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 probl

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.