, our perspective appears to intersect when distances become indistinguishable from a point.

X, Y and Z are *ALL* shrinking as we go further into the distance.

So when the X or Y distance hits zero - so the Z spacings of our columns ALSO hits zero - and you get an infinite number of columns packed together into that last screen pixel as we approach the vanishing point.

An THAT is why parallel lines meet at INFINITE Z and not 10 miles or 100 miles as FE'ers seem to believe.

Except our perspective lines of our vision aren't parallel.

Angular distances decrease to the limits of aperture of the optics so the distances between are indistinguishable, this is why the vanishing point and the horizon is finite, not infinite. You miss this entirely and pretend geometric angles can represent this when it can't.
The horizon is simply the distance in which the ground and sky are at angles smaller than the eye can see and so the horizon would be an illusion based on this.
You simply can't distinguish distances since your line of sight converges distances.

I can quite understand why this fooled you - and I have to say that it hurts my brain even thinking about it.  But regardless - this is what truly happens.

We aren't being fooled here, it's just you misunderstanding human perspective and applying it to geometric lines.

x' = k.x / z
   y' = k.y / z

(x,y,z) is a point in the real/virtual world (in a coordinate system where the "camera" is at (0,0,0) and z is distance away from the camera).
(x', y') is the point on the screen where that point ends up (in a coordinate system where the center of the screen is (0,0)).
   k     is a constant that relates to the 'lens' of the virtual camera and the size/resolution of the screen.

These two equations are built into every 3D computer game - every simulation, every CGI movie.  It's so fundamental that it's even built into the hardware of 3D graphics cards in your PC.

We do this because it's the only formula that produces realistic pictures.

So if one railroad rail is 1 meter to the right of the camera (x=+1) - then at what value of 'z' does it arrive at the vanishing point?

  x' = 0
  x  = +1

What is 'z'?

  0 = k . 1 / z

  z = k / 0

...hmmm - that's a problem because you can't divide by zero without getting an infinity for 'z'.

And that's the mathematical reason why parallel lines meet at infinity under perspective.

That's not perspective. Perspective would be the point which the distances between rails become unresolvable from a point.
You take parallel lines and they basically never meet, but you can't use them for perspective because perspective lines are not parallel, implying they meet at a distance by the angular distances receding.
Parallel lines meet at infinite distance, which means never, so you represent perspective lines as

When in reality, they are:

Therefore what you claim with the VP doesn't work.

The height of the image is the height of the subject (the tree) multiplied by the distance from the pinhole from the film and divided by the distance to the subject (the tree).

You make the mistake here as well. If I draw a straight line at an angle from an object at X height above the ground to the ground (where the the distance between objects to have a geometric vanishing point as you describe), it will always be at an angle above the ground unless the lines are parallel (which would mean infinite distance), so you conclude that the point of convergence or the horizon is at infinity. However, if this were true, then perspective lines could never approach each other, but they do, they would have to be parallel, which they aren't. This tears apart your flawed perspective model that doesn't work in reality.

The only way to discount this derivation of the math for perspective is to deny that light travels in straight lines - or to deny that the method of similar triangles is valid.

Actually, all I need to claim is that optics always have finite aperture for perceiving angular distance, and then what you claim is false when brought up against reality. Optics do always have finite aperture, therefore you are incorrect/

So the pinhole camera is proof of the equations - and the equations are proof of the laws of perspective.
The observation that perspective operates in Z as well as in X and Y is further proof that FET's concept of finite vanishing points is untrue.

No they aren't, they fail to represent perspective lines in reality, and so don't relate to perspective at all.

I think this argument is completely watertight - and so far, nobody in FE land has been willing to even discuss it.   Tom just says "it's just a diagram"...which is a rather fundamentalist anti-science, anti-math position - and if he were honest and consistent then he'd have to call "bullshit" on all of Rowbothams diagrams too!

A diagram of geometric lines isn't gonna represent the variable of human perspective limitations.

[AstralSentient]

To see if I understand properly, it sounds like you are saying that the change in angular velocity of an object as it passes has to do with the distance from the observer. This means that something farther away will have less change in angular velocity, until at some distance (say, 3000 miles), the change in angular velocity goes to zero. Is that correct?

Yes, the vertical perspective lines to the sky converge to where the angular distances between meet across to your horizon.

[StinkyOne]

Hey Super, can you explain to me how a low cloud can cast a shadow on a cloud higher in the sky around sunrise/sunset? For that to happen, the light source has to actually be below the level of the lowest cloud.

[AstralSentient]

No - they never "merge together" - that would happen only at infinity...which is OK in my view of perspective - but if your claim for perspective shrinking things to zero size only happens at 10 miles or whatever - then no - they have not "merged together".
But that can only happen at infinity - and the FE sun doesn't get to infinity...which is why it can never "set".

They never claimed it was at a nearby distance of 10 miles. Also, no, perspective lines meeting at infinity doesn't match reality, as I have pointed out. Perspective lines are not parallel, they are convergent. The horizon could only be a finite distance in human perspective.

Yeah - exactly.  The angle from your eye to the Cessna changes REALLY quickly when it's overhead and slows down to a barely perceptible angular change as it goes off into the distance.

It couldn't descend at a more constant rate by what you said, where vertical lines appear closer and closer together at farther distances regardless of object height. However, your model doesn't take the converging angular distances into account but assumes they never meet like parallel lines.

You FE sun would do the exact same thing.  It would track across the sky at crazy high speeds when overhead - and slow down to a crawl later in the day.

Already addressed in that post by Tom:

Consider that the vertical planks would also eventually merge together and into each other just like the horizontal planks do. The horizontal planks get so close together that they become one. The vertical planks would also merge into each other if they continued upwards far enough.

At higher altitudes, the vertical lines become more consistent in apparent distances.

BUT THIS ISN'T WHAT THE SUN REALLY DOES.   A simple measurement of the sun angle at regular intervals shows that it crosses the sky at a CONSTANT angular rate of around 15 degrees per hour.

Yeah, and it would do that with a high sun descending due to perspective on a flat plane.

The Flat Earth sun wouldn't do that - it would be maybe 30 degrees per hour when overhead and slow down to one or two degrees per hour in late afternoon.

From our perspective the horizon, the vertical 'planks' out in the distance converge to the same apparent angular distance as directly above, it gradually does at farther distances and the sun does it since it is beyond that point of convergence of vertical lines, and so descends constantly.

Your Cessna example is EXACTLY what we're saying your FE sun would do.   Since it clearly doesn't do that (and it doesn't change in size like the Cessna does either) - it's CLEARLY going in a circle around us.
Put this way:  If an object remains at the same size no matter what (true of Sun, moon, planets, comets and stars) then even with your "magic perspective" it cannot be changing in distance.

The sun does descend at a constant rate like the Cessna does to a larger extent at it's altitude, as you have pointed out.
You clearly haven't looked into the the position with the FES and Tom Bishop with the angular size of the sun as it descends, which you should before making a claim on it. Descent is independent of angular size as well.

If it's tracking across the sky at a constant angular rate of 15 degrees per hour and not changing distance - then it MUST be moving in a circle...not sliding along a horizontal plane as FET would have us believe.

And as explained already, it's high altitude would render it at a constant descent due to converging angular distances of vertical perspective lines.

So the only way you have out of this mess is to declare yet ANOTHER property of magic perspective.

It is not another new 'property', it has been known in basic perspective that perspective lines converge and aren't parallel.

* Magic perspective causes the sun to appear to be on the horizon.

Perpsective lines meet at a horizon, that forms the horizon.

* Magic perspective causes parallel lines to meet at the horizon.

Perspective lines aren't parallel, that's quite obvious in art.

* Magic perspective explains why the sizes of sun, moon, etc never change with distance.

It says no such thing, there isn't a breach of angular diameter here. Look into the FE views on the Sun.

Basically, so long as you never let yourself be tied down as to the actual path of photons through space - you'll continue to pile more and more unlikely properties into this vague "magic perspective" rabbit hole and hope we never find an inconsistency.

The path of photons into our eyes is limited by our perspective due to limited aperture, we can't perceive infinite light to see every angular distance distinction.

I suppose it's your best strategy - vagueness is definitely your best defense these days.

They aren't being vague here, it is a basic deducible concept.

If the jet was 10 times higher than the cessna and moving at 10 times the speed - and they were both overhead at the exact same instant and travelling in the exact same direction - then they'd appear to be in the same spot in your field of view.

This misses the point that vertical perspective lines meet at a high altitude and farther up to that point, the apparent angular distances between the vertical perspective lines become more similar since it is all viewed from you to the horizon and up. This implies a more constant descent of higher altitude moving objects.

The rate of change of angle would be the same for the jet as for the cessna...the law of similar triangles (or simple trigonometry)  proves that.

Which is wrong for our perspective of high and moving objects and disproven by the fact that apparent angular distances recede at distances even with vertical lines and looking up.

Go learn some high-school geometry...or draw a diagram if you don't believe me...I really can't be bothered to teach you basic math skills today.

They don't need to, you just keep missing the point.

That simply doesn't work.  So you're saying that once they are BEYOND the vanishing point...what exactly happens?

They disappear from our line of sight.

You know you're REALLY going to have to tell us where the photons go in these circumstances.

They may vary by other conditions but as interpreted by the limited aperture of your eyes, angular distances are indistinguishable after a finite distance, represented by convergent perspective lines.

[douglips]

If the jet was 10 times higher than the cessna and moving at 10 times the speed - and they were both overhead at the exact same instant and travelling in the exact same direction - then they'd appear to be in the same spot in your field of view.   The rate of change of angle would be the same for the jet as for the cessna...the law of similar triangles (or simple trigonometry)  proves that.

You've correctly deduced what I was getting at with my question.

If the FE position is that objects further away do not have a reduction in angular velocity, or have a reduced reduction in angular velocity, it is possible to design an experiment to prove or disprove this without relying on high school geometry, and you don't have to get a jetliner that flies 10,000 mph to do so.

If you are riding in a train and look out the window, you can see a mountain N miles away, and a lake N/2 miles away, and observe their angular velocities and see if the change in angular velocity is always the same.

Since Tom thinks that 45000 feet is enough to illustrate this proposal, we would only need to find a mountain that is 10 miles away from a railroad track.

The high school geometry model will tell us that the angular velocity of an object passing by at constant velocity v is v/r when it's at closest approach (90 degree angle to direction of travel), but at other angles the angular velocity is decreased by a factor of the sine of the angle from direction of travel. So, when something has moved 60 degrees from azimuth/closest approach, its angular velocity will be half of what it is at closest approach.

As a formula:
ω = (v/r) sin φ
where φ is the angle (less than or equal to 90 degrees) between the direction of travel and the direction the object is with respect to the observer

The Tom Bishop model is that angular velocity is v/r reduced by some other factor larger than the sine of the angle based on distance, tending towards 1 (no reduction) at 3000 miles. We don't have to guess what that factor might be, we could do this experiment and measure what that factor is to see if it differs from the sine in a measurable way. But, a reasonable guess for such a thing might be

If we did such an experiment, Tom Bishop, what results would prove to you that objects at any distance have the same angular velocity patterns? How far away should an object be to qualify to test this idea?

[AstralSentient]

Hey Super, can you explain to me how a low cloud can cast a shadow on a cloud higher in the sky around sunrise/sunset? For that to happen, the light source has to actually be below the level of the lowest cloud.

That is not relevant to the topic here (I frankly don't want to continue a conversation in the wrong thread), make a thread on it or point to me one to discuss it if you care to.

[douglips]

You SEE with your eyes that the two lines obviously meet - not very far (it seems) beyond the limits of the camera's lens or our visual acuity.  You never actually DO see the tracks meeting - but you presume that they must because you can draw the two lines on top of the photo - and it looks like they meet somewhere just fractionally beyond the resolution of the camera.

The limits of our visual acuity is the vanishing point. You said that we can perceive the distance between railroad tracks forever, but we can't, they converge at our angular resolution limit because we can't distinguish distances between points beyond that point, angles smaller than we can visualize.

It's ANGLES smaller than we can visualize, so the distance to the vanishing point depends on the size of the object or the distance between the perspective lines.

Here's an interesting image. If you take a picture of a long straight road from on a hill, the lines no longer seem to have a vanishing point, and you can clearly see the road still as a separate entity far in the distance. You can also see the edge of the roadbed that is significantly wider than the pavement, and it appears to be wider than the road the entire way.
https://i1.wp.com/unusualplaces.org/wp-content/uploads/2014/04/US50.jpg

So if something is large enough, we can see it at an arbitrarily large distance, no?

[Rama Set]

How do you distinguish between 1. lines intersecting and 2. the observer no longer having the visual acuity to perceive the distance between two points?

They are the same, perspective lines represent apparent distances converging.

Except I asked about intersecting, not converging.  It is obvious that lines converge at the vanishing point.  What is not obvious is when they intersect.

[AstralSentient]

It's ANGLES smaller than we can visualize, so the distance to the vanishing point depends on the size of the object or the distance between the perspective lines.

The distance between perspective lines at the line of sight decreases away from it not just straight out but out to the side as well. So, the apparent distances between perspective lines decrease as they are farther from our sight, so the perspectives lines appear to angle more when out of your line of sight to the horizon point within your line of sight. This means your field of vision as a frame shrinks to a point of convergence.
 
The distances between the perspective lines farther out the side get smaller since they are at a distance and so converge in association with your line of sight to the horizon.

So if something is large enough, we can see it at an arbitrarily large distance, no?

Yes, if it is a relatively large object like the sun, it can be seen in the sky a far distance. It also meets the horizon line which is the vertical angle of view, and the horizon is formed at an imperceptible angle.

[AstralSentient]

How do you distinguish between 1. lines intersecting and 2. the observer no longer having the visual acuity to perceive the distance between two points?

They are the same, perspective lines represent apparent distances converging.

Except I asked about intersecting, not converging.  It is obvious that lines converge at the vanishing point.  What is not obvious is when they intersect.

They are the same thing:


When lines intersect, they are converging. You asked how I distinguish between intersecting lines and the lacking of the visual acuity perceiving distances between two points. The answer is that the point where we lack the ability to distinguish between distances is the point of convergence. 'No distance' can only be represented by a point.

[Ga_x2]

Simplified in extreme, but will do. Does light travel in straight lines?

I don't necessarily accept that but am willing to grant it for this case, since light can travel in straight lines and what I'm saying here be correct.

Then draw a diagram of an object 6000 miles away and 3000 miles high, and draw the resulting perspective from the pov of a 2 m high observer with the correct field of vision for a human.

It's extremely relevant, I'm sorry. Our perception is a biological function. Look it up.

Not to perspective, I don't need to explain the biology of the eye to explain perspective lines, or that eyes have aperture like a lens.

see, that's where you are wrong. Aperture is not the only relevant thing. Lights enters the "lens" and hit the receptors at the back of your eye. The angle of incidence is preserved, that's how you see that something is higher than something else. If you lie on the ground, and look at the top of a 2 m high door, 4 m away, the light enters your eye with a ~20° angle. You see the door as higher than the floor. As you get further away, that angle diminishes, due to perspective. At a given point, the density of the receptors not being infinite, you can't resolve anymore and you can't perceive the height of the door anymore. Same thing with rail tracks.
Now. The sun, in your model, is 6000  miles away and 3000 miles up. That's a ~20° angle of incidence. You have plenty resolution to see it up in the sky. Basic perspective. End of the story.

EDIT: you can compare the density of the receptors in the eye to the resolution in pixels of a digital camera. The higher the resolution, the further away the tracks will "meet" in a single pixel, giving you the illusion that they actually meet.

[AstralSentient]

Then draw a diagram of an object 6000 miles away and 3000 miles high, and draw the resulting perspective from the pov of a 2 m high observer with the correct field of vision for a human.

Why? I don't see the relevance of bringing in a specific distance and height of objects and plotting a diagram of them. With the topic, we are talking about perspective and it working at distances and you want to bring in a specific dimension diagram of objects at a distance.

Aperture is not the only relevant thing.

What a way to criticize what I'm saying, that aperture is all that's relevant to perspective (I didn't imply it was all there is). You people completely ignored it and assumed all angles are visible to the eye since light is in straight lines and missed that we can't perceive every angle due to limitations of aperture and perspective angles to which we perceive as a horizon and point of convergence.

Lights enters the "lens" and hit the receptors at the back of your eye. The angle of incidence is preserved, that's how you see that something is higher than something else. If you lie on the ground, and look at the top of a 2 m high door, 4 m away, the light enters your eye with a ~20° angle. You see the door as higher than the floor. As you get further away, that angle diminishes, due to perspective. At a given point, the density of the receptors not being infinite, you can't resolve anymore and you can't perceive the height of the door anymore. Same thing with rail tracks.

Correct, the horizon is when the perspective lines approach each other at an angle we can't perceive, it's an illusion of perspective.
Farther perspective lines will converge steeper due to them being at a greater horizontal distance from our line of sight.

The sun, in your model, is 6000  miles away and 3000 miles up.

Who said my model? I'd be willing to entertain that the sun is at these dimensions but not claiming it must be and is not relevant to my point.

That's a ~20° angle of incidence. You have plenty resolution to see it up in the sky. Basic perspective.

Only, the sun's height line of descent would be steeper due to its vertical distance from our line of sight and so descends to meet the imperceptible angle at a larger angle. Think of a rail at a relatively far horizontal distance from your line of sight to convergence, the angle it reaches the point of convergence is larger due to its longer deviation from our line of sight. The same happens with the sun, it meets the horizon at the top of our uniform frame, where our entire field of vision converges. The top of that frame would be the steepest descent into the horizon. Higher objects move farther before reaching the same apparent horizon, which means they descend at a steeper angle, which is in proportion with a farther actual distance.
All objects will descend into our horizon line, which is from an imperceptible angle of view, by angling into it with accordance to altitude.
The angle of incidence you brought up misses that at higher altitudes, the perspective lines are meeting the same apparent horizon line from our perspective, this horizon defines all apparent relative movements and descents into convergence.

End of the story.

Hardly, an excuse to be able to forget it all won't work.

[Ga_x2]

Then draw a diagram of an object 6000 miles away and 3000 miles high, and draw the resulting perspective from the pov of a 2 m high observer with the correct field of vision for a human.

Why? I don't see the relevance of bringing in a specific distance and height of objects and plotting a diagram of them. With the topic, we are talking about perspective and it working at distances and you want to bring in a specific dimension diagram of objects at a distance.

you know, applying your model to an actual distance is the only way to ascertain whether it is correct or not.

Aperture is not the only relevant thing.

What a way to criticize what I'm saying, that aperture is all that's relevant to perspective (I didn't imply it was all there is). You people completely ignored it and assumed all angles are visible to the eye since light is in straight lines and missed that we can't perceive every angle due to limitations of aperture and perspective angles to which we perceive as a horizon and point of convergence.

the reason why we can't perceive every angle is exactly what I've explained about the density of the receptors. 

Lights enters the "lens" and hit the receptors at the back of your eye. The angle of incidence is preserved, that's how you see that something is higher than something else. If you lie on the ground, and look at the top of a 2 m high door, 4 m away, the light enters your eye with a ~20° angle. You see the door as higher than the floor. As you get further away, that angle diminishes, due to perspective. At a given point, the density of the receptors not being infinite, you can't resolve anymore and you can't perceive the height of the door anymore. Same thing with rail tracks.

Correct, the horizon is when the perspective lines approach each other at an angle we can't perceive, it's an illusion of perspective.
Farther perspective lines will converge steeper due to them being at a greater horizontal distance from our line of sight.

The sun, in your model, is 6000  miles away and 3000 miles up.

Who said my model? I'd be willing to entertain that the sun is at these dimensions but not claiming it must be and is not relevant to my point.

That's a ~20° angle of incidence. You have plenty resolution to see it up in the sky. Basic perspective.

Only, the sun's height line of descent would be steeper due to its vertical distance from our line of sight and so descends to meet the imperceptible angle at a larger angle. Think of a rail at a relatively far horizontal distance from your line of sight to convergence, the angle it reaches the point of convergence is larger due to its longer deviation from our line of sight. The same happens with the sun, it meets the horizon at the top of our uniform frame, where our entire field of vision converges. The top of that frame would be the steepest descent into the horizon. Higher objects will appear to move farther before reaching the same apparent horizon, which means they descend at a steeper angle proportion with a farther actual distance.
All objects will descend into our horizon line, which is from an imperceptible angle of view, by angling into it with accordance to altitude.

and this is where you stopped making sense, i'm sorry. Why should the sun be perceived differently from anything else? Suddenly you feel the need to change the methodology and come up with a different kind of perspective, where light stops working as it should, and the angles of incidence don't hold anymore. Please draw that diagram. If you don't believe me, do the reverse calculation. Look at what distance the sun should be from you, to be at a small enough angle to be near the vanishing point.

EDIT: I've seen know the image you attached, and that's a perfectly valid view. You do get how it works, why do you refuse to apply the method at the actual proposed distances?

[Rama Set]

How do you distinguish between 1. lines intersecting and 2. the observer no longer having the visual acuity to perceive the distance between two points?

They are the same, perspective lines represent apparent distances converging.

Except I asked about intersecting, not converging.  It is obvious that lines converge at the vanishing point.  What is not obvious is when they intersect.

They are the same thing:

(Picture clipped)

When lines intersect, they are converging.

Incorrect, not all converging lines intersect and intersecting lines are no longer converging, they have converged.

You asked how I distinguish between intersecting lines and the lacking of the visual acuity perceiving distances between two points

No I did't, I asked how you would distinguish between converging lines, lines that are coming to an intersection, but have not converged.

The answer is that the point where we lack the ability to distinguish between distances is the point of convergence. 'No distance' can only be represented by a point.

So then, you believe that the vanishing point is a literal convergence?  Train tracks are intersecting at the vanishing point?

[model 29]

How far away (when viewed from the side) would something 3,000 miles long need to be for it to appear as a single point in the distance?

[Ga_x2]

How far away (when viewed from the side) would something 3,000 miles long need to be for it to appear as a single point in the distance?

to be pedant, the question is not well posed... the human eye can resolve I believe ~0,02° so to the naked eye it should be I dunno a few million miles away? You do the math, it's late here 
But if you use a telescope you'll push it farther away
EDIT: I mean, by way of comparison, and I know it might not fly well in here, the moon is ~2000 miles wide, and ~240.000 miles away, and you still see it quite clearly

[3DGeek]

As usual, FE'ers can't get their heads around perspective - and efforts to explain it to them do not do well.

But perspective is just an artifact of the fact that light travels in straight lines - and the fact that to form an image of the world (either on your retina or a camera) you have to focus  rays of light to a point.

So an easier way to move the conversation forward is to take a step back and ask the more fundamental question:  How to photons travel?

We all agree (I think) that they travel in straight lines.

So it should be easy for FE'ers to explain which straight line the light travels along when their "magic perspective" makes it look as though the sun is setting.

Tom Bishop has repeatedly refused to answer this question - and Junker recently deleted an entire thread of mine that attempted to call him out on this (and he didn't even have the guts to post a notice saying that he'd deleted it).

So perhaps our new FE magic-perspective expert 'Sentient' will step up to the plate:

So here is the problem.  Our hero is standing in Texas - looking towards the rising sun (OK - so I accidentally drew the "sunset" diagram backwards!).

Sadly, the sunrise is partially hidden by a tree, ten miles away on the horizon.



Meanwhile, in Morocco, it's noon and the sun is somewhere close to zenith.   FET says that the sun is 3,000 miles overhead (give or take) and the distance from Texas to Morocco isn't known - but it's probably between 1,000 and 10,000 miles away.   I'm putting 6,000 miles into my diagram - but I'm prepared to be flexible on that point.



So - ignoring for the moment where the sun APPEARS to be.   What path do the photons of light take when leaving the sun, skimming past the tree and into our hero's eyes?

If it's a straight line (and Tom was so kind as to assert that light does indeed travel in straight lines) then the dark blue line is the path it MUST take - and none of it is blocked by the tree.  So you'd have to ask how come the tree is indeed blocking the light?   Even if some weird artifact of human vision - or some other "perspective" argument applies - the photons weren't blocked by the tree.

Now - if the light follows the pink path - then it is indeed blocked by the tree - but now it has a kink in it's path...which isn't right because light travels in straight lines.

Can you just PLEASE tell us what path the photons took from the sun to the eye without saying the word "perspective"?  I don't care what happens inside the eye - or how the image is resolved - just tell us very simply:  Which path did the light take?

[model 29]

How far away (when viewed from the side) would something 3,000 miles long need to be for it to appear as a single point in the distance?

to be pedant, the question is not well posed... the human eye can resolve I believe ~0,02° so to the naked eye it should be I dunno a few million miles away? You do the math, it's late here 
But if you use a telescope you'll push it farther away
EDIT: I mean, by way of comparison, and I know it might not fly well in here, the moon is ~2000 miles wide, and ~240.000 miles away, and you still see it quite clearly

Right.  The reason I asked is because if the sun is 3,000 miles high, it would need to be over 240,000 miles away to appear a distance above the horizon that even comes close to being equal to the size of the moon (since you provided the specs on the moon, I'll just use that). 

We're left with the sun and moon physically getting lower, or perspective causing the light to curve.

[Ga_x2]

Right.  The reason I asked is because if the sun is 3,000 miles high, it would need to be over 240,000 miles away to appear a distance above the horizon that even comes close to being equal to the size of the moon (since you provided the specs on the moon, I'll just use that). 

We're left with the sun and moon physically getting lower, or perspective causing the light to curve.

precisely. I realized later that that 3000 figure wasn't random
Anyway that's the point. If you accept that light travels in straight lines, then it's basic geometry. I tried using an online trig calculator, because i'm lazy, and to have 3000 miles within a 0,02° angle the result was above 8 million miles. I won't bet my life on the figure being correct, but it looks reasonable to me.
Of course it's out of wack with reality, but that doesn't seem to have ever given pause to the good folks here