No Paradigm With Paradigm

Properties of Complex Systems

The story you told to make it simple.

HierarchicalMany levels of constraint

Links: large and small

different typesfast and slow

HierarchicalMany levels of constraint

Links: large and small

different typesHighly organized

fast and slow

No!

Narratives and Analogies

So if we can’t use reduction and models, what to do? Rosen(2000) says we can use analogy and tell narratives.

Hamilton wrote a dictionary for Newtonian particles into Optical Geometry. (c.f. Voltage ≈ water pressure.)

Newtonian particles

Optical geometry

Reduction

Wave mechanics

Quantum mechanics

Reduction

B i o s p h e r e

B i o m eLandscape

Ecosystem

Community

Population

Organism

These are

TYPES

SCALE SCALE

NO WAY

T. F. H. A

Community

Organism (tree)

Ecosystem (decaying log)

Landscape (upper surface of log)

Population (of mosses on log)

T. F. H. A

Type vs Scale

• TYPE• Identifies what is in

the foreground• Gives criteria for

observation• Gives equivalence to

a class

• SCALE• Grain • Extent• Spatial size• Natural frequency in

time

Allen TFH & TW Hoekstra (1992) Toward a unified ecology. Columbia Press

Type (Criterion) In the Observed

• Meets criteria that were there in abstract. Requires observation. Does what I see meet the definition of the type

In the Protocol

• Choose the criterion for observation. Gives something to be met, but is itself a definition.

Allen TFH & TW Hoekstra (1992) Toward a unified ecology. Columbia Press

In the Protocol

• Prescription of Grain for observation prescribes finest distinction.

• Prescription of Extent of the universe of discourse.

In the Observed

• The size of the thing you see.

• Scales an example of a type.

Scale

Allen TFH & TW Hoekstra (1992) Toward a unified ecology. Columbia Press

Laws vs Rules• Laws are:

• Inexorable• General• Rate dependent• Structure independent• Dynamical

• Rules are:

• Local• Arbitrary• Rate independent• Structure dependent• Linguistic

H. H. Pattee (1978) The complementarity principle in biological and social structures. J. Social Biol. Struct. 1: 191-200

Organism enters worldtelling a narrative

T. F. H. A

Richard Nixon

T. F. H. A

UPPER VS LOWER

General

• Role

• Essence

• Type

• Relational function

Specific

• Incumbent

• Realization

• Individual

• Organized structure Simon, 1962

Rosen, 2000

Salthe 1985

Bailey 1990

LAWS

RULES

LOWER

UPPER

INFINITE

BOUNDED INFINITE FINITE ALLOWED

FINITE ACTUAL

LAWS

RULES

LOWER

UPPER

∞

∞?

Other Observer

LAWSINFINITE

RULES

LOWER

UPPERBOUNDED INFINITE FINITE ALLOWED

FINITE ACTUALOBSERVEROTHER

Example defines the criterion

Criterion verified by

example

Realize structure

Reinforcetype

• 0. Have a perception

• 1. Ask a question

• 2. Define type of the thing (assign to class)

• 3. Choose a scaled measure of type (to fit size of example

• 4. Notice a phenomenon

• 5. Evaluate model

Steps to modeling

0

Ahl V & Allen TFH (1996) Hierarchy Theory, a vision, vocabulary and epistemology. Columbia, NYC

5

1

2

3

4

LAWS

LOWER

INFINITE

FINITE, ALLOWED

FINITE ACTUAL

OBSERVER

OTHER

1

The thing raising a question

Example demandsa type

Class to which Structure belongs

Verify that type applies to example

0Perceive rather than observesomething

3 Choose a measurement regime for example and type of structure. This gives level of observation

4 Class defines the level of organization of the phenomenon

5

BY RULES

Evaluate model relative to assessed performance of the other

Define typeof the thing

2

2 3 4 510

LAWS

LOWER

UPPER

INFINITE

BOUNDED INFINITE

FINITE ACTUAL

OBSERVER

OTHER

Essence is realized in structure of a certain size

Success reinforces Essence

Realized Structure

0

Structure enters observable world

1

Structure is successful

essence4Cause of

phenomenon here

5 Equivalence in the equivalence class is the

model of the essence

2

Mutual modification of structure and essence

3

Dynamics becomes measurable

LAWSINFINITE

Loop that generates formand modifies essence

Essence that causes pattern & structure

The thing you see

Model invoked by equivalence

FINITE ACTUALOBSERVEROTHER

Loop of model building

Model evaluation5

LAWS (Material Necessities)

Evolved resistance to poison

Effect of poison on target

versus allelopath

Model for allelpathy

OBSERVEROTHER

Resistant target plants

Natural selection of target population

Tests for effect of poison

Failed experiments

Model ofToxicity

Fish Subjectedto Toxins

Contextin which Fish

Evolve

OBSERVEROTHER

Experimentalcalibration

Adapted individuals realized

Naturalselection

Assigned to class

History Observer Decision

Laws(Material Necessities)

LAWS (Material Necessities)

Complicated political events

Symbolic Representation

Never challenges Narrative

Peace time Politics

OBSERVEROTHER

Cycle is isolated

Realize structure

Modifycontext

Pundits proclaim, and the narrative becomesstuck inequivocation

LAWS (Material Necessities)

Readily interpretable Real-time wins

and losses

Plans generate Real-time actions

that change eventsunpredictably

War time strategiesPlans and predictions

OBSERVEROTHER

Cycle is informed

Realize structure

Modifycontext

Narrative gets real-time tests often and usually is shown to be of poor quality.

LAWS (Material Necessities)

Forest pestilence,Forests products

Good growth

Plans generate Real-time actions

that change eventsunpredictably

Adaptive managersof forests

OBSERVEROTHER

Plansfail or succeed

Realize structure

Modifycontext

New plans turn on past management outcomes. Managers learn and identify tested principles

LAWS (Material Necessities)

Real ecological problems

Symbolic Representation

Never challenges Narrative

Ecologists in general, population biologists

in particular

OBSERVEROTHER

Cycle is isolated

Realize structure

Modifycontext

Model becomesarcane and are rarely tested in realistic situations

Fish Subjectedto Toxins

Context in which Fish Evolve

OBSERVEROTHER

AdaptiveSystem

History Observer Decision

AdaptiveManagement

Laws(Material Necessities)

Physical system

processes

Actual External Gradient

Linguistic planning element. Internal to System, external to thermodynamics

Anticipated decline in resources influences plan

Plan

External Gradients

Plan

Present vs Future

Unplanned adjustment in

dissipation

Past vs Present