1. The Kingdom of Circular Processes: The Logical Foundations of Systems Thinking

An interesting historical review of the life and works of the founders of systems theory and cybernetics can be found in Ramage and Shipp (2009). An encyclopedic collection of systems theory is available in the extensive website “Principia Cybernetica” at: http://​pespmc1.​vub.​ac.​be/​

Bateson’s schema can be summarized as follows: (1) A mind is an aggregate of parts of interacting components. (2) The interaction among the parts of the mind is activated by difference, and difference is a non-substantial phenomenon, not situated in space or time; more so than energy, difference is linked to entropy and to negative entropy. (3) The mental process requires collateral energy. (4) The mental process requires chains of circular (or more complex) determination. (5) In the mental process the effects of the difference must be considered to be transformed (that is, codified versions) by the difference preceding the effects. The rules of this transformation must be relatively stable (that is, more stable than the content), but in turn they are subject to transformation. (6) The description and classification of these transformation processes reveal a hierarchy of logical types immanent in phenomena (Bateson 1979, p. 92).

Let us remember Thomas Aquinas in his Summa Theologiae (part one, Quaestio 2, Article 3: I q. 2 a. 3): The existence of God can be proved by taking five ways. The first, and most evident, way is the argument from motion. […] It is necessary to add a first mover put in motion by no other: and this everyone understands to be God. The second way is from the nature of the efficient cause. […] it is necessary to admit a first efficient cause, to which everyone gives the name of God. The third way is taken from possibility and necessity. […] it is necessary to postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity. This all men speak of as God. The fourth way is taken from the gradation to be found in things. […] there must also be something which is to all beings the cause of their being, goodness, and every other perfection; and this we call God. The fifth way is taken from the governance of the world. […] an intelligent being exists by whom all natural things are directed to their end; and this being we call God. The Summa is published in Latin and in English in the following website: http://​www.​sacred-texts.​com/​chr/​aquinas/​summa/​

“La calunnia è un venticello – Un’auretta assai gentile – Che insensibile sottile – Leggermente dolcemente – Incomincia a sussurrar. […] Alla fin trabocca, e scoppia, – Si propaga si raddoppia – E produce un’esplosione – Come un colpo di cannone, – Un tremuoto, un temporale, […]”. Translated by Gabriela Ramírez-Carr for The Schiller Institute. www.​schillerinstitut​e.​org/​educ/​reviews/​2009/​barber_​seville.​html

In order to understand the extreme behavioural complexity of a system with memory it is enough to consider the incredible number of behaviours [input-states-output] that a machine with memory can produce. The extreme computational complexity of machines with memory has been well described by Heinz von Foerster (2003, p. 143), the father of “second-order cybernetics”, who views a machine with memory – defined as non-trivial – as a complex system deriving from the interconnection of machines without memory, or trivial machines (which in Systems Thinking represent the elementary processes between two variables based on a cause-effect relationship).

In any case, the number that can be constructed under such conditions is not astronomical. It is meta-astronomical! If we have only two inputs (A and B) and two outputs we can construct 2¹⁶, that is, 65,536 different AB machines. Producing these 65,536 machines is quite difficult; however, it is still doable. A fast computer can give us all the possible machines in around two minutes. But suppose we want to calculate the number of machines with four inputs and four outputs (a machine of the ABCD type). There are 2⁸¹⁹², that is, 10²⁴⁶⁶ different ABCD machines. If we consider that the age of the universe calculated in microseconds is 10²⁸, this means that if we had a fast computer that could calculate one machine each microsecond, we would need a time period of 10²⁴³⁸ times the age of the universe to calculate the number of possible ABCD machines. You are strongly urged not to undertake a similar enterprise. You would lose your shirt, your money, and everything else.