Linear Solutions to Non Linear Problems

Some samples of linear solutions to non-linear problems may be useful. For example, there are two definitions of the word

'work'. These are the linear, or Newtonian definition, and the nonlinear, or biological definition. When the two are confused, we can get some curious muddles. Thus, lifting a weight off the ground constitutes Newtonian work. But holding that weight off the ground does not. Nor does carrying the weight to a different place. However, putting the weight back on the ground recovers all of the Newtonian work. Try telling this to the person who is holding the weight.

Similarly, it requires a fixed amount of Newtonian work to ride a bicycle up a hill. Gears on the bicycle will not alter this amount of work and, in linear terms, will not increase efficiency. But, to use this as an argument against gears on bicycles is to apply a liner solution to a non-linear problem. A cyclist is a biological unit with an optimum rate of converting energy into work. The bicycle gears can ensure that this optimum is maintained, regardless of different slopes in various parts of the hill.

There is another obvious reason why we cannot solve nonlinear problems with linear solutions. The linear solutions do not work because the non-linear systems are unpredictable. The linear solutions cannot take this unpredictability into account. This unpredictability is partly due to the 'butterfly effect', which says (somewhat whimsically) that if a butterfly flaps its wings in the

Amazon Valley, it may trigger a sequence of events that culminate in a hurricane hitting the east coast of the United States. A suboptimising linear solution (also whimsical) to this non-linear problem would be to spray the entire Amazon Valley with DDT to kill all the butterflies. We have not been quite that blind in crop science, but we have often attempted, unsuccessfully, to solve nonlinear problems with solutions that are both linear and suboptimising.

A linear solution to a non-linear problem may also involve the simple but total control of only one subsystem. This control involves linear science applied to only one subsystem of a complex, adaptive, non-linear system. The three-fold suboptimisation of the vertical subsystem (see 5.3) is a classic example of this kind of error. However, in justice to biologists in general, and crop scientists in particular, it must be noted that the distinction between linear and non-linear systems is very recent.

In comparison, a non-linear solution is holistic, and it relies heavily, even totally, on the self-organisation of the system itself. Such external control as may be applied is simply to guide the self-organisation in the required direction. This is the origin of the concept of self-organising agro-ecosystems (see 11).

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