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Biogroovy
2012-May-24, 01:55 PM
Question: I was in the Black Rock Desert, a huge salt flat in NV, and over head, maybe twenty feet, some guys were shooting a massive green laser out across the desert. Looking out at it, it looked like the laser beam was curved and curved precisely as what appeared to be the curvature of the Earth. The best explanation I could come up with is that the Earth is flat. What do you think? Is it simply an optical illusion. Is the Earth being round an illusion?

korjik
2012-May-24, 03:03 PM
1) Light is affected by gravity

2) Light is refracted by air

3) The curvature was the illusion.

All three of these are possibilities for what you saw. The Earth being flat isnt a possibility.

amazeofdeath
2012-May-24, 03:16 PM
How did you measure the curvature of the light beam? How do you know it matches the curvature of the Earth? And most importantly: Why would a flat Earth produce a curved laser beam?

Light is refracted by the atmosphere. As the density of the atmosphere strongly depends on the distance from the ground level, the refraction index is also dependent on the distance.

Bob Angstrom
2012-May-24, 04:09 PM
I have seen the same effect and it is amazing. My conclusion is that the Earth being flat is is an illusion. The laser beam is straight although the atmosphere may cause it to curve slightly downward- not upward. When we compare the curved “flat” Earth surface with straight laser beam, the laser appears to be curving upward. You can see the same effect if you stand under telephone lines running across a perfectly “flat” landscape but it is much less pronounced. Phone lines appear to curve upward at first and then curve down to meet the horizon. A laser beam just keeps going up but it is an illusion.

R.A.F.
2012-May-24, 04:16 PM
Is the Earth being round an illusion?

I always considered the Earth's shape as an oblate spheroid, not "round".

glappkaeft
2012-May-24, 04:22 PM
I always considered the Earth's shape as an oblate spheroid, not "round".

It's closer to a geoid shape.

amazeofdeath
2012-May-24, 04:49 PM
It's closer to a geoid shape.The aberration from true sphere shape is negligible in regard to the question at hand, in any case.

pzkpfw
2012-May-24, 07:39 PM
Question: I was in the Black Rock Desert, a huge salt flat in NV, and over head, maybe twenty feet, some guys were shooting a massive green laser out across the desert. Looking out at it, it looked like the laser beam was curved and curved precisely as what appeared to be the curvature of the Earth. The best explanation I could come up with is that the Earth is flat. What do you think? Is it simply an optical illusion. Is the Earth being round an illusion?

Is this really just a question, or will you argue in favour of Earth being flat? I ask, as this is the wrong part of the forum for a question, so will move the thread depending on your answer.

chrlzs
2012-May-24, 09:17 PM
And how have you taken perspective distortion into account??? Eg crepuscular rays, or even standing near a long straight wall should show you that the eye's perception of 'curves' is NOT correct/trustable. Your eye consists of a lens and a curved retina. Long straight lines WILL curve (in your view). It's the same effect that causes the moon's illumination to not appear in a straight line from where the sun is..., the same effect that causes all the bending of lines in a fisheye lens view.

It's not an illusion, it is simply an optical effect.

korjik
2012-May-25, 07:47 AM
I always considered the Earth's shape as an oblate spheroid, not "round".

Spheroids are round, just not spherical.

sirjon
2012-May-26, 01:47 PM
Contradiction in geometry... the Earth is round but we always hear. "...that the floor is flat". (just a comment)

stutefish
2012-May-26, 03:35 PM
Contradiction in geometry... the Earth is round but we always hear. "...that the floor is flat". (just a comment)

grapes
2012-May-26, 05:11 PM
It's closer to a geoid shape.That's arguable, since the geoid is predominantly an oblate spheroid, and all the continents deviate from the geoid (the geoid is sea-level, essentially).

Long straight lines WILL curve (in your view).

It's the same effect that causes the moon's illumination to not appear in a straight line from where the sun is...,
Not true. That illusion can be dispelled by holding up a ruler to the sky. Unless you think a meter stick looks curved to you.

the same effect that causes all the bending of lines in a fisheye lens view.

It's not an illusion, it is simply an optical effect.I disagree. Fisheye lens are optical distortions, but the others are illusions--because they can be dispelled by using non-optical props.

As to the OP, I'm curious how the curvature of the earth was seen, from apparently the vantage of standing on the salt flat surface.

NEOWatcher
2012-Jun-01, 04:26 PM
1) Light is affected by gravity
2) Light is refracted by air
3) The curvature was the illusion.
All three of these are possibilities for what you saw. The Earth being flat isnt a possibility.
This is probably the best concise answer to the OP.

BioGroovy.. if you have stuck around, and still question it, I would like to see your explaination for various other effects based on the curvature of the Earth.
- People that have gone to a high enough altitude to see the curvature of the Earth (not just astronauts)
- Why the largest suspension bridge towers are built with the base closer in distance than thier tops.
- Sun angles in various parts of the world. Particularly starting with Ptolomy's experiments.
- The behavior of satellites at different altitudes.
- The dissappearance of a ship over the horizon.
I think that is plenty for a start.

Bob Angstrom
2012-Jun-01, 05:58 PM
I have seen the same illusion and can put some personal perspective on it. There was a small student observatory in New Mexico testing a new green laser. The observatory was about ten miles from a mountain range and I was midway between the observatory and the mountains with the laser beam passing almost directly overhead towards the mountains. The beam was directed slightly upward but parallel to the land because the land also sloped upward towards the mountains. I could imagine a straight line extending from the laser beam and striking the mountains in the lower foot hills but instead the beam appeared to curve upward and passed completely over the mountains a good five thousand feet above where I thought it should be. The illusion was dramatic and persistent and could not be dispelled by intellectualizing what I saw.

chrlzs
2012-Jun-02, 12:33 AM
Long straight lines WILL curve (in your view).
May i offer a thought example...

You are standing at the base of a high wall, let's say 3 metres tall, that stretches to the left and right for a very long distance. You look up at the top of the wall, and see the top of it. Now you look to the left, and over there in the distance, the wall nears the horizon vanishing point. You turn your head to look to the right, and there is the top of the wall again, this time at the opposite horizon vanishing point. The top of that wall is a straight line. But unless you are LEVEL with the top of the wall, or absolutely directly underneath it, you *must* perceive it as curved. It's exactly the same effect as crepuscular/anticrepuscular rays - they start at the Sun, 'fan out' and rejoin at the opposite horizon. Same with railroad lines that fan out at your feet, but meet at both opposite horizons - they cannot possibly do that unless they are *truly* curved from your viewpoint - the only way you can make those lines appear straight is to get down so your eye is level with the line, and then look in one direction (just as the *only* crepuscular rays that are straight (from your perspective) are the ones that are either directly overhead or those that are going along the horizon).

So it's not an illusion in the strict sense of the word - it's perspective distortion - the fact that you cannot accurately 'project' a 3D scene onto a 2d representation (which is what your viewpoint is). If it was a true illusion, you could make the illusion 'vanish' by using an 'appropriate' corrected lens - but there is no way to do that as the effect is real...

And if that one meter ruler is a bit longer then it too will curve in your view, depending on your location relative to it...

Bob Angstrom
2012-Jun-02, 04:07 AM
The top of that wall is a straight line. But unless you are LEVEL with the top of the wall, or absolutely directly underneath it, you *must* perceive it as curved. The top of the wall is not straight even though it appears straight when sighting along the top. It curves with the surface of the Earth and a laser beam following the top of the wall would appear to curve upward when compared to the “straight” line of the wall.

If it was a true illusion, you could make the illusion 'vanish' by using an 'appropriate' corrected lens - but there is no way to do that as the effect is real...Illusions, perspective distortions, and what we see through a lens all sound like variations of the same thing to me. A "true illusion" is an oxymoron.

chrlzs
2012-Jun-02, 07:10 AM
The top of the wall is not straight
Sorry, but it was a thought experiment - so it IS straight as it's a laser-beam leveled wall in a gravity free environment! :) It STILL converges (ie drops down towards your perceived horizon to both left and right), yet .. it is ABOVE you, where you are. A straight line can't really do that, but it definitely does.. And it's because we are trying to map a 3d straight line onto a 2d projection.

Forget the wall - think about the railway lines that you stand in the middle of. From your perspective (and those are KEY words) the rails near you are spread apart, and yet they converge at the vanishing point/horizon to your left and your right. And that's NOT possible unless they are, from your perspective, curved. Yes, you can change your location by dropping your viewpoint down to the rail and sighting one way to verify that in 3d reality they are straight.. But if you are standing above/below and beside that straight rail (or any straight line) it will bend from your perspective.

A "true illusion" is an oxymoron.
Then what's the point of the word? :) IMHO, a 'true' illusion is something that is not an actual effect, like this classic (http://en.wikipedia.org/wiki/File:Optical_illusion_greysquares.gif). That's a 'true illusion'. Perspective distortion is .. perspective distortion. It's NOT because you have a faulty brain or are a poor observer..

In the case of these 'bent' lines, while it is not an actual effect as far as the line/laser/wall is concerned, in actual 3d reality, it IS an actual effect as far as viewing that line as a 2d projection is concerned. And because that is how we look at things, it's real.

I repeat, I am NOT saying the line is curved - in 3d space it is not. But straight lines do get 'curved' when we (or a camera) view them from any perspective other than vertically (ie beneath or above) or horizontally (beside).

Finally, to relate this back to the OP.. If Biogroovy could have climbed up on something to get his eye at the same level as the ray, he would have found the bending effect would have miraculously disappeared (just as crepuscular/anticrepuscular rays that run along the *horizon* do not 'bend' from perspective distortion, just like the railway line when you get down and sight along it).

grapes
2012-Jun-04, 09:00 PM
May i offer a thought example...
Let me offer one. If your viewpoint is at the exact center of a large circle, would it look curved to you?

chrlzs
2012-Jun-04, 10:49 PM
I don't understand your point.. Aren't we talking about straight lines in a 3d space, viewed from an *offset*?

Of course if your eye is in the centre of a circle it will appear as either a circle (if you are above or below it), or a 'straight' line if you are level with it. I'm happy to proceed with this analogy to see where it leads ..?

But again, I would refer you to the railroad example. You are standing between the lines - you look down and they are spread apart. You look at them as they head to the vanishing point, and they 'meet'. You turn exactly 180 degrees towards the other vanishing point, and they 'meet' again. Yet at your feet they are spread out. How can you explain this except by perspective distortion? Look at the following picture - it shows the vanishing point, and the 'curve' which *must* happen as the rails spread out around your feet, and then reconverge as they head off to the opposite vanishing point.
17017
It *isn't* just a lens effect!

The Wiki on perspective projection distortion (http://en.wikipedia.org/wiki/Perspective_projection_distortion) uses a similar example, and I quote:

Imagine that on an infinite plane there is an infinitely long and infinitely straight railroad, and that you are standing between the parallel rails. As you peer down the track in one direction the rails appear to intersect (on the horizon). As you peer in the opposite direction they again appear to intersect. You look at your feet, and the rails are far apart. It logically follows that if the rails intersect, as it would appear, one or both of the rails are curved. To determine which, you put your eye onto one rail and sight down it. You discover that it is straight in the sighted direction. You then sight down the same rail in the opposite direction. You discover that it is straight also in the opposite direction. It logically follows, then, that the other rail must be curved. You similarly test the other rail and discover it too is straight. How can this happen? one knows not.

Again, this is exactly the same effect as crepuscular and anti-crepuscular rays, and the same effect that bent the laser in the OP. The observer was standing beneath and to the side of the ray, so from his perspective, it *was* bent. Had he been able to get his eye level with the ray, the bending would have vanished.

You can find another description of this effect, along with some others, here (http://www.lhup.edu/~dsimanek/3d/moonillu.htm) - scroll down to 'Anisotropy of Visual Space', and note the diagram showing the same 'spreading effect' of parallel lines, that leads to the apparent curvature.

grapes
2012-Jun-04, 11:04 PM
I don't understand your point.. Aren't we talking about straight lines in a 3d space, viewed from an *offset*?

Of course if your eye is in the centre of a circle it will appear as either a circle (if you are above or below it), or a 'straight' line if you are level with it. I'm happy to proceed with this analogy to see where it leads ..?If you are level with it?

You realize that a straight line and a point off the straight line define a plane, right? So, from any point of view, you are always "level" with a straight line.

When you are level with the circle, it will looked straight. "Of course." And the part you can see will be indistinguishable from a straight line behind it. The geometry doesn't make straight lines looked curved, your brain does. If you are very observant, they don't look curved.

ETA:

How can this happen? one knows not. I haven't read the article, but aren't they implying your brain has fooled you? :)

EETA: OK, now imagine that you are viewing from the exact center of a sphere. None of the great circles would look curved to you, of course, because you are at their center and level with them. But, they intersect. Without looking at all curved.

chrlzs
2012-Jun-04, 11:47 PM
You realize that a straight line and a point off the straight line define a plane, right?
Yes. And your eye can be *above or below* that defined plane, or level (ie *on* it)... That really is the key point that is being missed.

Things on that plane will be distorted depending on your level above or below it. So for instance if there is a circle drawn on a plane that is, say above and to the left of you, it will appear as an ellipse, correct? If it directly above you, it will be a circle, but any other angles it becomes an ellipse (or if you get level with it, a straight line). Agreed? Is that an illusion? Of course it isn't - it IS a genuine ellipse from those offset viewpoints - it has been distorted (bent) by perspective distortion. Just like the railway lines, the crepuscular rays, the laser.

It is only if you get directly above or below the circle that it becomes a circle from your perspective.. In the case of a straight line on that plane, the same distortions will happen, and over a distance, cause the perceived curve.

So, from any point of view, you are always "level" with a straight line.
Why did you replace the 'plane' with the straight line? This is where it all goes wrong - you are conflating the plane (in 3d) with the straight line on it and its appearance from different viewpoints relative to that plane (in 2d projection).

I haven't read the article, but aren't they implying your brain has fooled you?
No, exactly the opposite, so perhaps you should.

Clearly I'm going to have to come up with some diagrams that better illustrate this... :D

grapes
2012-Jun-05, 12:56 AM
You realize that a straight line and a point off the straight line define a plane, right?

Yes. And your eye can be *above or below* that defined plane, or level (ie *on* it)... That really is the key point that is being missed.
It is a key point. :)

If you take the straight line, and the point which is your point-of-view (your eye), that line and that point define a plane. The eye cannot be above (or below) that plane, because by definition of that plane, it is in the plane (level with it).

Don't look at photographs, they're almost always distorted. Just go outside and look at a straight line (if you can find one, the edges of crepuscular rays are pretty good), if it doesn't look straight to you, hold out a meter stick alongside it--maybe that will convince your brain.

Bob Angstrom
2012-Jun-05, 05:08 AM
The illusion mentioned in the OP is different from crepescular and it curves in the opposite direction. The moon illusion article says and illustrates with a picture, “Physically the cloud canopy is nearly a flat plane, as is the earth under our feet, because the radius of their curvature is so large compared the distance to the visual horizon.”
We know the cloud canopy is not flat because it follows the curvature of the Earth so a straight laser beam running just under the clouds would appear to curve upward and through the clouds. Our senses appear to be telling us that the curvature of the earth is less than it really is so a truly straight line, when compared to the curvature of the earth, looks curved.

chrlzs
2012-Jun-05, 09:01 AM
I'm going to stop after this post for the moment, given the fact that no-one seems interested in actually addressing the examples given, nor looking at the articles. .. but I WILL be back later to expound on this in the painful detail that is obviously required! For this is most assuredly NOT an optical illusion. It is perspective distortion - please research the topic properly before digging further!

To Bob - it is EXACTLY the OP situation! He says he was beneath and to the side of the overhead laser. I quote:

over head, maybe twenty feet, some guys were shooting a massive green laser
That's the same when crepuscular rays go up/out from the Sun, then reconverge at the opposite horizon (as anticrepuscular rays), they too are above and to the side of the observer in exactly the same way as the laser was for the OP.

a straight laser beam running just under the clouds would appear to curve upward and through the clouds
But the OP said the opposite!! Here:

it looked like the laser beam was curved and curved precisely as what appeared to be the curvature of the Earth
To me that clearly says it was curving downward to follow the curvature of the earth (as it should from perspective distortion) - perhaps the OP may wish to clarify, but I can't see how that can be interpreted as curving upwards...

Please, guys, THINK about the sunray situation. Here's a very wide image showing how the rays curve upward and away from the Sun, reaching the top of their arc at right angles to the observer, and then curve down again to meet the other rays at the opposite horizon, precisely 180 degrees from the source:
17019
Here's another example:
http://www.pbase.com/missouri_skies/image/126596663/large

Please THINK very carefully about those images! In particular, think about the rays that are not directly overhead, or at the horizon. It's all the ones between those extremes, eg at 45 degrees, that are most affected by perspective distortion. Those rays curve up and then back down again from the observer's perspective. There is no way you can hold your meter rule up to that image (please visualise it and think about it) and say the lines are 'straight'. From your perspective they are curved. You guys keep saying that a straight line has to be straight from all viewpoints - but NO, it doesn't, just as circles don't appear to be circles if you change your perspective. You say it's an illusion, but if so, you need to answer this question.

What 'straight' line can be drawn from one point on the horizon upwards to about 45 degrees, and then down again to the precisely opposite point on the horizon, 180 degrees away?

Because that is precisely what crepuscular/anticrepuscular rays do. They are straight lines in 3d, but your perspective distorts it. It is NOT an illusion. It is NOT a lens effect.

If it's any consolation, there was a time when I didn't get this either, but I took enough time to think about it and research why the effect (not illusion) occurs.

Anyway, I'll be back later to go through this in some detail, but right now... I've had enough.

grapes
2012-Jun-05, 09:35 AM
I'm going to stop after this post for the moment, given the fact that no-one seems interested in actually addressing the examples given, nor looking at the articles. .. but I WILL be back later to expound on this in the painful detail that is obviously required! For this is most assuredly NOT an optical illusion. It is perspective distortion - please research the topic properly before digging further!
I read the wiki perspective article. It is about the distortion of projecting onto a 2D surface--clearly, we can make an image of what we see by just framing it and mapping it into the frame, but the resulting image will be undistorted only if you view it from that same position. If we step back, or move to the side, the 2D image will look distorted (the principle behind the fascinating anamorphic images).

Other than that, the article seems to make the same point I made about the great circles. That, from a single POV, straight lines look straight.

What 'straight' line can be drawn from one point on the horizon upwards to about 45 degrees, and then down again to the precisely opposite point on the horizon, 180 degrees away?
You'd trace a great circle, with yourself at the center of the circle, "level" with it. Which, as you've said, would look straight.

We had this discussion on BAUT before, and I think some posters actually went out with meter sticks and verified all this! :)

Luckmeister
2012-Jun-05, 05:57 PM
Look at the following picture - it shows the vanishing point, and the 'curve' which *must* happen as the rails spread out around your feet, and then reconverge as they head off to the opposite vanishing point.
17017
It *isn't* just a lens effect!

You showed a photo with obvious lens distortion to make your point. Here's another photo. put a straightedge up to these tracks.... no curvature. That's why you can't use a photo for proof.

http://home.comcast.net/~mcluster/RRtracks.jpg

chrlzs
2012-Jun-05, 11:35 PM
One of the tenets of perspective is that IF you restrict your view to a limited (eg 90 degree or less) view, then you *can* generally ensure that perspective distortion is not shown - the whole idea of photography and painting and any attempt to portray reality nicely is to make everything look 'right', and correct those distortions.

BUT, as soon as you extend the angle of view you run into inevitable problems. As I said above, and nobody has yet addressed...
1. At your feet, the rails are spread out - the further apart, the more the spread. Yes or No?
2. At the horizon/vanishing point in front of you, they effectively meet, or at least are MUCH closer together. Yes or No?
3. At the horizon/vanishing point behind you, they effectively meet, or at least are MUCH closer together. Yes or No?
(Note that we have NOT changed our viewpoint, *just* the direction we are looking - ie we have enlarged the field of view.)

Now, feel free to tell me again that you can draw a straight line to represent that scene. The one that is wider than the 60-90 degrees in which you CAN straighten the lines out.

Similarly, have you ever actually SEEN crespuscular/anticrepuscular rays as they curve up from the Sun and then curve back down again to the point that is exactly 180 degrees opposite? Tell me again how you can draw a truly straight line to join those three points. One in front of you at horizon level, one at 45 degrees above the horizon to your left or right, and the last at 180 degrees directly opposite the first.

There are also quite a few images out there (here's one (http://www.upenn.edu/emeritus/essays/MyersMoon.html)) showing the Moon's terminator pointing to a light source above the horizon, yet the Sun has set. Again, tell me about the straight line that allows that... Already I've seen the concession above that yes, that's rather like a great circle. But that's exactly my point - it is a REAL effect, it's NOT an illusion!

Relevant paper here (http://www.edgj.org/index.php/EDGJ/article/viewFile/52/51), refer section 2 and the conclusion. Let me be VERY specific - the truth of the matter is that all 'straight lines' that are not orthogonal to the viewpoint are, in an observer's view, curved. That's the point I was trying to make above when I referred to the OP's viewpoint being below and to the side of the source of the laser.

The curve is slight for views restricted to about 90 degrees (which is ~normal for the eye). And of course we are used to straight lines, and are often able to get our eyes level (orthogonal) to the line sight along it and verify it is truly straight (and by doing that we remove the perspective distortion).

The real *illusion* here is that your brain normally corrects for this, and lenses are also designed to correct for this as in the rail photo - and both can do so relatively easily for small (ie 90 degree or less) fields of view. But as soon as you get straight lines in a 3d environment that are VERY long and you then try to perceive them from non-orthogonal viewpoints, things go pear-shaped (pun intended). That's why fish eye views and panoramas (which I happen to specialise in as a photographer) have all sorts of weird effects and curved lines. It's perspective distortion. NOT illusions.

And precisely BECAUSE of the above, trying to test this with little bits of string or rulers is effectively useless, as your view of them is normally limited to a short distance, and of course if you were to manage to properly line them up to cover the entire distance that you are measuring, they will bend too - from your perspective..

grapes
2012-Jun-06, 12:16 AM
Similarly, have you ever actually SEEN crespuscular/anticrepuscular rays as they curve up from the Sun and then curve back down again to the point that is exactly 180 degrees opposite? Tell me again how you can draw a truly straight line to join those three points. One in front of you at horizon level, one at 45 degrees above the horizon to your left or right, and the last at 180 degrees directly opposite the first.

There are also quite a few images out there (here's one (http://www.upenn.edu/emeritus/essays/MyersMoon.html)) showing the Moon's terminator pointing to a light source above the horizon, yet the Sun has set. Again, tell me about the straight line that allows that... Already I've seen the concession above that yes, that's rather like a great circle. But that's exactly my point - it is a REAL effect, it's NOT an illusion!
Which concession?

The point I make ("the key point") in post #23, is that from their center, great circles look like straight lines--all the way around us. There's no escaping that. And straight lines look like great circles viewed from their center.

Relevant paper here (http://www.edgj.org/index.php/EDGJ/article/viewFile/52/51), refer section 2 and the conclusion. It'll take some time to read, and I'll get around to it later, but I've read the abstract, and I already disagree with it.

The paper presents a unique approach in associating perspective projection with the image beheld by the eye and
demonstrates that all graphical and photographic perspective projections must contain distortion when compared to
the image beheld by the eye.Simply frame whatever you're interested in, duplicate the scene in that frame, and situate the eye at the same place everytime you look at it. No distortion.

If you look at the photo from the side, there will be distortion--that's the basis of anamorphic pictures. But I disagree with his conclusion that there must be distortion when compared to the image beheld by the eye.

ETA: OK, I see where he concedes my point above in the second paragraph on the third page. Weird, he just says that it's improbable that the eye could be at the place where the distortion disappears, but in the abstract he implies it's impossible. Still, all he's saying is that photography has inherent distortion from what we see--that just means that no photograph is going to be solid support for either side of this argument, then.

chrlzs
2012-Jun-06, 12:58 AM
I'll be back later with a mathematical demo. Two parallel lines, one orthogonal, one not. One viewpoint.

grapes
2012-Jun-06, 01:00 AM
Orthogonal to what?

ETA: In post #28, you say "orthogonal to the viewpoint" but I'm not sure what you're meaning by that. Is it in that article? I'll check.

John Jones
2012-Jun-06, 01:16 AM
Orthogonal to what?

That's what I was wondering. I was taught that orthogonal meant mutually perpendicular.

Bob Angstrom
2012-Jun-06, 02:37 AM
To me that clearly says it was curving downward to follow the curvature of the earth (as it should from perspective distortion) - perhaps the OP may wish to clarify, but I can't see how that can be interpreted as curving upwards... The OP statement is lacking in detail and it would be nice for some clarification but, as one who has seen the illusion, the laser beam appears to curve strongly upward. He says the laser beam appeared curved but failed to mention if it curved up or down. A downward curve towards the horizon would hardly be apparent since the beam appeared to be about twenty feet overhead. A laser beam that appeared to curve downward would not give one the impression that they were looking at a flat Earth in curved space. A straight laser beam running above a curved surface that looks flat would appear to be curved upward by comparison. Therefore the conclusion that he was looking at a flat Earth in curved space. To quote from the OP again:
Question: I was in the Black Rock Desert, a huge salt flat in NV, and over head, maybe twenty feet, some guys were shooting a massive green laser out across the desert. Looking out at it, it looked like the laser beam was curved and. The best explanation I could come up with is that the Earth is flat. What do you think? Is it simply an optical illusion. Is the Earth being round an illusion?I understand the OP as asking if space (the laser beam) is straight while the Earth is curved or if the Earth is flat while space is curved. I can see from your examples how one can interpret the mentioned curvature as being downward but it would take an apparent upward curvature counter to the curvature of the Earth to prompt the question.

Luckmeister
2012-Jun-06, 03:03 AM
To quote from the OP again:I understand the OP as asking if space (the laser beam) is straight while the Earth is curved or if the Earth is flat while space is curved. I can see from your examples how one can interpret the mentioned curvature as being downward but it would take an apparent upward curvature counter to the curvature of the Earth to prompt the question.

The way I read it, the OP was thinking that if the laser beam curved down following the curve of the Earth and the curving of the laser beam is an illusion, then the curving of the Earth might also be an illusion; therefore the Earth might really be flat.

Bob Angstrom
2012-Jun-06, 07:30 PM
The way I read it, the OP was thinking that if the laser beam curved down following the curve of the Earth and the curving of the laser beam is an illusion, then the curving of the Earth might also be an illusion; therefore the Earth might really be flat.It never occurred to me to interpret the OP as saying the beam curved downward but I see how someone can read it that way. I was trying to explain why the beam appeared to curve up and others were trying to explain why it appeared to curve down and that is the source of confusion. In my experience, the beam curved obviously upward. It would be nice if the OP or someone who has had a similar observation could describe how a powerful laser beam looks when observed from below.

chrlzs
2012-Jun-06, 10:32 PM
An apology - I'm very busy, so a more formal proof of this will have to wait a day or three.

But orthogonal means exactly what it is supposed to mean. An orthogonal line is one that is to you, as the observer, at eye level (or directly overhead), and extends at right angles to a line drawn from your viewpoint to the closest point on that line. That line will be straight... but a line that (as in the OP's example) is at a different level, eg at 45 degrees 'up' from your viewing plane (using the horizon as that plane) and is therefore *further away* from you despite being parallel to the first.. that's the one that gets 'bent' from your perspective.

This stuff is the keystone of perspective, and is a rough analogy of 'great circles'.. and also the behavior of the ecliptic - it's approximately 'straight' from your perspective when overhead or at the horizon, but curved when at any other angle to your viewpoint. I will demonstrate all this by way of diagrams and numbers when I get time. And some of it *is* counter-intuitive! Your brain is *really* effective at correcting this stuff...

grapes
2012-Jun-06, 11:50 PM
But orthogonal means exactly what it is supposed to mean. An orthogonal line is one that is to you, as the observer, at eye level (or directly overhead), and extends at right angles to a line drawn from your viewpoint to the closest point on that line. That line will be straight... but a line that (as in the OP's example) is at a different level, eg at 45 degrees 'up' from your viewing plane (using the horizon as that plane) and is therefore *further away* from you despite being parallel to the first.. that's the one that gets 'bent' from your perspective.

By that defintion, all infinite straight lines are orthogonal to a single Point Of View. Another line drawn from the POV to the closest point on that infinite line will be at right angles to the infinite line. All finite straight lines can be extended to be a part of an infinite line.

All 2D objects viewed from within their plane look like straight lines, including disks (as you've said). A straight line is always viewed within the plane from a POV

That is why great circles look straight from the center of a sphere. It is also why all straight lines look straight.

That said, environmental clues and confusions can contribute to impressions that the straight lines are not straight--an optical illusion.

Your brain is *really* effective at correcting this stuff...Or, getting it confused. :)

chrlzs
2012-Jun-07, 12:40 PM
I'll very frankly admit that I am unsure of the best way to get to the nub of this. I'm not a perspective genius nor trained in the science, but I do work with this stuff to get the panoramic images I create, and it is something I have considered at some length..

So, who knows, I may prove myself completely wrong with this approach and you guys may be able to poke huge holes in my logic... but.. we'll see! :D I may have some comments to make at the end of this about some of the responses above..

So, do follow along and if you have any issues with my approach, be it relevance, broken logic, mathematical or geometric errors, whatever .. I would genuinely appreciate your constructive criticisms.. There is actually a fair bit to cover here and I apologise in advance for the slowness with which I will be proceeding.. if you don't like it, come back to the thread in a week or so and pore over the wreckage... I may also invite some other folks over who are a little more educated/respected than me, if they will agree.. The more the merrier!

Before starting, I would just like to note that I don't see this topic covered very well (or easily!) elsewhere - and I believe that is largely because:
- it is actually a bit more complicated than it looks
- what we are usually trying to do is correct perspective so that 3d spaces can be represented by 2d images/drawings/ projections, not try to define why our 2d view is so flawed
- in the vast majority of cases, we are concerned with a simple front on view that covers less than 90 degrees. For those angles, perspective correction isn't all that difficult. But once you start trying to work with 'fisheye' views, and infinitely long lines like the laser in the OP, or crepuscular/anticrepuscular rays, or the "Moon Tilt Illusion", things start to break down and sometimes become counter-intuitive.

Anyway, for further reading while waiting for me to possibly self-destruct :), you may like to also look at this page:
http://termespheres.com/6-point-perspective/
in particular the discussion of 4-, 5- and 6-point perspectives, and critically, why those techniques are required, and what is said/shown about supposedly 'straight' lines.

I'm still a bit time challenged, so this will be in pieces, but I'll start with defining a basic situation - single observation point, two parallel, infinitely long, straight lines.. Let me know if you think I haven't clearly defined anything, if you dispute anything or need clarification. I apologise in advance in that it will take a few posts to get to the crux, but I need to lay some groundwork properly first. So...

You are an observer located at position O. (At least, your EYE is there.)

To simplify matters, let's say you have zero height and your eye is at 'ground' level. That will be our basic reference (but as you will see, we can and will change it later and see what happens..) I'll arbitrarily pick some nice round, handy numbers for the next part - I'll talk in kilometres for no particular reason other than that usually we are talking about distant and long lines. If you would prefer to think in metres, inches or furlongs, or use different numbers, be my guest.

In the distance, there is an infinitely long line. It is 4 km away from your location, at ground level. On that line the closest point to your location I shall nominate as point A. So, obviously the distance O-A is 4km.

Directly above that line (perpendicular to the ground) and perfectly parallel to that first line, there is another infinitely long line. The closest point to your location (directly above A) is point B. Let's say the line is 3km higher than the first line, ie the distance A-B is 3km.

Using a little Pythagoras, the distance from your viewpoint to the nearest point on the upper line O-B is 5 km.

To the observer at O, the altitude angle (call it ӨB)to point B is ~37°.. (I'm rusty on my trig, but I think that's right..)

Next, let's put some points a reasonable distance along the two lines, say 8km to the right and left... I'll call the first of these points LL, for the one on the lower/closer line at the left and LR to the right, and UL on the upper line to the left, UR on the right.

Now, to the observer at O, the angle (call it ӨUL) to point UL is ~18.5°.. (As is the angle from O to point UR, ӨUR.)

Here's a picture (neither to scale or perspective-corrected, obviously!) - if it isn't clear, or I've typo'd anything, let me know...
17045

Before I move on (which may be a day or so..), is there anything that is unclear or disputed with the image or my statements above?

Please note, I will be covering what happens when you change the 'ground' level later - I'd appreciate it if we don't start changing that aspect around just yet, for reasons that will become clear (I hope!) later - but don't worry, I am NOT avoiding it! By that time, the problem/anomaly (and it's quite a nasty one!) should be making itself clear (if it isn't already) - and if not, I'll have to concede defeat..

Hornblower
2012-Jun-07, 02:02 PM
All we have from Biogroovy in the OP is that he saw a laser beam that appeared curved to him, and that it appeared to match the curvature of the Earth’s surface. Since he presumably expected the laser beam to be straight, he wondered if the Earth might actually be flat.

I don’t know what he meant by “what appeared to be the curvature of the Earth”, and since he has not been back it is hard to get a clarification. In general a large salt flat will appear flat, especially if surrounded by higher ground that prevents seeing an effect like that of a ship disappearing over the horizon at sea. At least that was my perception in the Bonneville Salt Flats in Utah.

I just now checked out the perspective effects of looking at parallel lines extending far in both directions from a nearby viewpoint. I stood close to a long straight wall in my living room and initially just stared at the center directly in front of me. The top and bottom edges looked reasonably straight and parallel, though having them in my upper and lower peripheral vision made them rather indistinct because of the inherent lack of focus. When I looked directly at the midpoint of each one, that line definitely looked straight.

Next I turned toward the corner and stared at it. Now the top and bottom edges looked straight and diverging toward me, just as the railroad track did in an earlier post. Looking at the other corner gave the same view except for being reversed.

So far these are static views. When I started sweeping my vision from one corner to the other the visual perception underwent a major addition. Now I had a progressive sensation built up by scanning and memory. As I swept along the wall, the top and bottom edges started out as diverging, leveled off as my vision swept over the midpoint, and finished by converging. The overall perception now was vividly that of a pair of curved lines, very similar to what the fisheye image showed with the crepuscular rays. The crucial difference in viewing the latter is that it is a static view of a distorted image of a 180 degree scene, reduced to a much smaller field of view, while the former is not a single static view but rather a sequence built up by the brain into an integrated perception. When I stare at any part of the scene, I don’t see much of anything in the peripheral area unless it is moving or otherwise changing, or has very high contrast over relatively large areas. I need to be scanning to build a detailed visual perception of the whole scene.

chrlzs
2012-Jun-07, 02:30 PM
When I looked directly at the midpoint of each one, that line definitely looked straight.
...
As I swept along the wall, the top and bottom edges started out as diverging, leveled off as my vision swept over the midpoint, and finished by converging.
..
The overall perception now was vividly that of a pair of curved lines, very similar to what the fisheye image showed with the crepuscular rays. The crucial difference in viewing the latter is that it is a static view of a distorted image of a 180 degree scene, reduced to a much smaller field of view, while the former is not a single static view but rather a sequence built up by the brain into an integrated perception. When I stare at any part of the scene, I don’t see much of anything in the peripheral area unless it is moving or otherwise changing, or has very high contrast over relatively large areas. I need to be scanning to build a detailed visual perception of the whole scene.
That's a really useful and perceptive (this time no pun intended!) set of observations - thanks, Hornblower! I've bolded a couple of bits that I will come back to later - they allude to what I am trying to demonstrate... You have also hinted at the superb ability of your mind to sort/straighten all this stuff out so that you aren't aware of what it is up to... Which makes my job of proving that it *isn't* illusory, a fair bit harder..

But I'll get there!

grapes
2012-Jun-07, 02:53 PM
Thanks Hornblower, nice observations!

Before I move on (which may be a day or so..), is there anything that is unclear or disputed with the image or my statements above? All dimensions look OK, to nearest two decimals.

I would add another orthogonal line at C, 1.25 "behind" (from the observer, line C is completely hidden by line A) A, but you don't need to add it to the illustration. Since B is also orthogonal, the angle OBC will be 90 degrees, so the diagram with only B and C (with O) will be identical to your A and B (with O) diagram, with all dimensions multiplied by 1.25. We can go one step further and use units of 1.25 kilometer for the OBC diagram, and the OBC diagram will be exactly the same as your OAB diagram, just turned over.

I do that because anything you say about the straightness of A can be applied to B, by the same reasoning. Likewise, anything you say about the curvature of B can be applied to A.

Please note, I will be covering what happens when you change the 'ground' level later - I'd appreciate it if we don't start changing that aspect around just yet, for reasons that will become clear (I hope!) later
I'm not sure if what I've done is what you mean by changing the level, but regardless I think it goes to the key point, quickly.

Swift
2012-Jun-07, 03:13 PM
As Biogroovy has abandoned the discussion, and the thread has evolved into a discussion of mainstream science, the thread is moved from ATM to S&T. Carry on...

grapes
2012-Jun-07, 03:17 PM
I think I see where you are going here. In order to represent both lines in a 2D illustration, you assume one is going to be the straight one ("level"), and the other has to curve. My point is that you can choose either line to be straight, because there is no geometrical bend to either, when you look at each one.
ETA:

Anyway, for further reading while waiting for me to possibly self-destruct :), you may like to also look at this page:
http://termespheres.com/6-point-perspective/
in particular the discussion of 4-, 5- and 6-point perspectives, and critically, why those techniques are required, and what is said/shown about supposedly 'straight' lines.
Nice!

I guess you are talking about the discussion in the four-point perspective, where parallel lines are said to be like footballs?

The Termesphere ("6 point perspective"? no that's different) looks like it might be like the gnomic projection in reverse. All straight lines would get mapped to great circles.

chrlzs
2012-Jun-07, 11:13 PM
I think I see where you are going here. In order to represent both lines in a 2D illustration, you assume one is going to be the straight one ("level"), and the other has to curve.
Exactly, but I wish to take this a bit further, in particular to prove my original assertion that it is not an illusion, it is the inevitable distortion that is inherent in not just our perception, but also *any* attempt to represent the mapping of the line onto a projection, be it a camera, line drawing, whatever.

My point is that you can choose either line to be straight
Yes...

because there is no geometrical bend to either, when you look at each one.
I disagree with this because of your proviso! At any given moment you have to look at one, and when you do then the other *is* geometrically bent! That's where I'm heading with the illustration I shall continue with later. There *is* a geometrical bend in *any* line/object that is not on your plane of view. Under normal circumstances it isn't all that significant, and if you constrain your field of view to ~90° or less, it can be corrected for (and is, in high quality lenses, for example) and your brain 'fixes' it. But what such a lens (and your brain) is doing is distorting the actual view! The lines *should* be bent, and if you are making images that span more than 90 degrees like I do, eg a 240° panorama, you quickly learn that lines not in the plane of view *must* bend. If you tilt the camera up/down in order to straighten a line, then all other lines above and below that one are bent (except those now directly above and below, of course).

So that's the anomaly. It's why the Moon can look as if it is being illuminated from above horizontal when the Sun has set. It's why crepuscular/anti-crepuscular rays *do* bend upwards and then back down to the opposing vanishing points. It's why rail lines bend outwards at your feet and then re-converge at each horizon point. Yes, you can line yourself up with one line, but then the others get bent...

I maintain it is not a 'confused brain' issue, except that it is counter-intuitive and extremely weird. But real.

BTW, the Sun and Moon are quite nicely placed at the moment to demonstrate the problem - take a look at the Moon at about an hour after sunrise.. The illumination is clearly coming from *above* horizontal, yet the Sun is lower to the horizon...? If you tilt your head up to 'level' the two of them, it's a straight line alright, but now the horizon is horribly bent even though your brain does its best to hide that..

I've taken some photos this am to illustrate the issue and I'll post them later when I have time to make them look presentable.. Gotta work now..

grapes
2012-Jun-07, 11:40 PM
Yes, you can line yourself up with one line, but then the others get bent...

As I showed earlier, the viewpoint O is lined up with both line A and line B, there's no movement necessary geometrically.

I maintain it is not a 'confused brain' issue, except that it is counter-intuitive and extremely weird. But real.
If someone cannot look at a straight line and see it as a straight line, it is an optical illusion. There's no getting around that. The geometry is not going to differentiate between the two.

grapes
2012-Jun-10, 03:09 PM
Universe Today article today, crepuscular rays and anti-crepuscular rays, at the same time:
http://www.universetoday.com/95762/astrophoto-double-crepuscular-rays/