My hat would fall down over my eyes

Rick and Peter were in a mental hospital. Annually 2 patients were freed on the basis of 2 questions. If they answered the questions correctly, they're deemed cured and free to go.

Rick was called into the doctor's office first.

The doctor said, "Rick, what would happen if I poked out one of your eyes?"

Jon said, "I will be half blind."

"That's correct. What if I poked out both eyes?"

"I will be completely blind." The doctor stood up, shook Rick's hand, and told him he was free.

On Rick's way out, as the doctor filled out the paperwork, Rick mentioned the exam to Peter. He told him what questions were going to be asked and gave him the answers.

So Peter came in. The doctor went through the formalities and asked, "What would happen if I cut off one ear?"

Peter, remembering what Rick had said was the correct answer said, "I will be half blind."

The doctor looked a little puzzled, but went on. "What if I cut off the other ear?"

"I will be completely blind," Peter answered.

"Peter, can you explain how you'd be blind?"

"My hat would fall down over my eyes."