Who has something to show?
From the traditional professor’s vantage point, beyond the class’ students was a wall of windows looking out toward the student union building, with young coeds climbing and descending the long flights of stairs between here and there. But this was a class conducted in the tradition of Moore’s Method: I stood in what would be his position at the front of the class, and he sat near the back of the room, his back to the more pleasant view, focused upon us.
I explained to my peers and the professor that I believed I had some insight into this or that and proposed it as a potential theorem. I had constructed what I believed would be the framework for a proof and wanted to work through my thoughts at the board.
The floor was mine.
May I erase your work?
In Moore’s Method, one might take to the blackboard to amend a flawed argument, to propose an alternative approach, to begin a new argument, or anything else.
Proper respect in this setting, our professor explained, included showing proper respect for your colleague’s work. It did not matter whether the construct on the board was a work of art or an artifact demonstrating someone’s complete and total misunderstanding: after a colleague had put his heart and soul into constructing his proofs at the board, nothing could be more insulting than for someone else to take the stage and, with a single wipe of the eraser, to cut through his work without a thought. Be mindful of your peers.
Yes, of course. Thank you.
In my mind, the problem was extremely complex, and moving my multidimensional understanding from within my mind to the two-dimensional, linear blackboard was problematic. I would look for the elegant solution—the proof in “God’s book,” as Erdos might say—later; for then, it was a good exercise on many levels to attempt to share what I had as best as I could.
I filled the board at center stage, walking, talking, and exhausting my chalk. Once filled, I moved to the board at stage left, filling it with more pictures, symbols, propositions, and explanations. Occasionally someone, possibly the professor, would interject with a question or comment, challenging points as they arose. As a result of such questions, great discussions can ensue: holes in logic can be revealed, improvements or simplifications can be discovered, gaps can be bridged as a result of the collaboration. But as I moved to the blackboard at stage right, the professor’s interjections became more frequent and grating.
What followed remains something of a blur… but it certainly ended as a moment etched permanently in time with a crystal’s clarity: There was absolute silence, my fellow students’ mouths all agape, eyes opened wide, staring at me with disbelief. The professor sat back lit by the sun, obscuring the details of his expression, but he seemed to be nodding his head slightly…
Others recounted the story and filled in the gaps: The professor had increased the rate and intensity of his onslaught of questions until he finally claimed I was off track. I snapped: In an instant, I spun around and, interleaved with a string of curses, I forcefully and expressively indicated to him that had he been paying attention to me instead of crafting his next nitpicking attack, he might have been able to follow my argument.
Silence, and a nodding head without a face…
I was 26 or 27 years old, having recently completed four years in the Army. I held no particular awe of rank or authority in the military, so I was certainly not going to be intimidated by a person holding the rank of professor. Still, from my seat I was distracted by the thought that I may have made a terrible mistake…
As class ended, I caught the professor at the door and offered my apology.
No longer obscured by the sun, I saw the old man’s devilish grin. In response to my contrition he offered these words:
No one said that learning isn’t confrontational.
That was the day this professor became my mentor and I became his student.
Over the subsequent years, he and I would spar with tremendous intensity. People in the department certainly must have known that this was our way of hammering through mathematical proofs—and just about any other argument—though I wonder how a stray undergraduate walking down the hall might have been jarred on hearing us. At least no one ever called campus security… And how amazing it was that one could argue, argue, and argue some more against a point with complete sincerity and with such intensity and then, suddenly, be happily stunned with the realization: “Ah—there it is. I see it! You’re right!! Good job!!!” At the end of the day when this practice was over, we would sit outside and watch the pretty coeds go by or sit in the pub with a beer—again, watching the pretty coeds go by.
Passion and intensity speak to my soul. Conflict is one arena wherein this energy is expressed. And what is life without this energy? What is the point of life without conflict, passion, or intensity?
And how better to learn to generate, to use, and to deal with such energy than among friends?
In retrospect, this was one occasion wherein I had discovered an Aikido dojo before my physical practice had ever begun.