Decompositional reasoning

Example

I want to find out how a Rubic Cube operates. I pull it apart to see its hidden workings. By reassembling it slowly, I am able to explain its apparently magical cohesion as a whole in terms of three-dimensional geometry.

I listen to your argument and take note of each element. I then argue against each element in turn. Having destroyed the parts, I then assume I have destroyed the whole argument.

Discussion

Much of science takes a decompositional approach to things, breaking them down into parts, atoms and smaller still. The notion that a thing is the sum of its parts and no more hence has a highly credible air.

A problem with decompositional thinking is that the whole thing can easily be more than the sum of its parts. A person is more than bone and muscle. You cannot understand a car by studying each item in isolation.

A trick in effective decompositional reasoning is to use it as lens, understanding the parts but not assuming that they fully describe the whole. The biggest trick is in understanding the relationship between the parts. The problem with this is that relationships increase with the square of the number of parts, making full understanding of even a simple device potentially very difficult.

Decomposition is a very useful lens and often does tell the whole story, but there are many situations where this is an inadequate approach.

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