Imagine you are standing in front of a bathroom mirror; how big do you think the image of your face is on the surface? And what would happen to the size of that image if you were to step steadily backward, away from the glass?
A recent article in the NYTimes (Mirrors used to explore how the brain interprets information) has some interesting nuggets in it. The one that stood out was the rather straightforward one quoted above…
According to the researchers quoted in the article, most people answer the questions with some variation of the following:
To the first question they say, well, the outline of my face on the mirror would be pretty much the size of my face. As for the second question, that’s obvious: if I move away from the mirror, the size of my image will shrink with each step.
Turns out both of these typical answers are wrong!
I knew the answer to the first one – that the outline of my face in the mirror would be exactly half of the size of my real face. There are two main reasons for this. The first is the basic geometry of the fact that the mirror is exactly halfway between me and my image and second, that our brains over-compensate for size differences with distance (known as the size constancy effect). It is the combination of the two that (a) leads to the smaller, exactly half, size and (b) to our inability to realize that.
However, I had not truly understood the consequences of the geometry… So even though at some intellectual level I knew that that the image of my face would always be half its size in the mirror, I didn’t understand the consequence that it would always have to be that, irrespective of how far (or how close to the mirror I was). Wow… Turns out even things I thought I had understood, I didn’t fully understand!!
A good example of a véjà du moment!
You can find out more about size constancy by going here