Why vanishing points don't work that way [Math intensive]

The crux of the Flat Earth Wiki's argument for the Sinking Ship Effect is vanishing points, is it not.  The beginning of the argument is that humans cannot see to infinity, so there has to be a finite vanishing point.  Mathematically, this cannot and does not make sense.

If the actual height of an object is d and the distance to it is x, the perceived height h(d,x)=d/x.  It's that simple.  (All values assumed to be non-zero)

At the vanishing point, wherever it is, h(d,x)=0.  That's what it means by vanishing.  Let's solve for a distance x where this happens.  0=d/x -> 0*x=d -> 0=some non-zero number.  Hmm...  That doesn't quite work with math.  But what this shows, is that mathematically there cannot be a finite vanishing point.

So where is the vanishing point, then?  At infinity.  h(d,∞)=d/∞.  But wait.  We can't actually divide by infinity.  Thankfully, calculus has a way for us to do this, called limits.  lim(x+->∞)d/x=0.  The mathematical law at work here is that if the degree of the denominator (1) is greater than that of the numerator (0), it approaches 0 at infinity.  So this means that if an object could be seen from infinity, then and only then would its perceived height be 0.

First of all, this really isn't particularly mathematically intensive.


Second, you are misunderstanding something fundamental: f(x) does not have to equal zero. It simply has to be small enough that the human eye does not perceive it.

Now, the internet tells us that the smallest object visible to the human eye is ~0.1 mm. So h(d,x)<.0002 m.
d/x < .0002
For argument's sake, let's make the object 2 meters tall (btw, why is distance x and height d? Doesn't vice versa make more sense?)

2/x < .0002
2 < .0002x
10,000 < x

So that's 10 km, which sounds about right for a perfectly clear day on a perfectly flat plane that isn't a body of water. In fact, wikipedia tells us that in the arctic one can see as far as 100 km on a good day, so 10 km seems a perfectly reasonable estimate.

And this isn't even getting to the specifics of the theory, such as wave action.

You also have to consider that the atmosphere is not perfectly translucent, as well as waves getting in the way of your field of view.

Now, the internet tells us that the smallest object visible to the human eye is ~0.1 mm. So h(d,x)<.0002 m.
d/x < .0002
For argument's sake, let's make the object 2 meters tall (btw, why is distance x and height d? Doesn't vice versa make more sense?)

2/x < .0002
2 < .0002x
10,000 < x

So that's 10 km, which sounds about right for a perfectly clear day on a perfectly flat plane that isn't a body of water. In fact, wikipedia tells us that in the arctic one can see as far as 100 km on a good day, so 10 km seems a perfectly reasonable estimate.

See a person at 10km ?  That's good eyesight.  Wait until you're my age mate 

So at (ahem) 32miles in diameter (50km in modern measurements) should be visible at ~25,000,000 km.

But it disappears at night 

See a person at 10km ?  That's good eyesight.  Wait until you're my age mate 

A rock that looks like something else.  Mmmmmm

15?

Quote from: Major Twang on December 10, 2012, 01:39:47 PM

See a person at 10km ?  That's good eyesight.  Wait until you're my age mate 

Quote from: Major Twang on December 07, 2012, 11:51:19 AM

A rock that looks like something else.  Mmmmmm

15?

Hahaha - I'm 48, but my sense of humour is still going through puberty.

Quote from: Tausami on December 09, 2012, 07:25:20 PM

Now, the internet tells us that the smallest object visible to the human eye is ~0.1 mm. So h(d,x)<.0002 m.
d/x < .0002
For argument's sake, let's make the object 2 meters tall (btw, why is distance x and height d? Doesn't vice versa make more sense?)

2/x < .0002
2 < .0002x
10,000 < x

So that's 10 km, which sounds about right for a perfectly clear day on a perfectly flat plane that isn't a body of water. In fact, wikipedia tells us that in the arctic one can see as far as 100 km on a good day, so 10 km seems a perfectly reasonable estimate.

See a person at 10km ?  That's good eyesight.  Wait until you're my age mate 

So at (ahem) 32miles in diameter (50km in modern measurements) should be visible at ~25,000,000 km.

But it disappears at night 

before this gets ignored, please explain FE'ers

Quote from: canucks#01fan on December 10, 2012, 11:46:39 PM

See a person at 10km ?  That's good eyesight.  Wait until you're my age mate 

So at (ahem) 32miles in diameter (50km in modern measurements) should be visible at ~25,000,000 km.

But it disappears at night 

before this gets ignored, please explain FE'ers

Twang simply forgot to take mulitple variables into account. For example, the atmolayer is not 100% transparent. You can't see through air for long distances any more than you can see more than five meters in a thick fog. Eventually the light from the Sun ceases to reach you and from your observer standpoint, everything is dark.

Twang simply forgot to take mulitple variables into account. For example, the atmolayer is not 100% transparent. You can't see through air for long distances any more than you can see more than five meters in a thick fog. Eventually the light from the Sun ceases to reach you and from your observer standpoint, everything is dark.

Yes - it goes dark shortly after the sun has disappeared below the horizon.  Have you never noticed this phenomena ?

Quote from: Rushy on December 11, 2012, 06:48:34 AM

Twang simply forgot to take mulitple variables into account. For example, the atmolayer is not 100% transparent. You can't see through air for long distances any more than you can see more than five meters in a thick fog. Eventually the light from the Sun ceases to reach you and from your observer standpoint, everything is dark.

Yes - it goes dark shortly after the sun has disappeared below the horizon.  Have you never noticed this phenomena ?

Do you have any evidence to support this outlandish claim?

Quote from: Major Twang on December 11, 2012, 12:33:00 PM

Quote from: Rushy on December 11, 2012, 06:48:34 AM

Twang simply forgot to take mulitple variables into account. For example, the atmolayer is not 100% transparent. You can't see through air for long distances any more than you can see more than five meters in a thick fog. Eventually the light from the Sun ceases to reach you and from your observer standpoint, everything is dark.

Yes - it goes dark shortly after the sun has disappeared below the horizon.  Have you never noticed this phenomena ?

Do you have any evidence to support this outlandish claim?

other than everyone seeing it everyday with our own eyes?

Quote from: Rushy on December 11, 2012, 06:48:34 AM

Twang simply forgot to take mulitple variables into account. For example, the atmolayer is not 100% transparent. You can't see through air for long distances any more than you can see more than five meters in a thick fog. Eventually the light from the Sun ceases to reach you and from your observer standpoint, everything is dark.

Yes - it goes dark shortly after the sun has disappeared below the horizon.  Have you never noticed this phenomena ?

The horizon is a trick of perception related to refraction (from differing densities between aether and air, as well as the Earth's acceleration) and the eyewalls.

Quick question, what are eyewalls? I hope it's not what my imagination has come up with.

The sun doesn't get smaller and then disappear because the light " can't reach us anymore". It dips down below the horizon. You can't see the light because you can't see the sun anymore form your location on Earth.

The sun doesn't get smaller and then disappear because the light " can't reach us anymore". It dips down below the horizon. You can't see the light because you can't see the sun anymore form your location on Earth.

However, when I was a child living in Bolton, I used to be fascinated by the Winter Hill Transmitter. 

On clear evenings after sunset, you could see it still brightly lit up by the reddish light of the setting sun for a good 10 or 15 minutes after the sun had gone down.  You can also see the effect after sunset on aircraft, which are brightly lit by sunlight for a significant time after sunset.

And can I just remind everyone that it drops below the horizon at the precise time & position that is predicted by a fairly straightforward bit of spherical geometry, and a correction for the known refractive index of the air.

For this to work on a planar Earth, the effect of UA would have to somehow bend the light of the sun in the opposite direction to known refraction, and to do so by exactly the right amount needed to preserve the illusion of a round earth rotating & orbiting the sun no matter where you are, what time it is or what time of the year.

I don't understand how if the sun moved away like they describe, aircraft could be lit like you describe, as well as the moon. The light can't reach us but it reflects off the surface of the moon?

I don't understand how if the sun moved away like they describe, aircraft could be lit like you describe, as well as the moon. The light can't reach us but it reflects off the surface of the moon?

BOOM.


These guys are lost. It's sad that they don't realize it.

The medium between the sun and moon is not the same as the medium between the sun and the earth.

The medium between the sun and moon is not the same as the medium between the sun and the earth.

If the Earth was flat you would be able to stand in an open plane at night and see the sun in the distance

Quote from: Tom Bishop on December 20, 2012, 11:09:54 AM

The medium between the sun and moon is not the same as the medium between the sun and the earth.

If the Earth was flat you would be able to stand in an open plane at night and see the sun in the distance

Perhaps if terrestrial perspective were not a factor, our eyes could see infinity into the distance, refraction did not exist, and the atmosphere was perfectly transparent.

Quote from: Sphere on December 20, 2012, 11:16:14 AM

Quote from: Tom Bishop on December 20, 2012, 11:09:54 AM

The medium between the sun and moon is not the same as the medium between the sun and the earth.

If the Earth was flat you would be able to stand in an open plane at night and see the sun in the distance

Perhaps if terrestrial perspective were not a factor, our eyes could see infinity into the distance, refraction did not exist, and the atmosphere were perfectly transparent.

So even though the sun is bright enough to blind us and light up the ground to the point where we like to wear sunglass. It's not bright enough to see from, let's say 2000 miles away, and we can't see it, even though it shines on the moon very brightly


Yeah, right.....

Quote from: Tom Bishop on December 20, 2012, 11:17:21 AM

Quote from: Sphere on December 20, 2012, 11:16:14 AM

Quote from: Tom Bishop on December 20, 2012, 11:09:54 AM

The medium between the sun and moon is not the same as the medium between the sun and the earth.

If the Earth was flat you would be able to stand in an open plane at night and see the sun in the distance

Perhaps if terrestrial perspective were not a factor, our eyes could see infinity into the distance, refraction did not exist, and the atmosphere were perfectly transparent.

So even though the sun is bright enough to blind us and light up the ground to the point where we like to wear sunglass. It's not bright enough to see from, let's say 2000 miles away, and we can't see it, even though it shines on the moon very brightly


Yeah, right.....

Have you even seen a sunset? Most of the time sunsets look like this:

If the fet was true, it would move far off to the point where it's tiny. Not dip behind the earth

Sense. It makes none. So I guess the fet is false, huh?

As for the RET, and it makes perfect sense

The medium between the sun and moon is not the same as the medium between the sun and the earth.

Please provide evidence

Quote from: Tom Bishop on December 20, 2012, 11:09:54 AM

The medium between the sun and moon is not the same as the medium between the sun and the earth.

Please provide evidence

Can I ask you to engage your brain before further posting? There is no air between the sun and the moon. There is however air between the sun and you on earth.
Evidence: Breathing.

If the fet was true, it would move far off to the point where it's tiny. Not dip behind the earth

Sense. It makes none. So I guess the fet is false, huh?

As for the RET, and it makes perfect sense

But the sun doesn't dip behind the earth. It dips into a layer of atmosphere right above the earth.

Can I ask you to engage your brain before further posting?

Hahahaa - fair cop.

It made sense in my head because I was thinking of the earth as a big ball of rock in space with an atmosphere that's a tiny couple of hundred kilometers compared to the 6,800km radius of the planet and 147 million kilometers to the sun.

And I still strongly believe that the sun is diving below the horizon due to Earth's rotation, and if the earth was flat and the sun was cycling above it, the sun would not move down below, would it? No.

Now, onto another topic. Other planets. They have sunlight, but they are very far away. Explain.

Of course. To the completely understandable and uncontroversial Round Earth belief, the sun (A enormous object in the middle of the solar system) provides light for all planets in the solar system. That makes sense, and if you observe, you can easily see that.

But in the fet, the sun is a much smaller object that spins around a disk-like earth (Why is the earth shaped like a disk? Who knows, it doesn't make any sense) the sun surely couldn't provide light for planets millions of miles away, we would all be blind.

The medium between the sun and moon is not the same as the medium between the sun and the earth.

It doesn't just reach the moon! it reaches the moon, and is then reflected to us. the light reaches our eyes. You couldn't see it if our eyes couldn't pick it up.

Quick question, what are eyewalls? I hope it's not what my imagination has come up with.

Eyewalls are a part of the Aetheric Whirlwind on which sit the celestial bodies.