By
**Richard L. Coren**

**Abstract:**

Logistics is well established as a description of systems whose significant parameter(s) initially grows exponentially but then approaches a limit. It has had success in treating a very wide range of complex systems despite its great simplicity. A logistic phenomenon that has been largely overlooked is Rescalation,S describing the behavior of a system whose growth has reached saturation. If the evolving variable then changes its nature in some slight way, or if a different component becomes significant, a new cycle of logistic growth appears beyond the initial cycle. This behavior should be particularly pertinent where the system and parameter are multi-dimensional so a variety of parameter changes can occur. The predicted behavior is just that expected when evolution occurs through the mechanism of punctuated equilibrium, i.e., through emergence, where a new mode of structure, behavior and change appears, relatively abruptly. Logistic escalation is an alternative description of emergence. This report describes extension of the mathematical description of logistics to include escalation. Rather surprisingly, it results in the prediction of a semilogarithmic "trajectory" for the timing of metasystem changes vs emergent cycle number. Examples are given from the physical and social sciences.

In considering biological evolution we note that archeological evidence of the increase of species complexity, and of changes of clade dominance, form the basis of the divisions of geologic time into intervals (epochs, eons, etc.). On the geologic scale these changes seem to occur through emergence so that logistic escalation should describe their appearance.

Analysis of the time dependence of the geologic intervals , using the mathematical model of logistic escalation, discloses that they do conform to the trajectory representation as a series of logistic escalations. Extrapolation of this relation illuminates questions about the origin of organic complexity and its relation to entropy and to information.