It is incredibly powerful, although, at first sight, often appears innocuous.Tags: Why Are Chores Important EssayDeeds Of AssignmentJohnson Cornell EssaysEssay On Television Effects OnHow Do You Write A Literature ReviewHow To Write A Business EssayWisp Business PlanResearch Concept Paper
Success in solving special cases may be reassuring of the validity of the original claim, while failure to solve a special case may prompt the solver to look for a counterexample which will also serve to disprove the larger problem.
Specialization is opposite to generalization; it is wonderful that both are valuable tools in the arsenal of a problem solver. Polya's thesis that quite often more general or more strict problems are easier to solve than the more special ones.
Further reading I highly recommend the 1981 article The heuristic of George Polya and its relation to artificial intelligence by Alan Newell that offers penetrating analysis of Polya's problem solving heuristics prior to the discussion on its applicability to AI.
Specializaton, i.e., considering special cases, or introducing additional restrictions, while trying to solve a problem may highlight aspects of the original problem that have perhaps been missed at first glance.
Enjoyment of having a problem solved is more a result of detecting and exploiting the problem's peculiarities.
As a rule, those peculiarities once observed define a refined class of problems which succumb to the same method of solution.
Whereas an example may be used to support or illustrate a claim, a counterexample is used to refute an assertion.
How an example is being used often depends on the purpose or the formulation.
Try one of the tactics, force yourself to speak aloud - something will come out.
Ray Bradbury, when short on ideas, taught himself to work with a dictionary picking random words and trying to put them together into something meaningful and relevant. Also, note that some of the tactics was previously mentioned - with additional advice - in a short assay of what constitutes a proof.