Information Technology Reference
In-Depth Information
Systems Theory”, this symposium was an interdisciplinary event where 17 speakers
and over 200 participants included not only scientists represented General Systems
Theory and Cybernetics but also engineering scientists and philosophers. The pro-
ceedings, published by Mihaljo D. Mesarovic, were entitled
Views on General Sys-
tems Theory
. Indeed, this topic contains very different views and approaches as the
organizer emphasized in the preface:
“First of all, some of the participants took a definite stand, venturing to define a
system and then discussing the consequences of such a definition. A second group of
participants argued that the general systems theory should not be formalized since
this very act will limit its generating power and make it more or less specific. A
third group proposed to consider systems theory as a view point taken when one
approaches the solution of a given (practical) problem. Finally, it was expressed that
a broad-enough collection of powerful methods for the synthesis (design) of systems
of diverse kinds should be considered as constituting the sought-for theory and any
further integration was unnecessary. There were also participants that shared the
viewpoints of more than one of the above groups.” [49, p. xiv]
3.3.1
The “State” in System Theory
Zadeh based his contribution to this symposium on three concepts in System the-
ory: the input, output and state of a system. While input and output were not ex-
pected to offer any difficulties, the concept of state appeared problematic. Zadeh
noted that the idea of states had played an important role in the physical disciplines
for a long time. It referred to a set of numbers that contain all of the informa-
tion about a system's past and that determine its future behavior. The names of
the French mathematician an physicist Jules Henri Poincaré (1854-1912), the US-
American mathematician George David Birkhoff (1884-1944), the Russian math-
ematicians Andrei Andreyevich Markov (1856-1922) and Viktor Vladimirovich
Nemytskii (1900-1967), and Lev Semenovich Pontryagin (1908-1988) stood for
developments of more precise definitions of the concept of state in the fields where
it was applied, such as dynamic systems and optimal control.
Zadeh's starting points to place a general notion of state in system theory were the
fields of dynamical systems and of automata. As a simple example Zadeh presented
the Turing machine: “Roughly speaking, a Turing machine is a discrete time (
t
=
0
) system with a finite number of states or internal configurations, which is
subjected to an input having the form of a sequence of symbols (drawn from a finite
alphabet) printed on a tape which can move in both directions along its length. The
output of the machine at time
t
is an instruction to print a particular symbol in the
square scanned by the machine at time
t
and to move in one or the other direction
by one square. A key feature of the machine is that the output at time
t
,
1
,
2
,...
+
1andthe
state at time
t
+
1 are determined by the state and the input at time
t
.” [101, p. 858].
