Bull.1 May 1, 1997
A Course of Study on Homeokinetics:
The Physics of Complex Systems
Introduction
Arthur S. Iberall
Our overall course of study will consist largely of a pursuit of all the ‘antinomies’ of understanding - from a physical point of view, of all the threads that are involved in the matter-energy universe around and within us. As such, we consider this school to be a continuing branch of Aristotle’s ‘peripatetic’ school.
Antinomies, loosely for our purposes, are considered to be the paradoxes, not quite contradictory arguments and processes, that describe what is happening out there. We continue on, attempting a static and dynamic resolution. As such, we shall be concerned with stability of states and changes that ‘nature’ and ‘mind’ deal with.
Note: Whenever you see a term in single quotes, take it at face value to mean what a good dictionary or encyclopedia offers as its meaning in a so-called ‘natural’ language. Then, in time, we will help you - in a Bayesian sense - understand the term in a homeokinetic sense. Is that ‘hermeneutic’? Yes. We claim that all science is hermeneutic in that sense. In introducing the propositional calculus in a basic book in metamathematics, Kleene defines mathematic or symbolic logic as logic treated by mathematical methods, noting that the book is also a study of logic used in mathematics. He immediately confronts the paradox: "…how can we treat logic mathematically (or in any systematic way) without using logic in the treatment?" He goes on to say that the solution of this paradox is simple. We put the logic we are studying into one compartment, and the logic we are using to study it in another. These "compartments," he informs us, are "languages." The language we use for study is the observer's or metalanguage. The language we study is the object language and the object logic. Thus, the metalanguage and its logic are capable of developing mathematical methods which can be used to study symbolic logic.
On another hand, Russell and Whitehead use the propositional calculus to derive the fundamental set properties of numbers, and thereby serve up an introduction to mathematics. Russell always maintains that mathematics and logic are identical.
We operate from a related point of view. We do not intend to broker mathematics or logic. We are willing to accept what experts in those fields say their foundation or foundations are. But then we permit ourselves the required mathematical-logical mind space to move somewhat off their bases to accommodate the laws and principles of physics.
The major method of exposition that we shall use is a combination of engineering physics and a more academic pure physics. We intend to show that we use and have to use both to produce a physical science for complexity. We strongly believe that explanations for complex systems lie in the many details that have to be assembled. While on the pure side, our ‘god’ figures are Newton and Einstein (among others); in engineering physics, we think of von Karman, Prandtl, Buckingham, and Steinmetz.
Let us start with some words regarding complexity. As defined in our Science article (Iberall and Soodak, August 1978), a system is a collective of interacting ‘atomistic’-like entities. We use the word ‘atomism’ to stand both for the entity and the doctrine. As is known from ‘kinetic’ theory, in mobile or simple systems, the atomisms share their ‘energy’ in interactive collisions. That so-called ‘equipartitioning’ process takes place within a few collisions. Physically, if there is little or no interaction, the process is considered to be very weak. Physics deals basically with the forces of interaction -- few in number -- that influence the interactions. They all tend to emerge with considerable force at high ‘density’ of atomistic interaction. In complex systems, there is also a result of internal processes in the atomisms. They exhibit, in addition to the pair-by-pair interactions, internal actions such as vibrations, rotations, and association. If the energy and time involved internally creates a very large -- in time -- cycle of performance of their actions compared to their pair interactions, we say that the collective system is complex. If you eat a cookie and you do not see the resulting action for hours, that is complex; if boy meets girl and they become ‘engaged’ for a protracted period, that is complex. What emerges out of that physics is a broad host of changes in state and stability transitions in state. Namely, in our opinion, if we view Aristotle as having defined a general basis for systems in their static-logical states and tried to identify a logic-metalogic for physics, e.g., metaphysics, we view homeokinetics to be an attempt to define the dynamics of all those systems we may meet in the universe. What marks them?
They are found in or as nature, life, humankind, mind, and society. By the definition of their complex behavior, we consider them memory laden and stormy or changing weather systems. In somewhat simpler form, they make up the memory laden character identified as rheology. That deals with simpler peculiar engineering materials such as paints, asphalts, rubber, sewage, silly putty, plastics and the like. Physically, these materials are even more difficult to understand than the homeokinetic systems, because almost all of the peculiarities lie in the almost nongeneralizable details. It is enough to say, for now, that long-delayed complex systems give us a clear chance for a start.