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.
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