Notes on Reductionism: Why we must embrace holism?

On the Melange blog Mayank, wrote the following post on reductionism a problem solving technique:

"Reductionism has always been the problem solving technique in sciences and associated disciplines. In reality solving a problem by reduction means transforming the problem into simpler problems and constructing or deducing solution of the original problem from the solution of the new problem. For example a student is given a problem to calculate the sum of all numbers between 1 and 101 which are not divisible by 3. Working a direct solution for this will be tedious so it is solved reductively. The required sum is the difference between sum of all numbers between 3 and 99 which are divisible by 3. Both sums can be calculated as arithmetic series. Thus the original problem is subdivided into sub problems of calculating arithmetic series which is actually nothing but reductionism (Armoni, Gal-Ezer & Tirosh 2005, p. 114). On the hand the term systems approach derives its base from holism or holistic thinking. The term holism was coined by South African philosopher Jaan Christiaan Smuts. He argued (Anderson, H 2001, p. 155) that “a unity of the parts could be so close and intense as to be more than the sum of its parts.” Smut explains the philosophy behind holism and systems thinking. Systems thinking usually deals with complex systems. Now a complex system unlike a conventional single feedback system comprises of numerous subsystems and the overall behavior of the system relies on the interaction of these systems. So the system output is not as simplistic and is not merely a sum total of the constituent entities."
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