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19 February 2011

Simplification and Generalization in Problem Solving

You scatter toy towers of varying heights on the floor and ask some five old kid to arrange the towers in increasing order of heights. Most likely, he is going to knock of the puzzle. His first problem (and yours) will be understanding the problem - what needs to be done. Once he understands, he will complete the puzzles with your help here and there.After sometime, you ask him to sort toy circles in increasing order to circumference. Most likely he is going to finish off this taking lesser time than his previous. 

Both the instances are specialization of sorting - a basic algorithm that is known to human being. Human beings were sorting objects in life much before sorting algorithms were put forth. All those sorting were merely specializations and they work in specific scenarios but not all. Rather than saying it won't for all scenarios it is better to say that it was not tried having "all scenarios" in mind.

It is when we think about "all scenarios" we forget the specifics and the properties that is unique to the given problem and start to think about the "commonalities". When we think about "commonalities" we abstract ideas/concepts and bring many levels of abstraction based on the "commonalities". The specifics that are known at the time of abstraction forms as a boundary condition for abstraction. So, it is also very important to think widely about a specialization so as to make the abstraction more flexible & accommodative. Moving from specialization to a broader generalization is possible only when we simplify the problem domain and think about "many scenarios".

In order to understand the problem, you have to travel towards specialization and in order to solve it after understanding it requires simplification and generalization (and for achieving this you have travel further in time, by time i mean experience).

In next post, we will see some of the ideas on generalization from neuroscience's point of view.

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