[Tom Haws]

When you are standing on the earth at sea level and look at the earth's eye level horizon you are creating a right angled triangle with the hypotenuse laying upon the surface of the earth.

OK.


<---------------------------------------------
|  A                                  B  ___----
|                               ___----
|                    ___----
|  C      ___----
___----


The earth here does not look flat to me, even at less than 1/60 degree.

When you increase in altitude, the angle of the triangle change and it takes a greater distance to create the requirement for the Vanishing Point, and so it is pushed backwards further into the distance to where the perspective lines are once again separated less than a minute of a degree. The Vanishing Point is now a greater distance away and new lands have been revealed.

When you increase in altitude, the angle of the triangle changes

Why. Please give evidence. I say this is what really happens on a flat earth (and, yes, a flat earth is often is the best model for a small distance):


<|----____
| A          ----____
|                        ----____
| C                 B                ----____
---------------------------------------------

and it takes a greater distance to create the requirement for the Vanishing Point, and so it is pushed backwards further into the distance to where the perspective lines are once again separated less than a minute of a degree. The Vanishing Point is now a greater distance away and new lands have been revealed.

This is not true. Consider your eye on a table. Raise it the least bit above the table and you can see anything on the opposite end (regardless of the length of the table) that takes up a larger angle of your view (the real phenomenon behind what you call perspective) than anything between it and your eye including irregularities on the table and atmospheric disturbances. It's all solely about angle of view and simple geometry. Nothing more. Nothing less. Even at less than 1/60 degrees.

[Curious Squirrel]

I wonder what would cause this “broadening” of perspective and “pushing” of the “vanishing point”.  Is it that the air is less dense?  The atmosphere gets significantly less dense toward the high altitudes, but the same thing (sunset, sunrise, sunset) is seen with a radio controlled drone going up and down only a few hundred feet where there is no measurable change in atmospheric conditions.

When you are standing on the earth at sea level and look at the earth's eye level horizon you are creating a right angled triangle with the hypotenuse laying upon the surface of the earth. The Angle A is the right angle at your eye, Angle B is at the horizon/vanishing point, and Angle C is straight down at your feet.  The Vanishing Point is created where the perspective lines at Angle B approach each other at less than a minute of a degree.

When you increase in altitude, the angle of the triangle change and it takes a greater distance to create the requirement for the Vanishing Point, and so it is pushed backwards further into the distance to where the perspective lines are once again separated less than a minute of a degree. The Vanishing Point is now a greater distance away and new lands have been revealed.

So, first off your eyes don't form a 90 degree angle. BUT, let's disregard that for a moment, as you've now given us some rules for how perspective works to create the horizon. Shall we put them to the test?

Let's take the Bishop experiment, where you claim to see a beach 23 miles away with your naked eye. Let's see how high you have to be in order to see this distance using the information just given.

Angle A: 90°
Side C: 23 miles
Angle B: 0.01666° (roughly a minute of a degree.)
https://www.triangle-calculator.com/?what=asa&a1=90&c=23&b1=.016666&submit=Solve Solved for side B (observer's height)

Looks here like you would need to be about 0.007 miles above sea level, or roughly 36 feet in order to see that far. Were you 36 feet above sea level Tom? Because otherwise your own experiment is proving you wrong here.

Correct. 0.01666.. degrees is a minute of a degree. However, if we scroll up we will find that I said less than a minute of a degree, and this is echoed in Earth Not a Globe. A minute of a degree is at the limit.

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

[Tom Haws]

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

I do not see any holes in the reasoning of CS here. The esoteric perspective hypothesis allows calculating the distance of the horizon as 1/tan(1/60) * height of eye or 3400 * height of eye. In this case, the height of eye is less than 6 feet, so the distance of horizon must be less than 20400 feet or 3.9 miles, unless my math is wrong. CS, our numbers don't exactly agree, but they are in the same ballpark, and I do get 36 feet up for a 23 mile view horizon.

[Roger G]

All of this twaddle about perspective is a red herring started by our old conman and jokester Rowbotham. The resolution of the human eye is the only relevant major factor in determining the distance that we can see with the naked eye, unless we take the curvature of the earth into consideration. If we take something the size of a snooker ball and move it to a distance that it is no longer visible to the naked eye, that will be down to the eye's resolving ability and will have absolutely nothing to do with lines of perspective or angles to the vanishing point. It will also make no difference how elevated the eye is in relation to the ball, it will still become invisible at the same distance. However, if we then apply a telescope to the eye, the ball will become visible to the eye once more. This of course is exactly how things should work on a flat earth, if the object is large enough to be within the arc of resolution of the eye, then it should be visible from any distance at ground level. A smaller object would be visible will a suitable magnifying instrument. Just as we can see the light of a star from billions of miles away, we would also be able to see any light source of suitable magnitude, such as the sun or moon, from any point of a flat earth at any time.

The reason we cannot view these things is because the earth is a sphere!

Roger

[Tom Bishop]

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

I do not see any holes in the reasoning of CS here. The esoteric perspective hypothesis allows calculating the distance of the horizon as 1/tan(1/60) * height of eye or 3400 * height of eye. In this case, the height of eye is less than 6 feet, so the distance of horizon must be less than 20400 feet or 3.9 miles, unless my math is wrong. CS, our numbers don't exactly agree, but they are in the same ballpark, and I do get 36 feet up for a 23 mile view horizon.

Except that I said less than a minute of a degree and did not really specify how much less.

[Curious Squirrel]

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

I do not see any holes in the reasoning of CS here. The esoteric perspective hypothesis allows calculating the distance of the horizon as 1/tan(1/60) * height of eye or 3400 * height of eye. In this case, the height of eye is less than 6 feet, so the distance of horizon must be less than 20400 feet or 3.9 miles, unless my math is wrong. CS, our numbers don't exactly agree, but they are in the same ballpark, and I do get 36 feet up for a 23 mile view horizon.

Except that I said less than a minute of a degree and did not really specify how much less.

Then why bother saying "The Vanishing Point is created where the perspective lines at Angle B approach each other at less than a minute of a degree" if you don't mean that's where it happens. Going less doesn't help your case in your experiment anyway. It's known the angular limit of the human eye is about 0.02 degrees. So you're right on the money there. Should we see the angle taking Tom Haws 6 feet in height out to 23 miles?

https://www.triangle-calculator.com/?what=sas&a=6&a1=90&b=121440&submit=Solve We get an angle of 0.003 degrees. A far cry from a minute of a degree. We're talking just 10.8 seconds of arc. Your perspective needs to collapse long before then in order to form the sharp horizon that can be seen at roughly 3 miles out when standing. So again, either your theory of perspective is incorrect, or your experiment is incorrect.

[Tom Bishop]

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

I do not see any holes in the reasoning of CS here. The esoteric perspective hypothesis allows calculating the distance of the horizon as 1/tan(1/60) * height of eye or 3400 * height of eye. In this case, the height of eye is less than 6 feet, so the distance of horizon must be less than 20400 feet or 3.9 miles, unless my math is wrong. CS, our numbers don't exactly agree, but they are in the same ballpark, and I do get 36 feet up for a 23 mile view horizon.

Except that I said less than a minute of a degree and did not really specify how much less.

Then why bother saying "The Vanishing Point is created where the perspective lines at Angle B approach each other at less than a minute of a degree" if you don't mean that's where it happens. Going less doesn't help your case in your experiment anyway. It's known the angular limit of the human eye is about 0.02 degrees. So you're right on the money there. Should we see the angle taking Tom Haws 6 feet in height out to 23 miles?

https://www.triangle-calculator.com/?what=sas&a=6&a1=90&b=121440&submit=Solve We get an angle of 0.003 degrees. A far cry from a minute of a degree. We're talking just 10.8 seconds of arc. Your perspective needs to collapse long before then in order to form the sharp horizon that can be seen at roughly 3 miles out when standing. So again, either your theory of perspective is incorrect, or your experiment is incorrect.

The perspective theory is not in contradiction. The minute of a degree mainly refers to human eyesight. But the Monterey Bay experiment you are referencing uses a telescope, not just human eyesight. There is also an effect in our literature where objects beyond the Vanishing Point can be restored by looking at them through a telescope. See: https://wiki.tfes.org/Sinking_Ship_Effect

[StinkyOne]

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

I do not see any holes in the reasoning of CS here. The esoteric perspective hypothesis allows calculating the distance of the horizon as 1/tan(1/60) * height of eye or 3400 * height of eye. In this case, the height of eye is less than 6 feet, so the distance of horizon must be less than 20400 feet or 3.9 miles, unless my math is wrong. CS, our numbers don't exactly agree, but they are in the same ballpark, and I do get 36 feet up for a 23 mile view horizon.

Except that I said less than a minute of a degree and did not really specify how much less.

Then why bother saying "The Vanishing Point is created where the perspective lines at Angle B approach each other at less than a minute of a degree" if you don't mean that's where it happens. Going less doesn't help your case in your experiment anyway. It's known the angular limit of the human eye is about 0.02 degrees. So you're right on the money there. Should we see the angle taking Tom Haws 6 feet in height out to 23 miles?

https://www.triangle-calculator.com/?what=sas&a=6&a1=90&b=121440&submit=Solve We get an angle of 0.003 degrees. A far cry from a minute of a degree. We're talking just 10.8 seconds of arc. Your perspective needs to collapse long before then in order to form the sharp horizon that can be seen at roughly 3 miles out when standing. So again, either your theory of perspective is incorrect, or your experiment is incorrect.

The perspective theory is not in contradiction. The minute of a degree mainly refers to human eyesight. But the Monterey Bay experiment you are referencing uses a telescope, not just human eyesight. There is also an effect in our literature where objects beyond the Vanishing Point can be restored by looking at them through a telescope. See: https://wiki.tfes.org/Sinking_Ship_Effect

The sinking ship effect is not true and telescopes do NOT bring ships back above the horizon.


https://crberryauthor.files.wordpress.com/2015/08/shiphorp.jpg

[Pete Svarrior]

The sinking ship effect is not true

The Sinking Ship Effect is not true. Here is a picture illustrating the Sinking Ship Effect!

Buddy, pick a line and stick to it. It appears that you're trying to act as if you disagreed about the cause of the effect.

[Tom Haws]

The perspective theory is not in contradiction. The minute of a degree mainly refers to human eyesight. But the Monterey Bay experiment you are referencing uses a telescope, not just human eyesight. There is also an effect in our literature where objects beyond the Vanishing Point can be restored by looking at them through a telescope. See: https://wiki.tfes.org/Sinking_Ship_Effect

You are tantalizingly close ("human eyesight" and "restored by...telescope"), but you deny the implications of what you are saying. Your esoteric "perspective theory" flies in the face of the accepted fact that perspective is simply an artistic device (invention of artists) for projecting reality onto a painter's canvas. Perspective is not a physical reality.

Your 3000-mile-high Sun is 10 degrees above the horizon at 17000 miles away. Just how far away is your sun at maximum sunrise/sunset distance?

[Tom Haws]

The sinking ship effect is not true

Buddy, pick a line and stick to it. It appears that you're trying to act as if you disagreed about the cause of the effect.

StinkyOne, please clarify. I have often said that according to this site, nothing rises and sets. Sun, moon, stars, mountains, buildings, and ships do not rise and set; they just fade or shrink. And I believe that's very clear.

Are you referring to a "sinking ship effect" explanation in the Wiki?

[StinkyOne]

The sinking ship effect is not true

Buddy, pick a line and stick to it. It appears that you're trying to act as if you disagreed about the cause of the effect.

StinkyOne, please clarify. I have often said that according to this site, nothing rises and sets. Sun, moon, stars, mountains, buildings, and ships do not rise and set; they just fade or shrink. And I believe that's very clear.

Are you referring to a "sinking ship effect" explanation in the Wiki?

Sorry, I should have been more clear. Posting in a hurry is a bad idea. I'm referring to the FEH Sinking Ship effect where a ship's hull appears to have "merged" with the horizon. It claims the ship's hull can be visualized with a telescope after it has "merged". In fact, the hull has gone over the horizon and is no longer visible. They try to get around this by saying the ship is behind a "hill" of water.

[Tom Haws]

They try to get around this by saying the ship is behind a "hill" of water.

A hill of water that arises only in front of remote objects? Isn't this tantamount to invoking the Round Earth? Non-parallel gravity?

[StinkyOne]

They try to get around this by saying the ship is behind a "hill" of water.

A hill of water that arises only in front of remote objects? Isn't this tantamount to invoking the Round Earth? Non-parallel gravity?

As it turns out, these hills can be quite extensive and uniform.  Here, one of these hills hides the city of Chicago.


http://rockrivertimes.com/wpcms/wp-content/uploads/2015/11/chicago_lake-800x445.jpg

[Tom Bishop]

The sinking effect is addressed in Earth Not a Globe. You should read it sometime.

[Curious Squirrel]

The sinking effect is addressed in Earth Not a Globe. You should read it sometime.

Only if you believe what's written in there, but other parts of the book bring the whole thing into question.

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

I do not see any holes in the reasoning of CS here. The esoteric perspective hypothesis allows calculating the distance of the horizon as 1/tan(1/60) * height of eye or 3400 * height of eye. In this case, the height of eye is less than 6 feet, so the distance of horizon must be less than 20400 feet or 3.9 miles, unless my math is wrong. CS, our numbers don't exactly agree, but they are in the same ballpark, and I do get 36 feet up for a 23 mile view horizon.

Except that I said less than a minute of a degree and did not really specify how much less.

Then why bother saying "The Vanishing Point is created where the perspective lines at Angle B approach each other at less than a minute of a degree" if you don't mean that's where it happens. Going less doesn't help your case in your experiment anyway. It's known the angular limit of the human eye is about 0.02 degrees. So you're right on the money there. Should we see the angle taking Tom Haws 6 feet in height out to 23 miles?

https://www.triangle-calculator.com/?what=sas&a=6&a1=90&b=121440&submit=Solve We get an angle of 0.003 degrees. A far cry from a minute of a degree. We're talking just 10.8 seconds of arc. Your perspective needs to collapse long before then in order to form the sharp horizon that can be seen at roughly 3 miles out when standing. So again, either your theory of perspective is incorrect, or your experiment is incorrect.

The perspective theory is not in contradiction. The minute of a degree mainly refers to human eyesight. But the Monterey Bay experiment you are referencing uses a telescope, not just human eyesight. There is also an effect in our literature where objects beyond the Vanishing Point can be restored by looking at them through a telescope. See: https://wiki.tfes.org/Sinking_Ship_Effect

It is when you claim you can see the beach with the naked eye. Both in the wiki and in your original report on it. "On a very clear and chilly day it is possible to see Lighthouse Beach from Lovers Point and vice versa." Yes you then go on to say you can see people playing on the beach with a telescope (which there are many people remarking on the impossibility without magic optics).

[Tom Bishop]

The sinking effect is addressed in Earth Not a Globe. You should read it sometime.

Only if you believe what's written in there, but other parts of the book bring the whole thing into question.

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

I do not see any holes in the reasoning of CS here. The esoteric perspective hypothesis allows calculating the distance of the horizon as 1/tan(1/60) * height of eye or 3400 * height of eye. In this case, the height of eye is less than 6 feet, so the distance of horizon must be less than 20400 feet or 3.9 miles, unless my math is wrong. CS, our numbers don't exactly agree, but they are in the same ballpark, and I do get 36 feet up for a 23 mile view horizon.

Except that I said less than a minute of a degree and did not really specify how much less.

Then why bother saying "The Vanishing Point is created where the perspective lines at Angle B approach each other at less than a minute of a degree" if you don't mean that's where it happens. Going less doesn't help your case in your experiment anyway. It's known the angular limit of the human eye is about 0.02 degrees. So you're right on the money there. Should we see the angle taking Tom Haws 6 feet in height out to 23 miles?

https://www.triangle-calculator.com/?what=sas&a=6&a1=90&b=121440&submit=Solve We get an angle of 0.003 degrees. A far cry from a minute of a degree. We're talking just 10.8 seconds of arc. Your perspective needs to collapse long before then in order to form the sharp horizon that can be seen at roughly 3 miles out when standing. So again, either your theory of perspective is incorrect, or your experiment is incorrect.

The perspective theory is not in contradiction. The minute of a degree mainly refers to human eyesight. But the Monterey Bay experiment you are referencing uses a telescope, not just human eyesight. There is also an effect in our literature where objects beyond the Vanishing Point can be restored by looking at them through a telescope. See: https://wiki.tfes.org/Sinking_Ship_Effect

It is when you claim you can see the beach with the naked eye. Both in the wiki and in your original report on it. "On a very clear and chilly day it is possible to see Lighthouse Beach from Lovers Point and vice versa." Yes you then go on to say you can see people playing on the beach with a telescope (which there are many people remarking on the impossibility without magic optics).

Where does it specify with or without the naked eye in the quote "On a very clear and chilly day it is possible to see Lighthouse Beach from Lovers Point and vice versa" ?

[StinkyOne]

The sinking effect is addressed in Earth Not a Globe. You should read it sometime.

Actually Tom, I am reading it. Already made one post about the Earth floating on water. It's a very good study in the value of experts and the glaring limitations of the backyard Zetetist.

[Curious Squirrel]

The sinking effect is addressed in Earth Not a Globe. You should read it sometime.

Only if you believe what's written in there, but other parts of the book bring the whole thing into question.

Yes. So at a minute of a degree is where the horizon line would be. At 23 miles, you must be 36 feet in the air in order to have your perspective lines meet there to allow you to see that far. If you were say, only 10 feet up, your horizon would be 10 miles out. A far cry from your 23 miles in your experiment. Your experiment shows that your hypothesis for perspective is incorrect. It cannot work in the manner you describe, or you could not have seen the opposite shore 23 miles away. You have debunked your own hypothesis, unless your experiment was done in error.

I do not see any holes in the reasoning of CS here. The esoteric perspective hypothesis allows calculating the distance of the horizon as 1/tan(1/60) * height of eye or 3400 * height of eye. In this case, the height of eye is less than 6 feet, so the distance of horizon must be less than 20400 feet or 3.9 miles, unless my math is wrong. CS, our numbers don't exactly agree, but they are in the same ballpark, and I do get 36 feet up for a 23 mile view horizon.

Except that I said less than a minute of a degree and did not really specify how much less.

Then why bother saying "The Vanishing Point is created where the perspective lines at Angle B approach each other at less than a minute of a degree" if you don't mean that's where it happens. Going less doesn't help your case in your experiment anyway. It's known the angular limit of the human eye is about 0.02 degrees. So you're right on the money there. Should we see the angle taking Tom Haws 6 feet in height out to 23 miles?

https://www.triangle-calculator.com/?what=sas&a=6&a1=90&b=121440&submit=Solve We get an angle of 0.003 degrees. A far cry from a minute of a degree. We're talking just 10.8 seconds of arc. Your perspective needs to collapse long before then in order to form the sharp horizon that can be seen at roughly 3 miles out when standing. So again, either your theory of perspective is incorrect, or your experiment is incorrect.

The perspective theory is not in contradiction. The minute of a degree mainly refers to human eyesight. But the Monterey Bay experiment you are referencing uses a telescope, not just human eyesight. There is also an effect in our literature where objects beyond the Vanishing Point can be restored by looking at them through a telescope. See: https://wiki.tfes.org/Sinking_Ship_Effect

It is when you claim you can see the beach with the naked eye. Both in the wiki and in your original report on it. "On a very clear and chilly day it is possible to see Lighthouse Beach from Lovers Point and vice versa." Yes you then go on to say you can see people playing on the beach with a telescope (which there are many people remarking on the impossibility without magic optics).

Where does it specify with or without the naked eye in the quote "On a very clear and chilly day it is possible to see Lighthouse Beach from Lovers Point and vice versa" ?

My apologies. I should have taken the whole thing. I'll even bold the relevant bits, the first where it implies that sentence is speaking about unaided eyes, and the second where you explicitly call out using an unaided eye.

"On a very clear and chilly day it is possible to see Lighthouse Beach from Lovers Point and vice versa. With a good telescope, laying down on the stomach at the edge of the shore on the Lovers Point beach 20 inches above the sea level it is possible to see people at the waters edge on the adjacent beach 33 miles away. I can see children running in and out of the water, splashing and playing. I can see people sun bathing at the shore and teenagers merrily throwing Frisbees to one another. I can see runners jogging along the water's edge with their dogs. From my vantage point the entire beach is visible. Even with the unaided naked eye one can see the beaches along the opposite coast."

As I recall in this thread, or another here you were quite insistent on naked eye observations, but if you object I can certainly go looking for those too. This is however still YOUR experiment. I'm simply trying to interpret what has been written in the wiki and your original report. Both locations appear to be stating you were seeing at least the beach with your naked eye. Is this correct?

[Roger G]

Some of Tom's experiment report seems to be a bit contradictory. He talks about a clear and chilly day, but at the same time talks about people sunbathing on the beach and children splashing in the water and running into the sea. They must be very hardy people who use lighthouse beach, sunbathing on chilly days while letting their children play in the water in chilly conditions. Either that or Tom's nose has grown a little longer and there is some artistic license. I'm also surprised that he could see over the tops of all the waves whilst laying on the chilly beach!

Roger