Double contingency and social systems

[Loet Leydesdorff]

Dear colleagues,=20
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In a previous email I sepeficied the mechanism of double contingency in
terms of anticipatory systems as follows:=20
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x(t) =3D a (1 - x(t+1)) (1 - x(t+1))
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The next state of the system is determined by the selective operation of
expectations upon each other in a dyadic interaction. The simulations =
are
robust and show that the system can move erratically from the one to the
other side. (If one wishes, one can play with the parameters in the =
excel
sheet and follow the consequences; at
http://www.leydesdorff.net/temp.doublcont.xls ).
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In Chapter 3 of Soziale Systeme, Luhmann (1984) discussed "double
contingency" as central to the emergence of social systems. Borrowing =
the
concept from Parsons, he provides it with a completely new solution. In =
my
opinion, the simulations in terms of expectations accord with this =
solution.
Paul Hartzog (cc) sent me a short piece in which he explains Luhmann's
solution in English. (Can you bring it online, please, Paul?). It made =
me
aware that Luhmann moves fast in this chapter from "double contingency"
towards the emergence of social systems without a specification of the
mechanism. (In footnote 12, p. 157, Luhmann warns against Von Foerster's =
too
fast movement.) The social system "emerges" from double contingency (in =
the
singular!).=20
=20
I guess that a double contingency can go on forever when no third party
comes into play. Piet Strydom used the term "triple contingency" for
explaining the emergence of a modern communication society in 16th and =
17th
century. The third party becomes abstracted as a public. In priniciple, =
one
could model a triple contingency analogously using:=20
=20
x(t) =3D a (1 - x(t+1)) (1 - x(t+1))  (1 - x(t+1))
=20
This leads to a cubic equation of x(t+1) as a function of x(t). Cubic
equations have analytical solutions, and there is a (freeware) add-in in
Excel for solving them. The solutions may imply i =3D sqrt(-1), and thus =
be in
the complex domain.=20
=20
For all values of the bifurcation paramater a the system is highly =
unstable
and quickly degenerates into a complex one. One interpretation would be =
that
triple interactions provide a short-term window for organization
(decision-making) to step into the system. The relation between =
interaction
and organization would then be conditional for the emergence of the =
social
system.=20
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An alternative formulation is:
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x(t) =3D a (1 - x(t)) (1 - x(t+1))  (1 - x(t+1))
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x(t)/(1 - x(t) =3D a (1 - x(t+1))(1 - x(t + 1))
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By replacing [x(t) / (1 - x(t))] with y, the solution is similar to the =
one
for double contingency, but mutatis mutandis:=20
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x(t+1) =3D 1 =A1=C0 sqrt(x(t)/ (a * (1 - x(t)))

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This formula is in the simulation as stable as double contingency for =
values
of a =A1=DD 8, but I don't yet have an analytic solution for this. For =
lower
values of a, the system vanishes. Using an internal degree of freedom =
the
system might be able to change its value of a endogenously and thus
alternate between double contingency and its disappearance.=20

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In summary, in the case of a triple contingency, the system can show the
behavior of a window for organization to step in by using three =
incursive
terms (based on expectations), or bring a double contingency to an end =
by
bringing a historical contingency (modeled as a recursive term) into =
play.
Using the internal degree of freedom for changing the value of a, the =
social
system would also be able to generate double contingencies =
(interactions)
endogenously.

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>From entropy statistics, we know that a system with three dynamics can
generate a negative entropy in the mutual information among the three
(sub)dynamics. (I use this as an indicator of self-organization in other
studies.) However, there is still a missing link between the above =
reasoning
and the emergence of a social system as a possibility because the =
complex
system is not yet generated. I suppose that I have to bring the social
distributedness into play and not write x(t), but =A6=B2ixi(t).=20

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With best wishes,=20

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Loet

________________________________

Loet Leydesdorff=20
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681=20
loet at leydesdorff.net <mailto:loet at leydesdorff.net> ; =
http://www.leydesdorff.
net/ <http://www.leydesdorff.net/> =20

=20
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