We were recently invited to a Reform Jewish temple for Shabbat services, and while I was sitting there – a bit bored – I began thinking about how I would sketch certain parts of the room. There was a section where the ceiling height abruptly dropped by a couple of feet. There was clearly a 90 degree angle at the point where the ceiling dropped.
But when thinking about how to sketch that angle, I noticed that from my perspective the angle appeared closer to 20 degrees. If I were to draw on paper my perspective view of the ceiling, I would have to draw that much smaller angle. Yet someone viewing the sketch would immediately understand that the actual angle was 90 degrees.
Fascinating stuff, and it turns out that it has a name: perceived visual angle. The illusion created is called the perceived angle illusion. Try it out with this slightly more obvious example:
Take a thin sheet of paper and an pen that writes easily. Hold the sheet of paper up to the screen and trace the right angles of the boxes below. Don’t trace the entire box, just a small portion of each angle. You can move the paper around so each angle is in its own separate area. How many right angles do you see in the photo? How many on your paper?
When your mind sees the image it interprets the lines as depicting right angles, but many of the angles aren’t close to 90 degrees.
posted by yair