1 On Self - Organizing Systems and Their Environments *

1 I am somewhat hesitant to make the introductory remarks of my presentation, because I am afraid I may hurt the feelings of those who so generously sponsored this conference on self-organizing systems. On the other hand, I believe, I may have a suggestion on how to answer Dr. Weyl’s question which he asked in his pertinent and thought-provoking introduction:“What makes a self-organizing system?” Thus, I hope you will forgive me if I open my paper by presenting the following thesis: “There are no such things as self-organizing systems!” In the face of the title of this conference I have to give a rather strong proof of this thesis, a task which may not be at all too difficult, if there is not a secret purpose behind this meeting to promote a conspiracy to dispose of the Second Law of Thermodynamics. I shall now prove the non-existence of self-organizing systems by reductio ad absurdum of the assumption that there is such a thing as a self-organizing system. Assume a finite universe, U0, as small or as large as you wish (see Fig. 1a), which is enclosed in an adiabatic shell which separates this finite universe from any “meta-universe” in which it may be immersed. Assume, furthermore, that in this universe, U0, there is a closed surface which divides this universe into two mutually exclusive parts: the one part is completely occupied with a self-organizing system S0, while the other part we may call the environment E0 of this self-organizing system: S0 & E0 = U0. I may add that it is irrelevant whether we have our self-organizing system inside or outside the closed surface. However, in Fig. 1 the system is assumed to occupy the interior of the dividing surface. Undoubtedly, if this self-organizing system is permitted to do its job of organizing itself for a little while, its entropy must have decreased during this time: