Making hierarchy theory useful Tim Allen
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Transcript of Making hierarchy theory useful Tim Allen
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