We see using our eyes, but we perceive using our brain. Both take the duty very seriously, and occasionally, there is a turf war. In cases of Emmert's Law, the brain wins, and reality loses.
It's the brain that takes the shapes and colors that we see with our eyes and forms them into comprehensible objects. To do this it creates templates that the objects we see fit into. This is why sometimes you may see a clear image of a person or animal out of the corner of your eye and then turn to see that it's actually just a shadow. The brain formed a shape into an object and told us we saw it. It's only when we turn and get more information that we see it as it actually is.
Even comprehensible objects will bend and twist when the brain gets involved. Emil Emmert was a scientist who measured the afterimages of objects. He noticed that when the objects were projected onto a distant background, or just seemed to be, their afterimages looked larger to people than the afterimages of objects projected on a near background. Modern scientists expanded Emmert's law to the objects themselves. A quarter, projected onto a background that looks far away, will look massive. One projected onto a background that looks near will appear tiny.
You can try the illusion out for yourself by looking at this incredibly complicated image that the io9 graphics department came up with. (It was done by the same people who worked on Life of Pi.) Stare at the white circle for about 45 seconds. I know it's a long time, but you can listen to music while you do it. After 45 seconds, look at a piece of white paper on your desk. Then stand up so the paper is farther away from your face. Then look at a white wall. When I looked at the paper up close, the after-image of the white circle appeared roughly the same size it is on screen. When I backed up, it looked to be about the size of a clementine. When I looked at the wall, it was dinner-plate size.
Why? The brain understands that if you see an object only a few inches from your face, and it takes up a good deal of your field of vision, it's not that big. If you see something far away and it still obscures a good deal of your vision, it's large. The brain then provides you with the knowledge of that difference in scale, so you don't assume that a car on a distance highway is a model car close up.
Because of our experience on how things at different distances should look, the brain exaggerates the effect. We "know" that objects against faraway background are bigger, and so we see them as bigger. Nearby objects may look big but actually are small, and the brain insists this is the case despite their appearance to the eyes.
This isn't just people self-reporting. Actual monitoring of activity in the visual cortex has shown that people are seeing – with their brain – larger objects when those objects are projected against a distant backdrop. Under the right conditions, the brain literally won't let you get an accurate picture of the world.
Top image: Tiago Sousa.