661

Flat Earth Theory / Re: Some perspective on perspective

« on: April 30, 2016, 10:27:00 PM »

Well first of all, Greek math states that they DO appear to touch and that they don't physically touch, not the other way around.

No, they don't. We never learn that in Geometry class. The greek's geometry math assumes that we live in a continuous universe where resolution is infinite and where perfect circles could exist. The model says that two parallel lines should never touch in such a perfect universe.

For lines of finite length, this is true. This is a pretty good assumption. Why would this not be a good assumption?

However, two parallel lines do seem to touch, perhaps due to several other factors, and therefore, ...

Yes, but they only seem to touch if they are far enough away relative to the distance between them. The specific factor that causes them to seem to touch is the fact that cameras and eyes do NOT have infinite resolution.

...it follows that the model is not an accurate reflection of reality, especially at extreme distances.

If our eyes had infinite resolution, then perhaps that would indeed follow. But they don't, so it doesn't.

662

Flat Earth Theory / Re: Some perspective on perspective

« on: April 30, 2016, 10:03:18 PM »

If I understand you, you are saying that the line segments in the projection will meet if extended. I agree; they will meet at the vanishing point. But line segments that are projections of (actual, finite) parallel lines will not actually meet in the 2D plane, although they can come close enough so that the eye cannot tell the difference. In the same way, vertical lines like telephone poles will meet at the zenith if extended, but will not actually meet there without being extended.

You are exactly right about this. I was being too pedantic. Parallel line segments will never ever meet on the 2D projection. They only appear to meet if they are so far away that the human eye can't distinguish the distance between them.

Edit: blah blah blah... me being stupid... blah

I'm not sure what you mean here. In any case, I'm trying to keep things "as simple as possible, but not simpler." 

Feel free to ignore that part...

663

Flat Earth Theory / Re: Experiment showed me Earth is round, please expose the lie

« on: April 30, 2016, 09:55:48 PM »

It does not show the earth is round or a sphere.

That is sort of true.

If the earth is round, this experiment will determine it's radius.
If the earth is flat, this experiment will determine the height of the sun.

If you end up calculating a different height of the sun at each location at the same time, this shows a problem with the flat earth model. 

The suns rays need to hit the supposed globe in a perpendicular fashion.

No they don't.

Eratosthenes performed his experiment under the impression sunshine IS perpendicular.

No, he performed his experiment under the impression that sunshine was perpendicular at a particular location during the summer solstice, when the sun is directly overhead. He did this just to simplify the math. He did not assume perpendicular sunshine at the other location he took measurements at.

664

Flat Earth Theory / Re: Some perspective on perspective

« on: April 30, 2016, 09:29:35 PM »

The math of the ancient Greeks says that two parallel lines should never touch. But, as admitted, they visibly do touch. How is that a proof that the Greeks were correct in their world model? That is direct evidence that they were wrong about their world model.

The "math of the ancient Greeks" says that parallel lines SHOULD appear to touch on a 2D projection. And they do. What's the problem?

Please try to understand the distinction:
They DON'T actually touch in reality, by definition.
They DO touch in a 2D projection.

Minor correction: the projection of actually parallel lines from 3-D space onto a plane will always be separate lines that never meet. Projection onto a plane is just like looking through a window pane and imagining what you see to be painted on the glass. However, they could be so close together on the plane that the human eye could not tell whether they actually met or not. That's a question of human eye's perceptual capability, not geometry.

No. We are talking about a perspective projection here. The lines will absolutely always meet on a 2D perspective projection. They will meet at the vanishing point. The vanishing point is a very real and calculable point on the 2D plane. It has nothing to do with the human eyes' perception capability.

Lines (extended to infinity) will always meet at the vanishing point on the 2D perspective projeciton. Parallel line segments (that don't extend to infinity in 3D) will never actually meet on the 2D projection.

The vanishing point is NOT a real point in 3D space. I think this is what confuses people.

Edit: If you parameterize the lines according to their distance away from the observer in 3D space, then you can never reach the vanishing point on the 2D plane by increasing the parameter. Perhaps this is what you mean? If this is what you mean, I would advise against pushing this point, because it seems to be confusing Tom Bishop. Keep it simple as possible.

665

Flat Earth Community / Re: Curvature ?

« on: April 30, 2016, 09:21:56 PM »

If the horizon is the same distance away from left to right, then how much curvature does one expect to see from that elevation on a round Earth?

Well, my answer would be that since the horizon would be exactly the same distance in ever direction (symmetry), there is no curvature to be seen.

No, there is definitely curvature to be seen if you are high enough. The horizon forms a circle around you. If you are exactly in the middle of the circle, it just looks like a straight line. If you are above the circle, then you can see the actual curve of the circle. It's a bit complicated to calculate though.

666

Flat Earth Community / Re: Curvature ?

« on: April 30, 2016, 08:22:49 AM »

If the horizon is the same distance away from left to right, then how much curvature does one expect to see from that elevation on a round Earth?

Assuming:
90 degrees horizontal FOV
60 degrees vertical FOV
576 vertical resolution
The horizon is in the middle of the image to avoid optical distortion

The difference in height of the horizon from the middle of the picture to the edge of the picture doesn't even reach 1 pixel until the observer is 65 meters above sea level.

height (meters) -> change in height of horizon (pixels)
10 -> .4
100 -> 1.3
1000 -> 4
10000 -> 13

You have to get up pretty high to see any curvature. For example, this image taken at 6000 m (according to the source), with an iPhone 4 (according to the jpeg metadata).

60.8 degrees by 47.5 degrees FOV
1256 verticle resolution
6000 meters

I calculate that we should expect 10 pixel difference in height in the middle of the horizon if the earth is round. 0 if the earth is flat.




I count 13 pixel difference in height in the middle of the horizon.

Conclusion:
My round earth estimate was a bit low, but pretty close. If the picture was actually taken at 9000 meters instead of 6000 meters, my estimate would have been correct. Maybe they made a bad height estimate?

667

Flat Earth Theory / Re: Some perspective on perspective

« on: April 30, 2016, 04:53:22 AM »

The math of the ancient Greeks says that two parallel lines should never touch. But, as admitted, they visibly do touch. How is that a proof that the Greeks were correct in their world model? That is direct evidence that they were wrong about their world model.

The "math of the ancient Greeks" says that parallel lines SHOULD appear to touch on a 2D projection. And they do. What's the problem?

Please try to understand the distinction:
They DON'T actually touch in reality, by definition.
They DO touch in a 2D projection.

668

Flat Earth Community / Re: How we see the sun as setting while it has moving away?

« on: April 30, 2016, 12:14:33 AM »

The light bends the same way, whether through air or water, maybe the angles are a bit different, but it still bends in the same direction.

No, it always bends towards the medium with a higher index of refraction. Intikam's diagram would be roughly correct if the water and air were reversed.

669

Flat Earth Community / Re: Curvature ?

« on: April 30, 2016, 12:09:14 AM »

Ugh, stop trying to eyeball it and just measure it already...



After running it through edge detection to make marking the edge of the horizon and beams less biased:

• The middle beam is pretty straight.
• The bottom beam is curved up about 2 pixels in the middle.
• The horizon is curved up about 1 pixel in the middle.

Inconclusive.

If you want to draw some actual conclusions, you need to first calculate the expected curvature. Then you can compare it to a picture and determine who is right.

670

Flat Earth Theory / Re: Some perspective on perspective

« on: April 29, 2016, 08:04:54 PM »

Excellent writeup. Now we can use this thread to debate perspective instead of constantly derailing other threads.

I would like to expand on your response to the first quote by Tom Bishop:

Tom Bishop:
I'm asking for some sort of evidence that perspective works the way the Ancient Greek math says it works. Will two parallel lines really recede forever into the distance and never appear to touch? That seems extraordinary.

Why should we believe that just because an ancient greek philosopher said that a perfect world would be that way?

Parallel lines never touch, by definition. If they do touch, then they aren't parallel.

However, things get a little complicated when we project lines that are parallel in 3D space onto a 2D surface ("perspectiveG"). Look at the following picture:

• The lines that are parallel in 3D space, are no longer necessarily parallel when projected onto a 2D surface. This is what we mean when we say they "appear" to touch. They "appear" to touch at the vanishing point (V' in the picture). Just because they "appear" to touch in the 2D projection, does not mean that they touch in 3D space.
• The vanishing point only exists in the 2D projection, not in 3D space. If you follow the parallel lines in 3D space, you will NEVER arrive at the vanishing point. This is what we mean when we say "the vanishing point is at an infinite distance away"

671

Flat Earth Theory / Re: Google map debunk: You must draw an "S" if you want to go to Taiwan from Shangai

« on: April 29, 2016, 08:04:12 AM »

Wow, you've convinced me. Surely you will revolutionize the world of cartography. I normally save this video for special occasions, but you have earned it. Impressive.

672

Flat Earth Theory / Re: Google map debunk: You must draw an "S" if you want to go to Taiwan from Shangai

« on: April 29, 2016, 03:45:06 AM »

A simple google search would have given you your answer. From the article, it's a combination of reasons 4 and 5 from my above post. Taiwan and China are constantly involved in petty disputes.

Nicely done!  I love it when a reasonable explanation can be easily found.

Thanks! Very satisfying indeed.

Also, sorry about the paywall site. If you google "taiwan china flight path dispute" you can see the entire article behind the paywall. I'll add this related article that isn't behind a paywall to the original post. (Not that anybody actually wants to read the entire article... it's super boring)

673

Flat Earth Community / Re: How we see the sun as setting while it has moving away?

« on: April 29, 2016, 03:23:18 AM »

Did anyone notice the light in the diagram bends in an different direction then the light in the picture?

Intikam in the picture you provided it shows the sun would appear higher then it actually is.  In the diagram you show it would appear lower.

Yes. See my original response to his post. The lower refractive index should be on bottom for it to bend in the correct direction. Water has a high refractive index, air has a low refractive index.

Wouldn't air have a higher refractive index than the vacuum of space though?

Yep! It's a very slight difference though. This also contributes slightly to the sun appearing HIGHER than it actually is. (The opposite of Intikam's diagram)

674

Flat Earth Theory / Re: Google map debunk: You must draw an "S" if you want to go to Taiwan from Shangai

« on: April 28, 2016, 09:18:02 PM »

All these threads about indirect flight paths are completely irrelevant. There are many reasons not to take a direct flight path. Some reasons include:

1. Available emergency landing sites
2. Weather, turbulence, jet streams
3. Military no-fly zones
4. Airspace agreements between countries
5. Air traffic routing
6. Radar coverage

You are writing a fable. No one of these reason available on this issue.

https://tr.flightaware.com/live/flight/CAL503/history/20160417/0850Z/RCTP/ZSPD
...

There is no direct route. All routes are perfect "S".

All flyings between these two city Taipei and Shangai are following this route without exception. So you can't explain this issue except this route is the shortest route.

A simple google search would have given you your answer. From the article, it's a combination of reasons 4 and 5 from my above post. Taiwan and China are constantly involved in petty disputes.

Edit: Related article that isn't behind a paywall.

675

Flat Earth Theory / Re: Google map debunk: You must draw an "S" if you want to go to Taiwan from Shangai

« on: April 28, 2016, 07:53:14 PM »

All these threads about indirect flight paths are completely irrelevant. There are many reasons not to take a direct flight path. Some reasons include:

1. Available emergency landing sites
2. Weather, turbulence, jet streams
3. Military no-fly zones
4. Airspace agreements between countries
5. Air traffic routing
6. Radar coverage

676

Flat Earth Theory / Re: Google map debunk: Shangai to New Delhi is closer than Beijing to New Delhi

« on: April 28, 2016, 07:50:05 PM »

You are wrong.

It is not needed to across the high mountains.

The planes are flying about 30.000-40.000 feets already higher than the highest mountain on the world.

They avoid flying over the Himalayas for safety reasons. The main reason is that it is impossible to decrease to a safe altitude in case of depressurization.

All these threads about indirect flight paths are completely irrelevant. There are many reasons not to take a direct flight path. Some reasons include:

1. Available emergency landing sites
2. Weather, turbulence, jet streams
3. Military no-fly zones
4. Airspace agreements between countries
5. Air traffic routing
6. Radar coverage

677

Flat Earth Theory / Re: Experiment showed me Earth is round, please expose the lie

« on: April 28, 2016, 07:24:55 PM »

Not helping here. My eyes can see, just expose their lie please.

Your eyes can see what? Have you considered the possibility that they aren't lying, and that the earth really isn't flat?

678

Flat Earth Community / Re: How we see the sun as setting while it has moving away?

« on: April 28, 2016, 02:05:42 AM »

Did anyone notice the light in the diagram bends in an different direction then the light in the picture?

Intikam in the picture you provided it shows the sun would appear higher then it actually is.  In the diagram you show it would appear lower.

Yes. See my original response to his post. The lower refractive index should be on bottom for it to bend in the correct direction. Water has a high refractive index, air has a low refractive index.

679

Flat Earth Theory / Re: Shadows on clouds

« on: April 28, 2016, 01:49:06 AM »

Aha! Aha! Never heard of general relativity, have ye, mate? Posit a few black holes circulating above the earth, and there's your explanation for bendy light.

Flat earthers, feel free to adopt this explanation for the appearances and apparent motions of celestial objects, so long as you don't credit me for it.

Some people just want to watch the world burn...

Fixed my post, hope you approve!

NOOOOOOOooooooo!

Now they are going to incorporate that into their theory, and the burden of proof will be on us to prove that there aren't a bunch of completely undetectable black holes orbiting 3001^[1] miles above the earth, affecting light in mysterious and convenient ways.


^[1] They aren't at the same height as the sun, they are at about the same height as the sun

680

Flat Earth Theory / Re: How does a Full Moon appear Full for everyone?

« on: April 28, 2016, 01:34:15 AM »

I asked for a name of the scientist who studied perspective and was met with silence. I asked what evidence there was that perspective works in the way the ancient greeks described and I got silence. There is no evidence for me to refute.

I apologize. Wikipedia gives a very nice overview of the subject, with references if you want to dive deeper. It isn't a controversial or complicated subject.

Linear Perspective:

The two most characteristic features of perspective are that objects are smaller as their distance from the observer increases; and that they are subject to foreshortening, meaning that an object's dimensions along the line of sight are shorter than its dimensions across the line of sight.

As for names of people who studied it:

Italian Renaissance painters and architects including Filippo Brunelleschi, Masaccio, Paolo Uccello, Piero della Francesca and Luca Pacioli studied linear perspective, wrote treatises on it, and incorporated it into their artworks, thus contributing to the mathematics of art.

Also relevant is how the atmosphere effects our view of objects:

As the distance between an object and a viewer increases, the contrast between the object and its background decreases, and the contrast of any markings or details within the object also decreases. The colours of the object also become less saturated and shift towards the background color...

I bolded the main features of perspective. Do you have any reason to believe that any of this is not true? Be specific please.