Tolerance of Ambiguity

"If you think learning is hard, try unlearning."

In his wonderful speech -- You and Your Research -- the great computer scientist Richard Hamming has the following to say on the subject of ambiguity (my emphasis):

There's another trait on the side which I want to talk about; that trait is ambiguity. It took me a while to discover its importance. Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice tPublishhe flaws; if you doubt too much you won't get started. It requires a lovely balance. But most great scientists are well aware of why their theories are true and they are also well aware of some slight misfits which don't quite fit and they don't forget it. Darwin writes in his autobiography that he found it necessary to write down every piece of evidence which appeared to contradict his beliefs because otherwise they would disappear from his mind. When you find apparent flaws you've got to be sensitive and keep track of those things, and keep an eye out for how they can be explained or how the theory can be changed to fit them. Those are often the great contributions.

It's almost as if the revolutionary thinkers have a much-more fine-grained mental model of the world, once which allows them to cross the chasm of the unknown that lies between the current understanding to a "replacement theory".

Don't turn to the back of the book

Sometimes laziness has strategic advantages. When I was doing my PhD I did my literature review very late in the piece. This had the advantage of not contaminating me too much with existing ideas early on. And when I did get around to it I knew enough from my own trials and tribulations to be able to read the literature intelligently and critically.

I had a similar experience while teaching myself Operations Research in my first significant job in Industry. I had done a one-semester course -- not long enough to learn too much -- and so I was able to produce the real-life problems with a degree of freshness, rather than trying to (mis-) apply the known "solutions".

Generally speaking, I advocate mastery of fundamental ideas and techniques. These are often the most portable and adaptable. By contrast the advanced techniques can be quite specific, like an organism that has a evolved to fill a very narrow niche.

Turning to the back of the book, listening to lectures etc. may seem faster, but taking the slow hard road is a richer path. And in saying this I am in excellent company ...

Clearly Feynman was of the "no, don't tell me the answer" school of learning":

The deal this time was that Feynman would teach Fredkin quantum mechanics and Fredkin would teach Feynman computer science [27]. Fredkin believes he got the better of the deal:

`It was very hard to teach Feynman something because he didn’t want to let anyone teach him anything. What Feynman always wanted was to be told a few hints as to what the problem was and then to figure it out for himself. When you tried to save him time by just telling him what he needed to know, he got angry because you would be depriving him of the satisfaction of discovering it for himself.’

and

Feynman constantly emphasized the importance of working things out for yourself, trying things out and playing around before looking in the book to see how the experts’ have done things.

From Richard Feynman and Computation [pdf]