"Writing down the problem" sounds trivial, but it's often the hard part. Once you understand the question, the answer is obvious (as a commenter said).
I have to break down complex problems in order to come up with questions that I can understand.
The really hard part is in finding the right way to break them down, because not all modularities and boundaries between them will help to solve the problem. But all of this properly forms part of Feynman's step one, of writing down the problem.
I also often get a sense of what the answer should be - but it's very difficult to even begin to describe it in words, let alone define it clearly, and even harder to prove it is correct. Yet... it almost always is correct. This is properly in Feynman's steps two and three.
Computers are useless. They can only give you answers - Picasso
It is by logic that we prove, but by intuition we discover - Poincaré
and so another, even bigger, computer had to be built to find out what the actual question was - Douglas Adams
I completely agree - I studied algorithms because of a fascination with general problem solving and this idea came up frequently with my advisor.
I think problems occur at various levels of granularity and only those of a sufficiently fine grain are actually solvable in any real sense. I see it as breaking down the probability space of answers until a concrete solution emerges.
Extremely high level problems are extremely easy to write down:
1. How can a ship travel faster than the speed of light?
2. How do I live to be 500 years old?
3. How do I make $1M?
These problems have appropriately trivial sets of solutions:
3a. Steal it
3b. Make an advertising supported web app
3c. Make a freemium web app
3d. Make an iphone/ipad app
3e. Work hard and slowly invest
3f. Write a facebook app
and so forth. Then it's a cycle of prepending "How do I" until a feasible solution appears.
3ai. install a virus that steals fractions of pennies from each transaction
3aii. rob a bank
3aiii. blackmail a rich guy
3aiv. atm muggings (some solutions are more feasible than others)
3av. hijack a truck full of computers
3avi. rebill scams from spamming morons
3avii. steal CC #s
and on and on. At this level of granularity, sequential high level plans start to emerge. I realize these are very different than physics problems, but it's the same basic process of breaking down the solution space by writing it down from high level to concrete implementation problems to which insight/intuition can be applied.
Maybe Feynman was Feynman because he was willing to work at it longer and harder than other people around him.
I remember reading once that he was about to have an operation to remove his tumor within a week and it wasn't certain that he would survive. The doctor in fact told him point blank that there was a chance that he could die. A friend came up to him with a physics problem and he spent the entire day and evening working at it. They failed and decided to call it intractable.
So, Feynman goes home and later in the night he calls him up to say that he has a solution. That was a man a week away from near certain death. Is that something innate or someone with the sheer persistence and experience to bend things his way? I want to ask how many people who will be reading this would have done the same? I wouldn't have, and perhaps this is why Feynman was Feynman.
I think there was also part of him that just can't help but solving problems. He's spent so much time solving problems and became even better at it, but he was probably still extremely fascinated by his science and just couldn't help but solving this problem.
I have noticed a similar thing, where if a cs problem is interesting enough, I just have to think about it, even when other interesting things are going on in the real world. I think it might be an (unhealthy?) fascination with a certain field.
Having read Feynman's books and descriptions of him in other places it seems to me he was supremely gifted but also willing to indulge his curiosity about seeming trivial things that is uncommon in professional scientists - the whole thing with spinning plates being a good example.
There are so many supremely gifted people out there, but almost none of them reach the Feynman-ian stage of problem solving. I just remembered an extremely interesting thing I can't remember one example of his "gifts" in childhood. He messed with radios and had a personal lab, but even I did stuff analogous to that and I am certainly not "supremely gifted" or gifted at all. So did you and almost every HN reader.
His "gifts" become apparent in mid adolescence, and the interesting thing is that these are more a combination of hard work and his environment than gifts. Let's stop talking about Richard Feynman for a moment, did you know he had a sister Joan Feynman who became an extremely senior scientist at NASA? {see: http://www.popsci.com/scitech/article/2002-04/my-mother-scie...I'll put it up separately too it is worth it. [edit: It's up over here http://news.ycombinator.com/item?id=1520685]}
She was brilliant too and had the same characteristics as her brother. Now one would assume that his gifts would be unique, a genetic lottery. It is quite often that siblings of famous scientists achieve next to nothing in life compared to their brothers/sisters. However, here we have someone who fought her way up life pretty much the same way Feynman did.
Perhaps it wasn't a genetic lottery, but an environment constructed by an amazing father who taught his kids that in order to do anything in life you need to work hard at it until you fail, and then you try again.
You know it is so difficult to accept this, but Feynman the phenomena was nothing more than dollops of hard work and persistence with an open mind. No wonder he used to scoff at IQ tests. I have a higher IQ than Feynman's reported IQ and this being HN it is highly probable that the person reading this does so too, but am I "smarter" than him? No way.
However, there is one thing he had in him that most people don't have; creativity, but this too can be cultivated slowly over time...
Somehow, I doubt that Murray Gell-Mann, or any Nobel Prize-winning physicist could have been a slouch. Working one's ass off is a given at that level. And yet, even to Gell-Mann, Feynman was impossibly capable of solving difficult problems. Just putting in the hours and effort might be enough to make a great physicist, but it won't guarantee abilities on par with Feynman.
Didn't Gell-Mann say that the thing Feynman was truly the best at was inventing anecdotes about himself? You never know that much about other physicists because they generally don't publish multiple volumes of their own memoirs...
I'm often frightened by how spontaneously my brain seems to come up with something, because it could just as easily stop doing that and I'd have no idea how to fix it.
I once walked past a math book one of my friends had left open, glanced over, stopped, pointed to a formula, and said, "This is wrong." (Which it was.) I only did it that once, but it's the sort of anecdote you can tell for the rest of your life. And if my brain stopped doing that, I'd be screwed.
You're lucky! I'll never get the same innate ability for problem solving, but what I'm hoping is that it's actually possible to train my brain towards such spontaneity.
E.g., by spending time to solve a lot of challenging puzzles over a long period of time. It's like when you try to remember a shopping list by visualizing the items. After repeating the items enough times, you don't visualize the list anymore; you just know it.
I remember in fifth grade we were learning to multiply 3 digit by 3 digit numbers. My teacher wrote two 3 digit numbers on the board and I immediately blurted out the answer. He looked down at his notes, and just looked back at me, I had been right.
Like you, I've never had this experience again. It makes this feel true: http://xkcd.com/447/
A necessary precondition is to define a good problem. Speaking from experience, this is easily the hardest step for physicists.
For example "What is dark energy?" or "Are there baby universes?" are not good problem definitions, but to my surprise "What is the radius of the proton?" is still a good problem definition today [1].
There's another "Feynman Algorithm" which someone mentions towards the end of the article: he said he kept a small number of problems constantly in the back of his mind and whenever he heard of a new trick or method, he tested it against his problems.
I once wrote a blog post about whether the opposite method is effective: you keep your favorite tricks and techniques sharp and always look for new problems they might solve.
I don't know the context of the Gell-Mann quote, but having heard Gell-Mann talk about Feynman, it seems more likely to me that that is Gell-Mann's description of how Feynman imagined the Feynman algorithm.
Concur. When I head Gell-Mann talk about Feynman (probably this was in 1994) he seemed to think he was about equally smart, but Feynman somehow had much better PR. Probably Feynman writing a series of books of stories about how smart he was had something to do with it.
Attributed to Norbert Wiener: A student came to him with an incredibly difficult problem he couldn't solve. Wiener stared at the ceiling for about fifteen minutes, then wrote down the answer.
The student said, "I'm sorry, Professor, but I didn't quite understand how you came up with that."
Wiener stared at the ceiling again for fifteen minutes, and again wrote down the answer.
The student said, "I'm sorry, Professor, but I still don't get it."
Wiener, flustered, replied: "I've just shown you two different ways to solve this problem! What more do you want from me?"
Here's how I did my hardest take home exams in grad school:
- Attempt to solve problem using tools learned in the course
- Attempt to solve problem using "standard" tools
- Fail at the above
- Go to bed
- Wake up, shower, eat breakfast
There's research on intuition and the unconscious mind to back this up. Apparently, for a lot of problems the best way to solve it is by thinking very hard about it and then letting it go. Your unconscious mind will go on, especially when you're doing activities such as showering (which has little distractions), and all of a sudden you will have the solution.
I use this technique all the time, if I can't think of a solution for a hard problem I'll just leave it and go for a run, take a shower or work an another problem.
Unfortunately, I only have read a book from the Dutch psychologist Ap Dijksterhuis, which is unfortunately in Dutch, but I'm sure there are people here who will have some references in English.
Taking your (conscious) mind off a full day's work allows your subconscious to process it, let your conclusions "sink in". That's why people often have the solutions in our sleep.
The cool thing is that it's not even as facetious as it appears. "Writing down the problem" is a legitimate, and very useful, tool for problem solving, and one that is often skipped.
Another useful step is "Ask a friend for help." Not because they'll solve it, but because the act of reducing the problem to a complexity simple enough to be explained to another person often makes the solution obvious.
On the other end, writing down the solution, is also a good tool. The number of times I thought I 'figured something out' by thinking real hard (in the shower or whatever) only to find problems during this final stage is large. It is very much the same thing as telling a fellow developer about a bug you can't solve, only to solve a trivial issue half way thru the explanation. The writing down or explanatory phase is quite important.
My way to execute this algorithm is to try to get as distant as possible to the problem in step 2, taking as much experience into account as possible, and then hap-hazardly zooming in. Or something like that. And it seems to work.
I have to break down complex problems in order to come up with questions that I can understand. The really hard part is in finding the right way to break them down, because not all modularities and boundaries between them will help to solve the problem. But all of this properly forms part of Feynman's step one, of writing down the problem.
I also often get a sense of what the answer should be - but it's very difficult to even begin to describe it in words, let alone define it clearly, and even harder to prove it is correct. Yet... it almost always is correct. This is properly in Feynman's steps two and three.
Computers are useless. They can only give you answers - Picasso
It is by logic that we prove, but by intuition we discover - Poincaré
and so another, even bigger, computer had to be built to find out what the actual question was - Douglas Adams