“What’s the NP in NP-Hard stand for?”
April 2001, Orlando, Florida; the final round of a science fair for high school seniors. I had just finished my presentation about my research and gone into Q&A. One of the judges had asked me this question and was now awaiting my response, growing increasingly impatient as I didn’t answer.
My mind raced. I knew what an NP-Hard problem was —my research dealt with one example of a NP-Hard problem: vehicle routing (think FedEx deliveries) — and, in the course of my presentation, I had explained what the NP-Hard class of problems involved.
But I didn’t recall what the NP stood for.
“I’m sorry, I don’t know what the NP stands for.”
The judge’s face fell, his eyes glowered, and he began a rant: “How can you present research on an NP-Hard problem if you don’t know what the acronym stands for?” He went on.
I blushed, turning bright red. I blush easily and quite vividly even now, and the effect was much more pronounced when I was 17.
After the rest of the Q&A, a different judge came up to me. He apologized for his colleague’s reaction to my admission that I didn’t know the answer. In fact, he said, he was impressed that I had the courage to say that I didn’t know. I shouldn’t lose that, he said.
I thanked him, and wondered what he meant. Courage?
To my rational 17-year-old science nerd brain, it seemed logical that if you didn’t know the answer, well, the sooner you admitted that, the sooner you’d learn the answer.
I wish I had known the answer, and spared myself some embarrassment at the first judge’s rant, but well, I didn’t, and that was okay, because now I would never forget that the NP in NP-Hard stood for non-deterministic polynomial time.
In my childhood, I had been raised by two engineers who taught me that questioning wasn’t only okay, it was encouraged. My parents, immigrants from Poland, never hid their lack of knowledge if I asked a question they didn’t know. If it was the meaning of an English word, we’d look it up in the dictionary together. If it was a concept, off we’d go to the encyclopedia. There was no judgment, only the joy of learning something together.
I imbibed this attitude and assumed it was a natural as breathing air, because for me it was. Only as I went off to college at MIT did I realize that not everyone had the same approach to the problem of not knowing.
Some friends tried to fake knowledge, or avoided the question entirely. This worked, for a time, but usually resulted in panicked problem set study sessions late at night, as they finally confronted their lack of knowledge and had to swiftly seek to remedy it.
Others avoided topics they didn’t understand, retreating onto islands of things they knew, never venturing to sail the oceans of knowledge just off-shore.
Some shared my attitude, and together we explored and learned — where one did not know, another might, and if all of us didn’t know, there was great joy in trying different solutions together.
The problems could sometimes be nearly intractable. I remember my first-year physics class, 8.012 Classical Mechanics, taught by Prof. Frank Wilczek. Our study group would sometimes get stuck after hours of wrestling with a problem and so we’d send one of us to go to office hours and ask.
I remember once in office hours I had the gall to complain to the professor: “These problems sometimes feel we’re bashing our heads against the wall.”
At my off-hand comment, Prof. Wilczek’s eyes lit up and he smiled broadly. “Yes! That’s the goal!”
I looked at him incredulously: “The goal?”
“Yes, we want you to learn how to deal with tough problems, with problems that don’t yield at the first attempt — how to break through that wall. We make the problems hard so that you can’t solve them easily, so that you learn how to wrestle with them.”
That moment has stuck with me. Together with the notion that it was okay not to know, I’ve carried with me that it was okay to encounter a wall, and to seek help, and to feel powerless before a huge (or even not-so-huge) problem.
Because it was only when those feelings were okay, were acceptable, when I was comfortable with not knowing — only then, with the fear gone — only then could I be free to be creative and open to even the possibility of finding the solution.