Onderzoeken en simuleren van complexiteit

Cor van DijkumUtrecht University

Niek LamAchmea

William VerheulNivel

Wat is eigenlijk complexiteit?Een aantal citaten:

• Het ingewikkeld en moeilijk zijn (woorden.org)

• Mate waarin de verschillende functies, waaruit een systeem bestaat, groot in aantal en afhankelijk van elkaar zijn (woorden-boek.nl/woord/complexiteit

• Er zit veel hoogte in, het gaat al gauw naar een meter of vier. En dat maakt de show complex. (Lentetuinkrant 24 februari 2013)

• Als je vandaag de dag luistert naar bestuurders, politici, wetenschappers, ondernemers of de media dan is de kans groot dat het woord complex of complexiteit regelmatig voorbij komt. In veel gevallen blijkt men echter

ingewikkeld te bedoelen (top-innosense.nl)

Complexiteit: een korte geschiedenis

Henri Poincaré (1854 -1912) Drie Lichamen Probleem: Niet analytisch oplosbare bewegingsvergelijkingen: differentiaalvergelijkingen

Ed Lorenz (1960)Steeds andere uitkomsten in voorspelling van toestand van atmosfeer door computermodel (differentiaalvergelijkingen).Willekeurig kleine veranderingen in beginwaarden leidt tot heel andere uitkomsten

Mandelbrot(1980)Fractals: zich zelf herhalende afbeeldingen tot in het oneindige.

Chaostheorie

Complexiteit: een korte geschiedenis

• A new scientific discipline, called complexity theory, looks at complex systems and their environments in much the same way as chaos theory.

George Cowan founded the Santa Fe Institute, in New Mexico, in May, 1984. Stephen Wolfram began the Center for Complex Systems at the University of Illinois, in 1986.

• Both organizations were founded to investigate complexity. They have defined complexity as "a chaos of behaviors in which the components of the system never quite lock into place, yet never quite dissolve into turbulence either"

(Waldrop, 1992).

• Complexity lies at the edge of chaos (1988, Norman Packard) within the fine line that lies between order and chaos. Although this region is thin, it is vast, like the surface of the ocean. The edge of chaos is a transition phase, where life itself is thought to be created and sustained.

• Nicolis & Prigogine (1989) define complexity as the ability of a system “to switch between different modes of behavior as the environmental conditions are varied”

Complex is meer dan ingewikkeldMaar waarom dan toch al die misverstanden?

In de sociale wetenschappen ?

Herbert Simon (1993):

For our purposes, we can regard a system as complex if it can be analyzed into many components having relatively many relations among them, so that the

behavior of each component depends on the behavior of others.

Consider a dynamic system describable by N differential equations in N unknowns. We can represent this system by a matrix of the coefficients of the variables in the several equations. For simplicity of exposition we will assume the equations to be linear and consequently the coefficients of the matrix to

be constants.

From: Near Decomposability and Complexity: How a Mind Resides in a BrainCarnegie Mellon University. Research supported by the National Science Foundation.

Also in: HA Simon - The mind, the brain, and complex adaptive systems, 1995 - Westview Press

Complex is meer dan ingewikkeld Maar waarom dan toch al die misverstanden?

In de sociale wetenschappen

Sterman (1993):

Much of the literature in psychology and other fields suggests learning proceedsvia the simple negative feedback loops. Implicitly, the loops are seen as effectively first-order,

linear negative feedbacks that produce stable convergence to an equilibrium or optimal outcome. The real world is not so simple. From the beginning, system dynamics

emphasized the multiloop, multistate, nonlinear character of the feedback systems in which we live (Forrester 1961).

The decisions of anyone agent form but one of manyfeedback loops that operate in any given system. These loops may reflect both

anticipated and unanticipated side effects of the decision maker's actions; theremay be positive as well as negative feedback loops; and these loops will contain

many stocks (state variables) and many nonlinearities. Natural and humansystems have high levels of dynamic complexity.

From: Learning in and about complex systems. System Dynamics Review Vol. 10, nos. 2-3 (Summer-Fall 1994): 291-330

Complex is meer dan ingewikkeld

The real world is not so simple. It is complicated:multiloop, multistate

Many actors, a lot of interdependencies between actors, many influencing variables, several cause-effect relations, multiple values to take care.

Besides that the real world is more than that. It is complex:nonlinear character of the feedback systems in which we live (Forrester 1961).

HoweverTo understand feedback of causal processes is difficult, even when the feedback is linear

Even if our cognitive maps of causal structure were perfect, learning, especiallydouble-loop learning, would still be difficult. In order to use a mental model to

design a new strategy or organization we must make inferences about theconsequences of decision rules that have never been tried and for which we

have no data. To do so requires intuitive solution of high-order nonlineardifferential equations, a task far exceeding human cognitive capabilities in all

but the simplest systems (Forrester 1971).From Sterman: Learning in and about complex systems. System Dynamics Review Vol. 10, nos. 2-3

(Summer-Fall 1994): 291-330

A task far exceeding human cognitive capabilities ?!

NEE

Met de mogelijkheden en het begrip van ‘de niet lineaire wiskunde’ , snelle computers en meer geavanceerde software

is dit geen argument meer

Een aantal simpele demonstraties om dat te illusteren.

System Dynamics: StellaEen voorbeeld van een lineaire differentiaal vergelijking

population

incomingbirth

birth%

outgoingdeath

death%

Differentiaal vergelijking:dpopulation/dt = population*(birth%-*death%)

14:09 Thu 31 May 2007

2007.00 2019.50 2032.00 2044.50 2057.00

Time

1:

1:

1:

10000000,00

30000000,00

50000000,00

1: population

1

1

1

1

Graph 1 (Untitled)

Een ander voorbeeld: geremde groeiEen voorbeeld van een niet lineaire differentiaal vergelijking

population

incomingbirth

changeparameter

maxpopulation

Differential Equation of logistic growth (Verhulst 1838):dpopulation/dt= changeparameter*population*{(maxpopulation-population) / maxpopulation }

9:14 woe 27 jun 2001

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0,00

500,00

1000,00

1: size of population

1

1

11

Graph 1 (Untitled)

Een stap vooruit: het herkennen van order and chaos

Geremde groei uitgedrukt in Logistic model (differentievergelijking)

Perfect Order, one stable outcome: groeiparameter (r) < 3

1 * *(1 )n n nX r X X

16:42 Thu 28 Feb 2013

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0,00

0,25

0,50

1: p

11

1 1

Graph 1 (Untitled)

Een stap vooruit: het herkennen van order and chaos

Geremde groei uitgedrukt in Logistic model (differentievergelijking)

Order, two outcomes: groeiparameter (r) = 3

1 * *(1 )n n nX r X X

16:45 Thu 28 Feb 2013

0.00 10.00 20.00 30.00 40.00

Time

1:

1:

1:

0,00

0,40

0,80

1: p

1

1 1 1

Graph 1 (Untitled)

Een stap vooruit: het herkennen van order and chaos

Geremde groei uitgedrukt in Logistic model (differentievergelijking)

Chaos, infinite number of outcomes: groeiparameter > 3.6

1 * *(1 )n n nX r X X

16:51 Thu 28 Feb 2013

0.00 25.00 50.00 75.00 100.00

Time

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1:

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0,90

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Een stap vooruit: het herkennen van order and chaos

Logistic growth model

Een praktijk voorbeeld:

Model voor de communicatie tussen

Huisarts en Patient

Hoe communiceren huisarts en patient?

Patiënt Huisarts

• 2 persons • A role taking play• Topic: health situation patient• Within a limited consultation time

GP - Patiënt communication

How do social scientists observe the communication??

RIAS (Roter)• 26 categories• For GP and Patiënt • Unit of observation:

utterance

For example:• Biomedical questions• Psychosocial

information• Empathy• Shows agreement

Condensed in a Scheme

• Biomedical outcome(Task)

• Social emotional context (Social Emotional)

• Controlling the process(Process)

Empirical base

SSecond Dutch National Survey of General Practice. (NS2)

• 142 GP’s• 2784 consultations recorded on video• 2094 observed with RIAS

Our dataset

• 102 Hypertension consults• GP’s (77 male 25 female)• Patiënts (38 males, 64 females)• Coded: 23.721 RIAS utterances• At last put into SPSS files

To build a simulation ModelSimple Causal Hypotheses about the Feedback

such as

Social emotional utterances of the GP stimulates talking of the patient about social emotional topics as well as about biomedical topics.

Biomedical utterances of the GP amplifies itself and inhibits social emotional communication of the patient(and vice versa)

A Simulation Model of FeedbackA model of the GP

Three Components (to start with)

Task (biomedical)Social EmotionalProcess control

A Simulation Model of FeedbackProgrammed in Stella

Three related Components of Inhibited Growth(reference model: coupled logistic differential equations Van Geert 1991, Eckstein 1998, Maas 2006, Savi 2007 )

GPTask

GPSocemo

GPProcess

driveGPTask

DriveGPSocemo

DriveGPProcess

kGPTask

kGPSocemo

kGPProcess

rGPTask

rGPSocemo

rGPProcess

A Simulation Model of FeedbackA model of the Patient

PatientTask

PatientSocemo

PatientProcess

DrivePatienTask

DrivePatientSocemo

DrivePatientProcess

mltplfbckPStoPT

kPatientTask

kPatientSocemo

kPatientProcess

rPatientTask

rPatientSocemo

rPatientProcess

GP and Patient CoupledIn coupled logistic differential equations

Dijkum, C. van, Lam N., et al (2008). Non Linear Models for the Feedback between GP and Patients. Cybernetics and Systems, Vienna: Austrian Society for Cybernetic Studies, pp. 629–634.Dijkum, C. (2008), ‘Changing methodologies for research’, Journal of Organisational Transformation and Social Change 5: 3, pp. 267–289

2 Actors X (coupled)3 (task, social emotional, process)

Feedback loops in logistic differential equation:

Feedback from one process to another:

With coupling parameters e : internal and external

GP Patient

Task

Social Emotional

Process

Video observation of a Consult represented by SPSS in a qualitative time developing pattern

Qualitative Validation of the ModelNot yet entering chaos

At first a patient gives and ask (medical) Task information (red), then the GP responds and asks and gives medical Task information (yellow),

but the when the GP goes on, the patient falls back giving and asking (medical) Task information.

The question is: can the simulation model (re)produce such patterns?

Outcome of simulations of the model: in which in 3 runs the GP’s (medical) Task utterances are made stronger

Qualitative Validation of the ModelNot yet entering chaos

The GP’s social emotional utterances (brown: GPSocemo) stimulates patient’s social emotional utterances (violet: PatientSocemo), that stimulates at last patient’s biomedical utterances (red:PatientTask),

and the GP’s biomedical utterances (yellow: GPTask).

Again the question is: can the simulation model (re)produce such patterns?

Outcome of simulations of the model: in which in 3 runs the GP’s Social emotinal (Socemo) utterances are made stronger

Conclusion:with qualitative validation

Model can reproduce:In regions of order

essential hypotheses & essential patterns in data

Social emotional utterances of the GP stimulates talking of the patient about social emotional topics as well as about biomedical topics.

Biomedical utterances of the GP amplifies itself and inhibits social emotional communication of the patient(and vice versa)

Another step ahead: recognizing chaos An empirical example: communication model

GP-Patient

GP and Patient

X (coupled)

3 (task, social emotional, process)

Expressed in:

6 coupled logistic stochastic non linear differential equations

in regions of Chaos and Order

Now Programmed in MATLABExtending research in physics (Savi 2007, Physics Letters A, 364, pp. 389–395)

with 2 coupled logistic stochastic non linear differential equationsWe started with 3 coupled equations

Another step ahead: recognizing order and chaos

Programmed in MATLABTo grasp phenomena of order and chaos

By calculating the lyapunov exponent varying coupling coefficients (e)When > 0 : chaos

When < 0 : periodic behavior (order)

X in chaos and order with related lyapunov exponent and related S (1=order; 0=chaos)

Another step ahead: recognizing order and chaosAn empirical example: outcome variable of our communication model (GP-Patient)

Using Lyapunov and S to identify stable periodic behavior

4 period reflected in S

Another step ahead: recognizing order and chaos An empirical example: communication model GP-Patient

One of the surprising results:A 3 coupling of Chaos (CLM)

F1 (CLM)

F2 (CLM)

F3 (CLM)

Can produce (periodic) Order

2 period in e [0.0712,0.0715] Stochastic fluctuation of De = 0.001 reflected in S

To the extended Model2 Actors X (coupled)

3 (task, social emotional, process)

GP Patient

Task

Social Emotional

Process

When all components are in a certain state of chaos: can we produce order?

YES: WE CANIn Certain Conditions (for example: 0.9008 < e < 0.9009)

State GP State Patient S=1: indicator Lyapunov

WHAT CAN YOU DO WITH SUCH SIMULATIONS?

If you take the pattern into account, you can influence where you’re going!

If you don’t…

By understanding:

What patterns of coördinating chaos and order produces a stable outcome both for the GP as well for

the Patient?

And how can we illustrate that with video observation data of the communication between GP and Patient ?

And how can we transfer that insight in an instrument of training ?

For Practice:To improve the communication between GP and Patient