"You have had a year of physics, a year of chemistry, and a year of calculus in high school, yes?" Dr. Randolph said.
"We do not think in terms of courses. We think in terms of competencies. My job is to determine what you have already mastered and then lead you to master what you have not."
"And how long do we have to do that?" Alan asked.
"Until October, you will meet with me at least once a week, probably more. The point is not so much that you reach a certain goal as that you demonstrate the will and capacity to progress."
"In math and science?"
Dr. Randolph paused. "You know you will have a choice, if you are approved, at the end of the year."
"Of several different schools? Yes," Alan answered. Dr. Randolph then waited for a moment, as if to allow Alan's thoughts to run their course.
"Then let us begin," Dr. Randolph finally continued. He began to ask Alan questions in physics and calculus. They seemed to wander in a stream of consciousness.
"Is acceleration a scalar or a vector?"
"You can treat it in either way."
"What is the difference between a scalar and a vector?"
"A vector in Newtonian physics implies direction."
"Very good. Do you know anything about vectors in quantum physics?"
"Not much but I would like to."
And so the conversation continued for several hours. Sometime around noon, Mr. Fox poked his head in the door to see if they were ready for lunch, but they didn't even notice he was there.
"Show me the distance formula for one dimension on the board?" Dr. Randolph asked.
"Now show me how to derive a velocity formula in one dimension by taking its derivative."
After about an hour, Mr. Fox left and returned with a tray of tea and sandwiches, but they hardly noticed. Alan could tell that, while Dr. Randolph was wandering from question to question and from motion to Newton's laws, he was slowly checking off a list of knowledge and skills in his mind. At times he would say something like, "Physica 4 point 9," and a problem would appear on the screen. Alan would solve it and they would move on to the next question.
It was late afternoon before Alan started missing questions. He knew the basic equations and concepts. But as soon as Dr. Randolph would begin to probe, Alan would blank. The questions became more general, through thermodynamics and electromagnetism.
Although the day had begun rather seriously, you could see Dr. Randolph's spirits lighten as the day went on. It was about six when he suddenly stopped and looked at Mr. Fox, who had been sitting quietly in the back of the room working.
"Anyone feel like a good carbonara?" he said. "There's a great Italian restaurant in Cambridge."
"What's carbonara?" Alan said.