Thread: Flat Earth in Bent Space

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Flat Earth in Bent Space

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?

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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.

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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.

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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.

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Originally Posted by Biogroovy
Is the Earth being round an illusion?
I always considered the Earth's shape as an oblate spheroid, not "round".

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Originally Posted by R.A.F.
I always considered the Earth's shape as an oblate spheroid, not "round".
It's closer to a geoid shape.

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Originally Posted by glappkaeft
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.

8. Originally Posted by Biogroovy
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.

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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.

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Originally Posted by R.A.F.
I always considered the Earth's shape as an oblate spheroid, not "round".
Spheroids are round, just not spherical.

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Contradiction in geometry... the Earth is round but we always hear. "...that the floor is flat". (just a comment)

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Originally Posted by sirjon
Contradiction in geometry... the Earth is round but we always hear. "...that the floor is flat". (just a comment)
If you think that is a contradiction in geometry, then this will blow your mind!

13. Originally Posted by glappkaeft
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).
Originally Posted by chrlzs
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.

14. Originally Posted by korjik
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.

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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.

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Originally Posted by grapes
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...

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Originally Posted by chrlzs
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.
Originally Posted by chrlzs
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.
Last edited by Bob Angstrom; 2012-Jun-02 at 04:13 AM. Reason: added the last line

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Originally Posted by Bob Angstrom
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. 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).
Last edited by chrlzs; 2012-Jun-02 at 01:25 PM.

19. Originally Posted by chrlzs
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?

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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.
It *isn't* just a lens effect!

The Wiki on 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 - 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.

21. Originally Posted by chrlzs
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.

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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...

23. Originally Posted by chrlzs
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.

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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.

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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:
Here's another example:
http://www.pbase.com/missouri_skies/...26596663/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.

26. Originally Posted by chrlzs
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!

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Originally Posted by chrlzs
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.
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.

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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) 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, 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..

29. Originally Posted by chrlzs
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) 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, 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.

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I'll be back later with a mathematical demo. Two parallel lines, one orthogonal, one not. One viewpoint.

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