Posts Tagged ‘wheat and chaff’

wheat and chaffOne of the recurring myths of pop complexity is that in a complex system «the whole is greater than the sum of its parts». Whenever you read this anywhere, you can rest assured that the author is confused about the meaning on complexity.

It goes like this.

The properties of a linear system are additive: the effect of a collection of elements is the sum of the effects when they are considered separately, and overall there appear no new properties that are not already present in the individual elements. But if there are elements/parts that are combined and depending on one another (nonlinearity), then the complex is different from the sum of the parts and new effects start to appear.

In other words: Since a complex system, by definition, does not obey the superposition principle, its behavior as a whole does not reflect that of the composing elements. The system’s response R to the simultaneous application of stimuli S1… Sn is different from the sum of the individual responses to each stimulus when applied in sequence, R1+…+Rn.

However this does in no way imply that the systemic response be larger or smaller than the sum of the individual responses: it can be either, depending on whether positive or negative feedback takes place. Or it could be numerically equal, although it would still remain logically different. (For that matter, the assumption that an additive property be implied in all cases, is arbitrary).

You are encouraged to use the synergy metaphore statement to tell wheat from chaff (Matthew, 3:12) in complexity literature.