The Moon Terminator Illusion
Hey, Vsauce. Michael here. This is called the dolly zoom effect, and the optics that make it possible are also responsible for what's called the moon terminator illusion. A terminator is the line between an illuminated and dark side. Light arrives perpendicular to the terminator, but it doesn't always appear to. Maybe you've noticed this before. When the Moon and the Sun are up at the same time, and a good distance apart in the sky, the direction the Moon is being lit from won't always appear to line up with the position of the Sun.
What's going on here? The answer lies in visual angles. The further away from you something is, the smaller it will appear to be. In psychophysical terms, its visual angle shrinks - the angle within your field of view that it stretches across. Now, this means that everything we look at is foreshortened, that is, it diminishes in size towards the horizon line—a line infinitely far away. Things that far away are foreshortened to the point at which they have no height whatsoever.
This distortion affects everything that we look at. But it doesn't confuse us, because our brains know about it. We can look at an object that is foreshortened and figure out what it probably actually looks like. For example, a door is a rectangle, but it's wrecked by foreshortening when opened. Closer distances appear larger. The whole shape is different, but your brain isn't freaked out every time a door opens because it understands that different sensations don't necessarily mean different actual things. It's called subjective constancy.
Our brains cleverly factor in previous experience and perspective clues from the surrounding world to calculate in real time whether changes in what we sense are because of actual changes in the things we're looking at or are just merely products of their positions or the surroundings. For example, I, right now on this video screen, am vulnerable to foreshortening. But I probably look okay to you. However, if we frame in really closely and remove surrounding perspective clues, I can be made to look weird, strange, a little scary, distended.
I'm foreshortened without the necessary tools around me for you to mentally adjust. This is probably the crux of the Moon terminator illusion. Take a look at this. The line where that wall meets the ceiling is a straight line. Seriously, take a look. If you look to the left and right, it continues to look straight, and trust me, this building was built with level straight ceilings. But that's not what your eye senses.
A camera will help demonstrate this. It doesn't add in the post-sensation processing that our brains do, and we can also frame in to remove other clues telling us what to think. Now, sure enough, right in front of us, the line is level with the screen of the camera—it's a straight line—but if we move our eyes across the line, look what happens. If I pan this way, the slope changes, and now the line appears to be going up and to the left. And if I panned this way, the line appears to be moving up and to the right.
What's going on here? A straight line can't have changing slope; that's what a curved line does. Just like the curve we think we see between the Sun and the Moon. But wait. If the line between the Sun and the Moon is curved because of foreshortening, why don't we see lines like this one as curves? Well, here's a clue. Clues. We know what rooms are supposed to look like. We know how they're built. We have experience with them, and there are other things in the environment helping us. But when you look at the sky, there's not much to help you.
In the absence of clues about distance and perspective, our brains assume that whatever we're looking at is equidistant from us, making the sky a sort of dome surface, like a planetarium screen. The only clue we have then is the horizon, but it's a red herring because the horizon doesn't foreshorten. It's just a place where, due to foreshortening, everything becomes infinitely flat.
Brian Rogers and Olga Naumenko demonstrated that these things result in the terminator illusion by using a planetarium. They projected two dots onto its dome, mimicking our perception of the Sun and the Moon. They've then asked participants to place a third dot on the straight line connecting them. But just as in the Moon terminator illusion, people incorrectly placed the third dot. They were influenced by a desire to stay parallel to the horizon, as if it was subject to the same foreshortening rules.
Our brains also often fail to factor in foreshortening when it comes to crepuscular rays, light beams streaming through gaps in clouds. They appear to converge from a common point, as if the Sun is only a few thousand meters above Earth, but, of course, in fact, the Sun is extremely far away, and these lines are actually pretty much exactly parallel. It's true. They look like they converge for the same reason railroad tracks appear to converge. The visual angle of the distance separating them shrinks the further down you look.
Sometimes our brains do the opposite. They assume and consider foreshortening even when it isn't really there, like in this illusion where the cars seem to be different sizes, but in actuality, on the page, they are all the same size. Everything else in the image is affected by foreshortening, so our brains assume that the cars are too and decide that in order for them all to have the same visual angle, which they do, the more distant ones must be literally larger in real life.
The rate at which the visual angle of something you are looking at changes as you move toward it, or away from it, is not constant. In order to cut the visual angle of an object in half, its distance from you must double. That means objects really, really far away require a lot more movement to have their visual angle changed compared to nearer objects. This is called parallax, and it's a major reason moving allows us to learn so much about depth.
It's why stuff on the side of the road whizzes by you as you drive past while distant features of the landscape appear to only crawl past. A really distant thing, like, say, the Moon, 384,000 kilometers away, appears to move so little as you do, it can seem to be following you. It's not, of course. It's just geometry. For the same reasons, moving a camera through space will affect the visual angle of nearer things, like the Vsauce mug here, much more dramatically than distant things, like Jake Chudnow's album against the wall.
It is barely changing size as we move back and forth. But unlike moving, zooming increases the visual angle of everything equally, regardless of depth. Notice that when zooming, the distant album grows and shrinks right along with the mug. Now, if you move IN while zooming OUT, or vice versa, the zoom will be most apparent when looking at distant things, while the move is more apparent on near things.
The result can be trippy. Here I've been placed where both effects cancel each other out, so everything around me changes instead. Another great illusion that takes advantage of parallax is the popular star field or hallway illusion. Cover the middle of the video, and you'll appear to be moving much faster. But if you cover the edges, you'll appear to be moving much slower. All you're doing is altering the perspective clues your brain receives about movement.
The nearer stuff at the edge changes position faster than the distant stuff way ahead. So if you cover the slow distant stuff, your brain only has the faster moving stuff to judge speed from. But cover the faster near stuff, and the slower stuff becomes the new near. Your brain assumes that you've slowed down. The optics and mathematics behind all of these effects were understood at least thousands of years ago.
During the Renaissance, artists used that knowledge to produce paintings that imitated reality really well. I mean, the perspective is quite realistic. But... the renaissance? Why did it take so long for us to get there? I mean, look at this pre-Renaissance painting. What the heck is going on here? The perspective is all wrong. That's not at all what such a scene would actually look like. Artists and viewers contemporary to works like that saw the world just like we do; they saw foreshortening - they couldn't help but see it.
Foreshortening is right there in plain sight. No, foreshortening is plain sight. So, what gives? Were medieval artists all just a bunch of five-year-olds? No. No in the sense that the question is wrong. Realistic-looking perspective was used way before the Renaissance. Now, it might not have always been mathematically formal perspective, but foreshortening was understood.
Western art went from this to this, not because humans all of a sudden became smarter, but because of a difference in desire. What to us today might look unrealistic and thus bad was, in its time, deliberate and popular. The shift to imitating the world mathematically, as if seen through a window, was more about cultural interests and objectivity and the individual than it was about artists all of a sudden becoming smarter.
Furthermore, perspective illusions show that what we think we see isn't always what we're seeing. A child's drawing may seem crude in terms of objective mathematical imitation, but there are other things about the world and our experience of it worth imitating. Teasing out the less plainly obvious to show something personal is sometimes even harder than following perspective grids. Picasso put it this way: "It took me four years to learn to paint like Rafael, but a lifetime to learn to paint like a child."
And as always, thanks for watching.