By Robert E. Ulanowicz
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Additional info for A Third Window: Natural Life beyond Newton and Darwin
To a degree, such indirect effects can be written into the monist calculus of contemporary problem solving. What is more subtle, however, and absent from the conventional approach is the necessary and somewhat paradoxical role that chance and disarray play in the persistence of complex systems, because, without them, a system lacks the flexibility necessary to adapt and becomes defenseless in the face of novel perturbation. This relationship between the complementary dynamics of organization and chance is akin 8 Introduction to a Hegelian dialectic.
The procedure is repeated for many draws and replacements. , whether the ratio of red balls to blue balls in the container approaches a constant. Is the outcome nonrandom? It is rather easy to demonstrate that it is. 1, for example, depicts the ratio of red balls to blue balls after each of the first one hundred draws. 54591. During the course of any series of draws, the ratio becomes progressively less random. 5 raises a second question. , is it determinate? If the urn were emptied and the process begun anew, would the ratio converge to the same limit?
The Polya process is indeterminate. In fact, if the process is repeated a large number of times, it eventually becomes apparent that the ratio of red to blue balls can converge to any real number between zero and one. 3. 96806. 1. The ratio of red to blue balls after each of the first one hundred draws of a simulation of the Polya process. 2. 1. 3. A series of draws from Polya's urn that converges to a mixture heavily dominated by red balls. 32 Two Open Windows on Nature number of repetitions that what happens during the first twenty or so draws strongly influences where in the interval o to 1 that particular series will converge.