Why do people look up when thinking?

From what I understand, to clarify your question, people look to the right or left when thinking. Your left brain controls the more logical kind of stuff like math, and the right controls the more artsy type of thinking, so when you look left and upyou are using your right brain, and you might look that way to come up with a story, whereas you might look to the right and up when thinking about some math problem. Someone can clarify or expound upon what I am saying, but I know generally what I am saying has foundation.

So he is, but the principle is probably the same -- to avoid distraction while cogitating.

I believe in Meet the Fockers, where Robert DeNiro's character was a CIA agent, he could tell whether you were lying when questioned based on where your eyes wander.

pjotr has described what I learnt on my hypnosis course, in neuro-linguistic programming you're supposed to be able to work out how a person's thinking in reply to a question depending on where their eyes go, more or less as described. Presumably enough people were tested to discover the brain-eye relationship, just as some other actions are hard to do without making gestures or other physical responses.