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Fyi. With best wishes,  Loet


From: Loet Leydesdorff [mailto:[log in to unmask]] 
Sent: Sunday, March 25, 2007 2:46 PM
To: 'Diskussionsforum zur soziologischen Systemtheorie Niklas Luhmanns'
Subject: Double contingency

Dear Franz and colleagues, 
In a previous email I formulated:

	The codes interact (co-vary) in both inter-human interactions and
	In inter-human interactions the mechanism is double contingency. 
	In organizations the mechanism is decision-making.

The mechanism of decision-making and the consequent transformation of
organization and agency is endogenous to anticipation at the level of the
social system. The derivation can be found at pp 141ff. of "The
Knowledge-Based Economy" ("Hyper-incursion and the requirement of
I realized that I did not yet formulate a mechanism for double contingency. 
Double contingency is based on the expectation of Ego that Alter entertains
expectations. Thus, the expectations of Ego and Alter operate as selections
upon each other. In terms of anticipatory systems, I propose to model this
as follows:
x(t) = a (1 - x(t+1)) (1 - x(t+1))
x(t+1) = 1 + sqrt(x(t)/a) or x(t+1) = 1 - sqrt(x/a)
(a is the bifurcation parameter)
The following shows the result of a simulation of double contingency after
10,000 runs:
Figure 1: click here <> 
The excel sheet cannot be attached in this email system, but can be found
here <> . If one presses F9 (in
the excel file) the simulation changes, since it is assumed that the
alteration between Ego and Alter is random. The blue line provides the
simulation for a = 4 and the red line for a = 8 (because a is in the
nominator, the deviations from 1 become smaller with increasing values of
a). The dashed line represents the linear fit; by pressing F9 (in the excel
sheet) one can see that the slope can be negative or positive depending on
whether Ego or Alter is dominating the interaction. 
Without interaction, Ego and Alter grow to an equilibrium value. The value
of this equilibrium is: 
x = 1 + 1/2a ± 1/2a * sqrt(4a + 1). [a is the bifurcation parameter].
The corresponding chart is included in the excel sheet.
Single contingency can corresponding be modeled as: 
x(t) = a x(t) (1 - x(t+1)  → x(t+1) = 1; end of the process
x(t) = a x(t+1) (1 - x(t))
x(t+1) = x(t) / (1 - x(t)) * a
This latter formula can be shown to model reflection.
With best wishes, 

Loet Leydesdorff 
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681 
[log in to unmask] <mailto:[log in to unmask]> ; http://www.leydesdorff.
net/ <>  

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