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Vladimir A. Lefebvre, "Reflexive Systems". Presentation at the American Society for
Cybernetics Joint Conference with Bateson Idea Group in Asilomar, CA,
July 10-13, 2012.
What is a reflexive system? In the 1960's-70's, it has been understood that such
“objects” as personality, a group, a stratum, a society cannot be studied with the
classical methods developed in the natural sciences. The reasons are that, on the
one hand, a theory constructed about such an object may be generated by that
very object (for example, a society dictates a view on the society to a scholar),
and on the other, the fact of constructing the theory may change the object
(society) in such way that the theory becomes incorrect. These problems required
creating a new methodology for investigating such objects, which have been
named reflexive systems. Today this methodology is applied in sociology (ethical
systems, reflexive games), economics, military, and diplomacy.
Vladimir A. Lefebvre, "Is There Any Fundamental Connection Between Man
and the Universe?"
In: Astronomy and Civilization in the New Enlightenment, Eds. Anna-Teresa Tymieniecka and
Attila Grandpierre, Springer Netherland,
2011, pp. 119-120.
A human being appears for us in two aspects, whose connection is unknown to
us: as a physical process and as an object with a mental domain. In this note, we
discuss a problem if the mental domain is subordinate to physical laws.
Vladimir A. Lefebvre, "Reflexive Analysis of Groups."
In: Computational Methods for Counterterrorism, Springer, 2009, pp. 173-210.
This paper develops further a model of an agent facing a choice between the
positive and the negative poles. Agents, whose individual behaviors, depend on
a 'society' compounded by all of them are being introduced here. Four ideas
underlie the theory. The first idea is to consider relationship between the
sub-groups of agents, not just pairs of agents; this idea allows us to represent
a decomposable graph corresponding to an agent or a group of agents as a
tree of subgraphs. The second idea is to establish a correspondence between
deco-mposable graphs and polynomials, allowing us to replace a tree of
subgraphs with a tree of polynomials representing a computational process.
The third idea consists of the interpretation of the tree of polynomials as an
agent who has images of the self, which can have images of the self, etc.
Finally, the fourth idea is putting an equation into correspondence to the
agent, allowing us to find out the agent's state. The theory is illustrated with
several examples from modern geopolitics, including scenarios of current events.