Not sure that generalises outside of math. Is it really better to solve one problem really, really thoroughly, than to have a good-enough fix for five? Depends on the problems, perhaps—but without knowing anything else, I’d rather solve five than one.
I think the point of the quote is that in the first case you have five methods you can use to attack different problems. In the second case you only have one method, and you have to hope every problem is a nail.
Indeed, this story from Polya emphasises the necessity of trying different angles of attack until you have a breakthrough (via squeak time.com):
The landlady hurried into the backyard, put the mousetrap on the ground (it was an old-fashioned trap, a cage with a trapdoor) and called to her daughter to fetch the cat. The mouse in the trap seemed to understand the gist of these proceedings; he raced frantically in his cage, threw himself violently against the bars, now on this side and then on the other, and in the last moment he succeeded in squeezing himself through and disappeared in the neighbour’s field. There must have been on that side one slightly wider opening between the bars of the mousetrap … I silently congratulated the mouse. He solved a great
problem, and gave a great example.
That is the way to solve problems. We must try and try again until eventually we recognize the slight difference between the various openings on which everything depends. We must vary our trials so that we may explore all sides of the problem. Indeed, we cannot know in advance on which side is the only practicable opening where we can squeeze through.
The fundamental method of mice and men is the same: to try, try again, and to vary the trials so that we do not miss the few favorable possibilities. It is true that men are usually better in solving problems than mice. A man need not throw himself bodily against the obstacle, he can do so mentally; a man can vary his trials more and learn more from the failure of his trials than a mouse.
I don’t know the exact context of this particular quote, but George Pólya wrote a few books about how to become a better problem solver (at least in mathematics). In that context the quote is very reasonable.
Not sure that generalises outside of math. Is it really better to solve one problem really, really thoroughly, than to have a good-enough fix for five? Depends on the problems, perhaps—but without knowing anything else, I’d rather solve five than one.
I think the point of the quote is that in the first case you have five methods you can use to attack different problems. In the second case you only have one method, and you have to hope every problem is a nail.
Indeed, this story from Polya emphasises the necessity of trying different angles of attack until you have a breakthrough (via squeak time.com):
Nu, but a method that has already been used on five problems seems to be pretty good at converting problems into nails. :)
I don’t know the exact context of this particular quote, but George Pólya wrote a few books about how to become a better problem solver (at least in mathematics). In that context the quote is very reasonable.