Pythagorean Dream

This is a dream from my college days. In the dream, I’m taking a test in a large open testing area with many kids sitting at individual desks. Everyone had a blank piece of white paper and a pencil. A tester at the podium asked the one question on the test: “Imagine you are visited by an alien species with whom you cannot communicate in written or spoken language. What would you do to communicate with them? All you’ve got is paper and pencil and an hour. Go.”

For a long time, I sat in stunned dejection wondering how to respond. I finally decided to draw a right triangle and label the three corners A, B, and C. Then I wrote the equation: A squared plus B squared equals C squared. My idea was to demonstrate to this supposed advanced race that I also understood some principles of mathematics and to open communication with them on that basis. If they understood that the corners were labeled with the first three letters of our alphabet, they perhaps could understand how our alphabet works and we could develop a kind of substitution code, which would lead to the beginning of written communication. 

I didn’t know whether my answer was correct or useful. The person behind the podium asked us to bring our papers forward one at a time. She looked at each paper and then told the test takers which way to walk down the hallway, and which door would admit them. When I got to the podium she looked at the paper and told me to go down the hall and enter the second door on my left. When I got to the heavy wooden door I knocked. A slot opened up and the doorman asked me: “Who is the greatest philosopher of all time.” I said Pythagoras, not because I believed it but because of my response on the test. The door creaked open and I stepped inside. The doorway led to a short tunnel that opened into a large brightly lit theatre. It was filled with men mostly. Young and old. All of them were carousing and telling loud stories and laughing uproariously. I walked toward the stage and ended up in the beer line. There was a keg going. I got my cup full of beer and started looking around. Faces I’d seen before popped out to me. “Hey, fellow from school whose name escapes me. Hey, I’m glad you made it. Have a beer.” It seemed I knew many of the faces in that theatre. We were all so happy to have made it. We congratulated each other and toasted to our health. 

After an hour or so of this, I started to wonder why we were in the theatre. Was there to be a show? There wasn’t one. And every single person in that room started to wonder what the hell was going on. The beer continued to flow and each new person who came through the tunnel was welcomed with a shout. “Hey! Another Pythagorean! All right!” The dream continued after this fashion for a long time. Eventually, I became dissatisfied with this. And I realized that I had answered the question incorrectly. As I woke up, my mind told me the correct answer: to draw a picture, of course. It had nothing to do with mathematics at all. If you have no language to work with, you draw a picture. Duh!