Arrows

I was at a restaurant recently that had a set of puzzles on the place mats. One of these was the classic arrow optical illusion:

Which of the two line segments is longer?

arrows

Now, we've all seen this one, so we readily answer, "they're both the same", of course.

Well, actually, in this case I've modified the classic so that the upper segment is shorter than the lower (in the restaurant they were the same lengths).

What's the point of this? Well, I think the correct thing to learn from the arrows exercise is not that we should know that the lines are the same lengths, as everyone "knows", but instead that eyes can deceive and one should measure things. I believe we are doing ourselves and our children a disservice if we always print these puzzles with equal length lines. The only lesson they learn there is that the lines are of equal length, which is not the right conclusion at all.

Copyright 1997-2008, Ben Littauer (alternate email littauer@gmail.com)