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Vaniver comments on Rationality Quotes April 2013 - Less Wrong
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-- Albert Einstein
At least sometimes the formulation is far easier than the solution.
This is definitely true. General class of examples: almost any combinatorial problem ever. Concrete example: the Four Colour Theorem
Yes! Combinatorics problems are a perfect example of this. Trying to work out the probability of being dealt a particular hand in poker can be very difficult (for certain hands) until you correctly formulate the question- at which point the calculations are trivial : )
I think bentarm was offering "Combinatorics problems" as an example of the opposite of the phenomenon you describe. In particular the Four Colour Theorem is easy to formulate but hard to solve, and (as far as I know) the solution doesn't involve a reformulation.
Yes, upon re-reading I see that you are correct. I think there may be overlap between activities I consider part of the formulation and activities others may consider part of the solution.
To expand on my poker suggestion. When attempting to determine the probability of a hand in poker it is necessary to determine a way to represent that hand using combinations/permutations. I have found that for certain hands this can be rather difficult as you often miss, exclude, or double count some amount of possible hands. This process of representing the hand using mathematics is, in my mind, part of the formulation of the problem; or more accurately, part of the precise formulation of the problem. In this respect, the solution is reduced to trivial calculations once the problem is properly formulated. However, I can certainly see how one might consider this to be part of the solution rather than the formulation.
Thanks for pointing that out
In my experience it can often turn out that the formulation is more difficult than the solution (particularly for an interesting/novel problem). Many times I have found that it takes a good deal of effort to accurately define the problem and clearly identify the parameters, but once that has been accomplished the solution turns out to be comparatively simple.
Hmm. Einstein is perhaps most famous for "discovering" special relativity. But he neither formulated the problem, nor found the solution (I think the Lorentz transformation was already known to be the solution), but reinterpreted the solution as being real.
His "greatest error" was introducing the cosmological constant into general relativity--curiously, making a similar error to what everyone else had made when confronted with the constancy of the speed of light, which was refusing to accept that the mathematical result described reality.
Do you have an original source for that? All I can find is various quotation sites, which contain so amny other things that Einstein allegedly said I feel sceptical.
Nope, and I don't recall where I saw it attributed to him originally. (I did check by Googling it, but you're right that that only confirms that it's often attributed to him.)
In writing a story, it's easy to identify problems with the story which you must struggle with for weeks to resolve. But often, you suddenly realize what the entire story is really about, and this makes everything suddenly easy. If by the formulation of the problem we mean that overall understanding, rather than specific obstacles, then yes. For stories.