When SeanF talked about that requirement, he was talking about a fish eye lens, which does have considerable distortion. That's why they wanted the line to go through the center.

I haven't heard back about wagering. And I need the money. I think that is a good analysis. I think we totally agree, except about the conclusion.

That's between the two of you. We won't stand in your way.

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Wow, this is getting to be another "0.999...=1" thread!

Look at the stitched panorama tony posted, compared to the one lek posted earlier.

In lek's panorama, the horizon is straight but the line from the moon to the sun (perpendicular to the terminator) is curved. In tony's, it's the opposite - the moon-sun line is straight and the horizon (although it's not all visible) is curved.

In both cases, though, the curvature is a distortion result of the photography. In both cases, in real life, both lines were straight.

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I think it appears to be slightly curved in tony's as well. A pan from sun to moon would only preserve the straight line between them if the pan followed the straight line, but an equatorial pan in general might not do that.

Yeah, that's true. But if you did pan across that straight line and stitch the image together, the horizon would be curved.

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Any panned shot will distort the image somehow

I agree that the Sun / Moon line is not perfectly straight in my photo. It would be if I set up the picture better .

I was guessing the angle to set the tripod. I haven't measured it yet, but the roof angle on the left should give it away. I live at lat 38. Also, I would have wanted the Moon perfectly centered horizontally in the photo. The Sun too. (I don't even know exactly where the Sun is in that picture). Like you said, an equatorial pan wouldn't do that unless the Moon and Sun both had the same declination in the photo.

Regardless, its close enough to straight to make its point. I'd like to make a nicer one, but ever since Clop asked this question, we've had nothing but bad weather. I blame Clop for all this rain we've been getting.

Nice job, Tony, above and beyond.Even then, a line of constant declination is not a great circle!

Aren't there two questions here?

1) does the illusion exist
2) why does it exist.

Doesn't Martin's picture prove question 1? If we trust him that the Sun was low in the sky, then the line* othogonal to the terminator is pointing at least slightly up, whereas the Sun is slightly down.

*Of course, the terminator is slightly curved. I'm choosing the center point. Even then, there are an infinite number of lines orthogonal to any other line. I'm using the line in a plane parallel to my eyes when looking directly at the moon.

From my point of view, no pictures can prove the illusion exists, because it is an illusion, not an actual situtation. In other words, it is a result of how our minds process the visual clues--but the clues themselves do not produce the actual illusion.

On the other hand, others think that the picture we'll see in ten days or so will prove it.

But I said in my first post to this thread that the illusion does exist. I think everybody can now be convinced that it does.

Do you disagree that the line perpendicular to the terminator (and parallel to the lens/eyes) has a negative slope? (ie, relative to horizon, is pointing up and to the left)

When I've gone outside and looked, and imagined a straight line from the moon, perpendicular to the terminator, that line extended (straight) ends up at the sun.

Any straight line segment can be extended along a great circle path (centered on the viewer) so that it looks straight. But great circles intersect the horizon--so straight lines drawn from that moon could appear to go down to the horizon, depending upon where the moon and sun are.

PS: I just went back and looked at Martin Lewicki's photo again, and the diagram at the bottom. In the diagram, it shows the straight line and the great circle between the sun and the moon as two different paths--but I think from an observer's point of view, the two paths are coincident.

I think very many points made in this thread by everyone are all quite right.

If you hold up a long straight line, or use power lines for example you know go quite straight from left to right, you see that either the line is straight, or the horizon is straight (on level ground). The angular vertical distance from the line is greater in the middle than in the edges, so you can not see them both straight, you have to choose which one you see straight.

I guess most people would choose to see the horizon as straight, since that plane, defined by you and the line of horizon is where most people "live".
In reality, the horizon you see is not straight, because of earth's curvature, it would be seen as circle from above.

The panorama i posted reflects this view quite perfectly, the distortions in the photo aren't caused by the optics, but the plane the picture was taken in, which was chosen as the plane defined by camera, and the "straight" line of horizon.

EQ mount (if perfectly polar aligned) would do the panorama along the plane defined by the eplictic, which would still show moons terminator in slightly wrong angle as moon can be several degrees off that plane.

Fisheye lens on the other hand would show what you want it to show. Aim it at the horizon, and it's straight and moons terminator similarily tilted as in my panorama, aim it so that the real straight line goes through middle of the lence would make the case where the camera moon and sun are on same plane, such showing the perfectly aligned terminator and everything else severely curved.

And of course hhEb09'1 's way of just lying down (or tilting head) just right, aligns your sight to the plane defined by moon sun and eyes, and thus shows it as straight line (while horizon is curved).

edited to add, In couple weeks when you can actually see the moon and sun at the same time, and take pictures with normal 50mm lens, the situation should be the same as with the fisheye lens, altho the effect is much smaller of course, and who knows how much the brain can actually correct the view... Must test it anyway just to see the brain part of it

Ecliptic is the plane of Earth's orbit. I think celestial equator would be the correct term.

Almost. You don't have to lie down or tilt your head. So, both the line between the moon and sun is straight, and the horizon is straight--you just look at one or the other. From the point of view of the center of a sphere, every great circle is a straight line. The line between two points (the sun and moon) is a great circle, and the horizon is a great circle (approx., and adjusted for the height of the observer which doesn't make much difference)
In the sky, the ecliptic is the sun's path through the constellations (hey, it was originally defined by geocentrists ). The celestial equator lies halfway between the two poles, so the sun is only at the celestrial equator at the equinoxes.

oops... Thats right.

You can know they are "both straight" and maybe because of that you can also percieve them as such, but that doesn't mean it is so.
One is straight line, one is a circle, they both look (photo, no brain corrections) straigth only if they coincide (moon exactly in horizon).

So the horizon would always be a straight line to you then?

It's not because I am mentally adjusting things. I say that that is what we see in photos too.

But panoramic photos, or fisheye photos, introduce distortions--and the bet between clop and me rules out distortions.

Hmm.

Picture yourself standing in some huge, flat area. Flat all the way to the horizon. You are standing on a road that extends straight off to your left and right, all the way to the horizon.

You stand perfectly vertical with your head facing straight forward. Point your eyes to the point on the left horizon where the road meets the horizon (don't turn your head, just your eyes). Track your eyes across to where the road meets the horizon on your right. If you track your eyes along the horizon, they will simply move straight from left to right. However, if you track your eyes along the road, they will dip down and then back up - a curve.

But what happens if you lean forward and tilt your head so your face is pointing straight down at the road and do the same thing? Now you can track along the road with a straight left-to-right motion, but tracking along the horizon requires your eyes to move "up" (towards the top of your head) and back down.

So is it the road that is "actually" straight, or the horizon?

If you position your head such that the moon's terminator is perfectly "vertical" (relative to your head) you should then be able to get from the moon to the sun by tracking your eyes straight left-to-right. That's the path the sun's light is taking to illuminate the moon; it's orthogonal to the terminator, and it's a straight line - just as straight as the horizon or the road.

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No, the point i was trying to make, its a matter or perspective, geometry of the situation. Two lines, one truly straight with different declination than the horizon and the horizon itself, can not be seen as parallel, as their apparent angular distance doesn't stay constant (the powerline + horizon comparison). The line you "look" at is straight, while the other is curved.

Exactly the same effect as with the moon, except you cant see the "road" between moon and sun.

You turn your head / eyes perpendicular a plane, if that plane is defined by straight horizon and your location,(the most natural choise imo), you see both road and the moon-sun line as curved in opposite directions. But you can choose your "straight" line from your perspective to be any of those 3 lines, which automatically makes the others look curved.

It's not an illusion, its geometry. If your mind can make them all seem parallel, or even two of them, then it is your brain doing some "calibration" eg. an illusion.

edited for clarity

SeanF, Youv'e got it!

And you can ask, is it the near edge of the road, the stripe
down the middle of the road, or the far edge of the road which
is straight? All three lines converge at the horizons, so you
know that at least two of them must curve. Which one goes
through the center of your field of view? That's the straight
one. At that moment.

(Assuming you don't have astigmatism and aren't using a
view camera with an adjustable back!)

You've got it, too, lek!

I think this is an illusion, but it is clearly an illusion caused
by objective geometric effects as much as by subjective
perception and interpretation of those effects.

-- Jeff, in Minneapolis

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Why can't you "look" at them both? Why parallel? Is this a different illusion? I'd mentioned the converging railroad lines earlier.
When artists draw converging road lines like that, the lines are still straight though. They don't curve.

You can see both at the same time, but you look at certain point, if the point is within that "line", the other will look curved. Or equally you can look at the middle while both are curved to opposite directions.

It's the same thing as with converging railroadlines. As you stand next to the tracks, the angular distance of them varies because of the perspective.

As Jeff Root said already in his comparison of "this side of road or the other or the middle?" the two tracks in the railroad aren't seen as parallel all the way, which one is the "straight" one?

I have been thinking about all this stuff and I've found an interesting thing.

Close one eye, keep your head still and look at a long straight line passing across from left to right, high in front of you, like the top of your living room wall or an overhead power cable outside.

You see the line as straight, but the fact that, if you slowly pan along it, you have to tilt your head back and forward to keep it in the middle of your field of view, means that it's actually an arc. But you don't see the arc - even if you try to see it as an arc you still see a straight line.

Is this some fundamental accommodation by the brain in perceiving a curved line as a straight line due to context? This would explain the problem of lack of context with the sun moon line.

Or is it that the back of our eye is spherical, and the image projected onto the retina shows arcs as straight lines again. Kind of a sphere to sphere mapping. This might explain why a curved line appears as an arc in a photograph (where the film is flat) but appears straight in our visual perception (where the retina has the same curvature as the sky, but scaled down in size). And very long arcs (like sun moon) trick our brains because we can't image the whole arc without moving our eyes.

I hope I've explained that properly - to me these are two distinct issues.

clop

That's not entirely true: some very careful perspectivists do curve the lines if they are producing an image that subtends an unusually wide angle. M.C. Escher was a meticulous draftsman in this respect, and a number of his drawings, even naturalistic ones, have curved lines of perspective.
There is an extensive discussion of curved perspective lines in The Magic Mirror of M.C. Escher, by Bruno Ernst, using overhead wires rather than underfoot rail tracks as the example. It finishes like this:Grant Hutchison

I don't think so. Can you elaborate on that?All are straight. The perspective of a straight line is a straight line--it may disappear at a point at infinity, but between that point, and the point next to you, it is straight.
Careful there. It is a straight line, you see it as a straight line, but it's actually an arc?It's not a curved line, in that example.

It is a curve unless you move your head, unless you're near the equator (etc.). A photograph will show a curve.

For god's sake, somebody go and give the moon a push.

clop

But if you look at the whole picture, you see the tracks in front of you wide apart, and converge on both left and right, are the lines straight from your point of view?

I'm familiar with Escher's work, I've been a fan for almost forty years. But I was just using the canonical disappearing road as an example--most artists do have a little more interesting subject in the foreground. Hey, the Escher website even has a video of him at workI get some curved lines at the edges of my bifocals. But that is a distortion.

More from Bruno Ernst. After mathematically deriving the shape of the curves we see when projecting long straight lines into a cylindrical or spherical field of view, he deduces that they are sinusoids. So that's a mathematical construction based on perspective geometry. Does it correspond to what goes on inside people's heads? Well, it seems to fit what I see, and others here seem to have a similar experience.
So did Escher:Grant Hutchison