Tuesday, May 19, 2009

Uncertainty and non-linear systems.

For the past 400-years, science has advanced by using linear mathematical approaches to examine smaller and smaller pieces of the world on the assumption that, when these small pieces were assembled, they would explain the whole. But the world today is filled with complex phenomena that don’t behave in a linear fashion and can’t be explained by reductionism. Adding up the parts doesn’t give a good picture of how the whole behaves anymore because the interactions between the parts are as important as the parts themselves. In the real world, rather than having simple causes and general phenomenon, “everything depends.” There's no ultimate reality. We never have all the data and we influence the data we do have by our presence. A different kind of mathematics using a nonlinear approach is needed.

Measurement supposedly makes the ”indefinite thing definite.” But according to Heisenberg’s uncertainty principle, if you can only predict the outcomes of different kinds of measurements in terms of their probabilities, then you won’t be able to obtain at the same time all the information about an object or an issue that you might want to know. In theoretical physics, new insights into the behavior of complex systems have made it possible to begin to understand how assemblies of many interconnected objects can behave in collective ways that are by no means obvious or easily deduced from the behavior of single events in isolation. Here it helps to understand the mathematical properties of wave functions and how measurement probabilities are derived from them. This leads to the concept of “decoherence.” - (see Where Does The Weirdness End? by David Lindley, Basic Books, 1996). Today, the fundamental assumptions behind “reality” no longer hold true. In a dynamic world, there are no final solutions. The only way to grasp the general or the universal is in the particular and you can only get that from experience. Risky judgment rather than precise measurement is needed because the facts which have traditionally been the baseline for measurement no longer apply.

The bionomic view that solutions to the complex problems of the information age must be allowed to evolve from experience instead of being engineered in advance offends many managers and specialists. But self-organization is widely distributed. A system like the internet is the essence of life, innovation and progress. When the environment changes, this model thrives rather than self-destructs. Traditionally, we looked for an elegant solution that achieved a powerful result with a minimum of irrelevant complication. Today, we have to live with adaptive challenges - that is, problems without any apparent solution.

As G. K. Chesterton wrote in his essay on Orthodoxy in 1924, “The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. Life is not an illogicality, yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait.”

Success in the future pivots not on information but on interpretation - the ability to make meaning out of still-emerging patterns. The truly important events are not trends, but changes in the trends.

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