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 incise 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

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 is 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 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 you if 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 distance stuff way ahead.

So if you cover the slow distance 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 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 shows 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: "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.