The Parts of The Whole I

Reductionism

The Whole is the Sum of its Parts

This shall be a series of posts on the two contrasting viewpoints of the world that affect our way of thinking about everything(even about themselves).

Reductionism is the ideology that the sum of the parts make up the whole. Basic fractions that is

reductionism
Reductionism is basically like normal fractions

Reductionism is what we do every time we subdivide a problem into sub-problems. Or whenever we break down a machine into its parts. Reductionism is used widely by people to solve problems in this manner. Once you have divided your systems into independent subsystems it is far easier to piece together a big picture that gives you insight into the workings of the system.

vectors
Vector components are a wonderful example of reductionism

Reductionism lies at the heart of everyday mathematics and classical physics. Take a simple sum of natural numbers. Each number retains its identity in spite of interacting with other numbers, the interaction being through addition.

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Reductionism rules the roost in the classical physics, it is the heart of Newton’s vision of a clockwork universe, a vision that the universe that can be understood completely if you understand each and every part of it.

four_stroke_cycle_compression
A normal car engine can be reduced into the sum of the functions of its parts.

If you look at a standard car engine cylinder, you can easily see how we can break it down into its parts. The engine is then a sum of the functions of the fuel, valves, spark plug, piston and axle. This is a reductionist standpoint. Engineering relies on solving one subproblem at a time to reach the final goal. So we see how important and inherent reductionism is to the world view of engineering. To foster an engineering mindset has nowadays become alike to developing a reductionist mindset.

Reductionism is also a commonplace view in computer science. As any programmer will tell you, if you can cut down a problem into a few smaller ones of the same kind, lo you have learnt Dynamic Programming (even though the name suggests something entirely different). A simple example is a binary search: Take an ordered list of randomly spaced numbers. Say we need to find the position of a particular number in this list. While just looking at all the numbers seems easy, there is a faster way. To find a particular number, say 14, in the list we check just the middle element. Is it 14, greater than 14 or less than that. Since its greater than 14 we can eliminate the rest of the list. Notice how the problem has been reduced in half just by one lookup. And it has been reduced to the same kind of problem. If I solve the lower problems I can work my way towards the top level solution.

binsearch
Binary Search reduces the problem into smaller problems which are easily solved

Reductionism, we have seen is a very powerful view of the world. It is the way most of the science of the past centuries was conducted. Science has primarily focused on objects by adopting a reductionist methodology. Yet we must be careful not to equate reductionism with science in general. While reductionism provides a highly accurate understanding of systems on a practical level, as we dig deep into different fields we find that it provides a very complicated answer, sometimes too complicated to understand. At this point a different form of thinking arose to battle these odds. That is what shall be our next post. Stay tuned!

This article was first published at bit.ly/WholePart
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