One day Hamming was talking to a colleague who mentioned a tough problem someone else was working on. Hamming was intrigued:
page 134 pdf:
The more I thought about her casual remark the more I felt he needed real guidance-meaning me! I looked him up in the Bell Telephone Laboratories phone book and explained my interest and how I got it. He immediately wanted to come up to my office, but I was obdurate and insisted on meeting in his laboratory. He tried using his office, and I stuck to the lab. Why? Because I wanted to size up his abilities and decide if I thought his problem was worth my time and effort, since it promised to be a tough nut to crack. He passed the lab test with flying colors… Furthermore, I was soon convinced, although I knew little about the details, his experiment was important to physics as well as to Bell Telephone Laboratories. So I took on the problem. Moral: To the extent you can choose, then work on problems you think will be important.
Here’s the stroke of genuis: Hamming knew of another guy (Kaiser) that was working on a related problem, but…
Trouble immediately! Kaiser had always thought of a signal as a function of time, and the square of the area under the curve as the energy, but here the energy was the independent variable! I had repeated trouble with Kaiser over this point until I bluntly said, “All right, his energy is time and the measurements, the counts, is the voltage”. Only then could Kaiser do it. The curse of the expert with their limited view of what they can do. I remind you Kaiser is a very able man, yet his expertise, as so often happens to the expert, limited his view.
My contribution? Mainly, first identifying the problem, next getting the right people together, then monitoring Kaiser to keep him straight on the fact.
I want to say something grand about this that’s not “OMGMG, he’s so smart, right?!!”. I’m struggling. On the one hand, you might think that Hamming is the brilliant one, yet his contribution was genuinely small. Hamming had only passing knowledge in the domain, neither enough to ask the right questions nor know the right answers. But feeling the connection between these two problems is an immensely powerful creative act. And here’s why I think Hamming is so great: he built this capacity in himself.
pdf page 188.
Over the years of watching and working with John Tukey I found many times he recalled the relevant information and I did not, until he pointed it out to me. Clearly his information retrieval system had many more “hooks” than mine did. At least more useful ones! How could this be? Probably because he was more in the habit than I was of turning over new information again and again so his “hooks” for retrieval were more numerous and significantly better than mine were. Hence wishing I could similarly do what he did, I started to mull over new ideas, trying to make significant “hooks” to relevant information so when later I went fishing for an idea I had a better chance of finding an analogy.
This deliberate act of recognizing a strength in someone else, thinking hard about it, then emulating it is everywhere in Hamming’s book. Everywhere.
Sometimes great people are just born into, or unconsciously develop, their talents. They can’t tell us what the difference is between us and them. Hamming, on the other hand, started on our side but transformed himself into one of them. This, I think, is what makes a great teacher. He had “hooks” into the learning process because he worked so hard at it. Here’s another Tukey story:
Now to the matter of drive. Looking around you can easily observe great people have a great deal of drive to do things. I had worked with John Tukey for some years before I found he was essentially my age, so I went to our mutual boss and asked him, “How can anyone my age know as much as John Tukey does?” He leaned back, grinned, and said, “You would be surprised how much you would know if you had worked as hard as he has for as many years”.
One last story that brings these themes together:
Bill Pfann walked into my office one day with a problem in zone melting. He did not seem to me, then, to know much mathematics, to be articulate, or to have a lot of clever brains… I checked up on him by asking around in his department, and I found they had a low opinion of him and his idea for zone melting. But that is not the first time a person has not been appreciated locally, and I was not about to lose my chance of working with a great idea-which is what zone melting seemed to me, though not to his own department! There is an old saying; “A prophet is without honor in his own country”. Mohammed fled from his own city to a nearby one and there got his first real recognition!
So I helped Bill Pfann, taught him how to use the computer, how to get numerical solutions to his problems, and let him have all the machine time he needed. It turned out zone melting was just what we needed to purify materials for transistors, for example, and has proved to be essential in many areas of work. He ended up with all the prizes in the field, much more articulate as his confidence grew, and the other day I found his old lab is now a part of a National Monument! Ability comes in many forms, and on the surface the variety is great; below the surface there are many common elements.