This study adopts the logic of Systems Thinking and Control Systems,
presenting a simple but complete theory called the Theory of Combinatory
Systems. This new theory is able to describe, interpret, explain,
simulate and control collective phenomena and their observable effects.
Despite specific differences among these phenomena - many of which are
"one way", non-repeatable or reproducible - they can all be described or
explained, and thus understood, using the model, as simple as it is
general, of combinatory systems; that is, systems formed by
collectivities, or populations of non-connected and unorganized
individuals of some species, which appear to be directed by an invisible
hand that guides the analogous actions of similar individuals in order
to produce an emerging collective phenomenon. Combinatory Systems
function due to the presence of micro control systems which, operating
at the individual level, lead to uniform micro behavior by individuals
in order to eliminate the (gap) with respect to the objective that is
represented - or revealed - by the global information (macro behavior or
effect). The book also examines Combinatory Automata, which represent a
powerful tool for simulating the most relevant combinatory systems. In
stochastic combinatory automata, when both probabilities and periods of
transition of state are agent/time/state sensitive, the probabilistic
micro behaviors are conditioned by the macro behavior of the entire
system, which makes the micro-macro feedback more evident.
The Combinatory Systems Theory: Understanding, Modeling and Simulating
Collective Phenomena is composed of four main chapters. Chapter 1
presents the basic ideas behind the theory, which are analysed in some
detail. Chapter 2 describes the heuristic models of several relevant
combinatory systems observable in different environments. Chapter 3,
while not making particular use of sophisticated mathematical and
statistical tools, presents the Theory of Combinatory Automata and
builds models for simulating the operative logic of combinatory systems.
Chapter 4 tries to answer three questions: are combinatory systems
"systems" in the true sense of the term? Why is this theory able to
explain so many and so varied a number of phenomena, even though it is
based on a very simple modus operandi? Are combinatory systems different
than complex systems? The book has been written with no prerequisite
required to read and understand it, in particular math, statistics and
computer knowledge.
