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Thomas comments on Rationality Quotes April 2013 - Less Wrong
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Comments (281)
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.