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CAUSATION, ORGANISATION & EMERGENCE Fabio Boschetti and David Batten CSIRO, Australia
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CAUSATION, ORGANISATION & EMERGENCE
Fabio Boschetti and David Batten
CSIRO, Australia
Warnings
• Summary of lucubrations over many years• Work in progress• Clear conclusions need developing
Speaker’s background:
• Numerical optimisation• Modelling (physical, ecological, social)• Relation between computation and Complex System Science• Can we do CSS on a computer at all? What CSS?
What are the minimum ingredients I need to generate both causation and emergence?
Ultimate test
“You really understand an algorithm when you've programmed it” (Chaitin, 1997)a processmodelled
What are the minimum ingredients I need to generate both causation and emergence?
Understanding → Prediction
1. not all behaviours are ‘causal’2. it is useful for us to discriminate between entailment and causation3. it is useful to identify causation with intervention 4. there is a strong relation between causation and emergence
5. not all emergent processes are causal 6. all causal processes are emergent
7. it is very hard to make sense of this picture only in terms of behaviours8. it is easier in terms of interaction or relations or organisation
9. some relations act by constraining elements’ behaviour -> symmetry breaking (maybe these can be modelled)
10.some relation act by generating novelty (these require external intervention = open system)
Outline
Personal
choice
Consequence
1. not all behaviours are ‘causal’2. it is useful for us to discriminate between entailment and causation3. it is useful to identify causation with intervention
Entailment: logical necessity or physical inevitabilityP╞ Q or P→Q or If P then Q
Intervention: an action external to the system that produces an effect by altering the course of a process
Intervention: an action external to the system that produces an effect by altering the course of a process
Causation as intervention: by imposing a chosen perturbation on event a and observing the consequence on event b we may be able to unravel the underlying causal relation between a and b (Pearl)
“Useful causation requires control. Clearly it is valuable to know that malaria results from mosquitoes.
…while it is true that mosquitoes follow the laws of physics, we do not usually say that malaria is caused by the laws of physics (the universal cause).
That is because we can hope to control mosquitoes, but not the laws of physics” Pattee, 1997
Intervention: an action external to the system that produces an effect by altering the course of a process
Causation as intervention: by imposing a chosen perturbation on event a and observing the consequence on event b we may be able to unravel the underlying causal relation between a and b (Pearl)
Causation as control: “we can hope to control mosquitoes, but not the laws of physics” Pattee, 1997
Causation as agency: ”an event A is a cause of a distinct event B just in case bringing about the occurrence of A would be an effective means by which a free agent could bring about the occurrence of B.” (Menzies and Price, 1993)
Neither intervention nor agency imply human intervention; they represent a relation
Neither intervention nor agency imply human intervention; they represent a relation
Neither intervention nor agency imply human intervention; they represent a relation
Intervention: an action external to the system that produces an effect by altering the course of a process
Causation as intervention: by imposing a chosen perturbation on event a and observing the consequence on event b we may be able to unravel the underlying causal relation between a and b (Pearl)
Causation as control: “we can hope to control mosquitoes, but not the laws of physics” Pattee, 1997
Causation as agency: ”an event A is a cause of a distinct event B just in case bringing about the occurrence of A would be an effective means by which a free agent could bring about the occurrence of B.” (Menzies and Price, 1993)
Causation as asymmetry: asymmetry in correlation, asymmetry in agency/control,Principle of Independence (Hausman, 1998)
Causation as asymmetry: asymmetry in correlation, asymmetry in agency/control,Principle of Independence (Hausman, 1998)
1) Multiple effects of common causes need to be correlated; multiple causes of common effect do not
2) We can intervene in the cause to alter the effect; we can not intervene on the effect to alter the cause
3) Independence principle: every effect must have at least two independent causes
Intervention: an action external to the system that produces an effect by altering the course of a process
Causation as intervention: by imposing a chosen perturbation on event a and observing the consequence on event b we may be able to unravel the underlying causal relation between a and b (Pearl)
Causation as control: “we can hope to control bacteria and mosquitoes, but not the laws of physics” Pattee, 1997
Causation as agency: ”an event A is a cause of a distinct event B just in case bringing about the occurrence of A would be an effective means by which a free agent could bring about the occurrence of B.” (Menzies and Price, 1993)
Causation as asymmetry: asymmetry in correlation, asymmetry in agency/control,Principle of Independence (Hausman, 1998)
4. there is a strong relation between causation and emergence
5. not all emergent processes are causal 6. all causal processes are emergent
Emergence
Pattern Formation → Prediction
Intrinsic emergence → Information processing for trade agents
Emergence of causal power → we can intervene on the stock market and affect the economy
Causal emergence: “the arising of a system property on which intervention can be exerted without manipulating the system components” (Boschetti and Gray, 2007).
Cellular Automata Human
Pattern FormationCausal power
5. not all emergent processes are causal 6. all causal processes are emergent
Model
Rules ← Behaviour ofEconomically Rational Agent
Human decision making
Human action
Human action
Human action
…….
Observation
Human action
ExperimentalEconomics
Reminder of moral values
Intervention
??
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Enter
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Model
Enter
•Event c is not caused by b since after b happens c follows as a logic necessity•What changes c changes also b (correlated)•What causes c?•What do I need to do to actuate a chance in c?
•If I can not interact with the run, I have to change input or code•Control lies only in the input and code•Logic entailment (Rosen)
Two alternatives:
•If I can interact with the run •I need to preconceive all possible interventions, since they need to be written in the code
Impossible
??
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Model
Enter
??
Causation as intervention: by imposing a chosen perturbation on event b and observing the consequence on event c we may be able to unravel the underlying causal relation between b and c (Pearl)Causation as agency: ”an event b is a cause of a distinct event c just in case bringing about the occurrence of b would be an effective means by which a free agent could bring about the occurrence of c.” (Menzies and Price, 1993)Causation as asymmetry: asymmetry in correlation, asymmetry in agency/control, Principle of Independence (Hausman, 1998)
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Human decision making
Human action
Human action
Human action
…….
Observation
Human action
Model
ExperimentalEconomics
Enter
Logic entailment
Effective control / causation
Human decision making
Human action
Human action
Human action
…….
Observation
Human action
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Enter
Effective control / causation
Logic entailment
“Useful causation requires control. Clearly it is valuable to know that malaria …results from mosquitoes. ..
…while it is true that mosquitoes follow the laws of physics, we do not usually say that malaria is caused by the laws of physics (the universal cause).
That is because we can hope to control mosquitoes, but not the laws of physics” Patte, 1997
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Enter
Effective control / causation
Logic entailment
“Useful causation requires control. Clearly it is valuable to know that malaria …results from mosquitoes. ..
…while it is true that mosquitoes follow the laws of physics, we do not usually say that malaria is caused by the laws of physics (the universal cause).
That is because we can hope to control mosquitoes, but not the laws of physics” Patte, 1997
Human decision making
Human action
Human action
Human action
…….
Observation
Human action
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Enter
Effective control / causation
Logic entailment
Convert effective control into logic necessity
Project processes into ‘rule subspace’
Convert Causal Emergence into Pattern Formation
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Enter
Logic entailment
Convert effective control into logic necessity
Project processes into ‘rule subspace’
Neo Classical economic theoryRational Economic Agent
Nash ‘optimal’ equilibriumInvisible Hand
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Enter
Logic entailment
Convert effective control into logic necessity
Project processes into ‘rule subspace’
Distributed sensorsFeatures detection algorithm
New discoveriesNew scientific laws
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Enter
Logic entailment
Convert effective control into logic necessity
Project processes into ‘rule subspace’
AI Rules
Intelligence
Machine 1
Words = {00, 01, 10, 11}Transition = {00→01, 01→10, 10 →11, 11 →00}
Machine 2
Words = {00, 01, 10, 11}Transition = {00→10, 01→11, 10 →01, 11 →00}
00011011000110110001101100011011..
01101100011011000110110001101100..
Unit of InteractionInteractive identity machines
P = in(message).out(message).PWegner, P.Why Interaction is More Powerful than Algorithm.
Comm. ACM 40(5), 89–. 91 (1997).
Statistical Complexity = C1
Statistical Complexity = C2
Machine 1
Words = {00, 01, 10, 11}Transition = {00→01, 01→10, 10 →11, 11 →00}
..00011011000110110001101100011011
..0110110001101100011011000110
Machine 2
Words = {00, 01, 10, 11}Transition = {00→10, 01→11, 10 →01, 11 →00}
Change in statistical complexity..non stationarity..
11
1011..
00..
Statistical Complexity = C1
Statistical Complexity = C2
→C1’
→C2’
Machine 1
Words = {00, 01, 10, 11}Transition = {00→01, 01→10, 10 →11, 11 →00}
Machine 2
Words = {22, 23, 32, 33}Transition = {22→23, 23→32, 32 →33, 33 →22}
00011011000110110001101100011011..
22233233222332332223323322233233..
Unit of InteractionInteractive identity machines
P = in(message).out(message).PWegner, P.Why Interaction is More Powerful than Algorithm.
Comm. ACM 40(5), 89–. 91 (1997).
Machine 1
Words = {00, 01, 10, 11}Transition = {00→01, 01→10, 10 →11, 11 →00}
Machine 2
Words = {22, 23, 32, 33}Transition = {22→23, 23→32, 32 →33, 33 →22}
00011011000110110001101100011011
22233233222332332223323322233233
halt
halt00
22
Machine 1
Words = {00, 01, 10, 11}Transition = {access memory 3 steps back and copy two consecutive symbols}
Machine 2
Words = {22, 23, 32, 33}Transition = {22→23, 23→32, 32 →33, 33 →22}
0100100101000110110001101100011
22233233222332332223323322233233 halt
13..
What happened
• ’13’ is not a possible word for either Machine 1 or Machine 2
• It is not a wff (well-formed-formula) for either systems
• It is genuinely novel
33
01
Machine 1
Words = {00, 01, 10, 11}Transition = {access memory 3 steps back and copy two consecutive symbols}
Machine 2
Words = {22, 23, 32, 33}Transition = {22→23, 23→32, 32 →33, 33 →22}
0100100101000110110001101100011
22233233222332332223323322233233 halt
13..33
01
Ingredients
• Some behaviour • Some basic interaction• Some ability to handle novel input
Machine 1
Words = {00, 01, 10, 11}Transition = {access memory 3 steps back and copy two consecutive symbols}
Machine 2
Words = {22, 23, 32, 33}Transition = {22→23, 23→32, 32 →33, 33 →22}
010010010100011011000110110001133
2223323322233233222332332223323310 halt
13..
Types of behaviours
• Entailments • Relations• Generation of higher level unit• Causation
1. not all behaviours are ‘causal’2. it is useful for us to discriminate between entailment and causation3. it is useful to identify causation with intervention 4. there is a strong relation between causation and emergence
5. not all emergent processes are causal 6. all causal processes are emergent
7. it is very hard to make sense of this picture only in terms of behaviours8. it is easier in terms of interaction or relations or organisation
9. some relations act by constraining elements’ behaviour -> symmetry breaking (maybe these can be modelled)
10. some relation act by generating novelty (these require external intervention = open system)
OutlinePerso
nal
choice
Consequence
What are the minimum ingredients I need to generate both causation and emergence?
Summary1) Entities need to ‘do’ something; have properties or behaviours
2) Entities need to interact; in order to have anything ‘new’ happening
3) Interactions may happen as entailments; which creates a ‘new’ closed system/unit
4) Some interaction may be causal; these are characterised by a special kind of relation; they require certain asymmetries to occur
5) At a different scale/scope, the relation allowing intervention may not be detected and the system may appear as an entailment
6) The behaviour should not be fully determined in order to generate ‘real’ novelty
7) The behaviour should not be determined only in terms of structures in the system; there should be some space to process structures not seen before
8) Normally, in our models, we do not account for interaction and we fully specify behaviours and properties
Summary Limitations of formal systemsClosed systems, No novelty, Uncomputability, Chaos
Closed | Complex Systems | OpenFar from equilibrium, energy & information flows, Novelty
Importance of organisation to generate new behaviours
Self-organisation, Prigogine, Laughing..
Causation as a relation between entities/processes
Agency theory, Menzies and Price, Pattee..
Causal asymmetriesHausman (1998)
Statistically novel causal behaviours
Statistically novelnon-causal behaviours
Ability to handle novel situations
Genuinely novelcausal behaviours
Genuinely novelnon-causal behaviours
Interaction
Internal to the systemExternal to the system
Things to check
•Mathematical / formal tools to describe changes in context and structure (group theory and beyond)
Shadelength = Poleheight * F [Sunangle ]
F [Sunangle ] = Poleheight / Shadelength
Shadelength ← Poleheight * F [Sunangle ]
F [Sunangle ] ← Poleheight / Shadelength
Group = {A, Property, Property, …, .. } → Closed to interaction
Forward problem
Inverse problem
Things to check
Ultimate test
“You really understand an algorithm when you've programmed it” (Chaitin, 1997)a processmodelled
Ultimate question
•Mathematical / formal tools to describe changes in context and structure (group theory and beyond) •Relation between hardware and software – computer science and biology•More on causal asymmetries and Hausman•Intuitive perception of causality from shape and symmetries in terms of history of an entity•In general many of the things I do not know are surely well known in other fields..
Human decision making
Human action
Human action
Human action
…….
Observation
Human action
Input + Rules
Event a
Event b
Event c
….
Output
Event z
Enter
Effective control / causation
Logic entailment
Convert effective control into logic necessity
Project processes into ‘rule subspace’
Convert Causal Emergence into Pattern Formation
References
•Hausman, D., 1998. Causal asymmetries. Cambridge University Press., Cambridge.•Menzies, P. and Price, H., 1993. Causation as a secondary quality. The British Journal for the Philosophy of Science 44:187-203.•Pattee, H., 1997. Causation, Control, and the Evolution of Complexity. In: P.B. Andersen, C. Emmeche, N.O. Finnemann and P.V. Christiansen (Editor), Downward Causation. University of Århus Press, Århus, pp. 322-348.
•Laughlin, R., 2005. A Different Universe: Remaking Physics from the Bottom Down Basic Books, New York.
•Leeuwen, J and Wiedermann, J, The emergent computational potential of evolving artificial living systems. Source, AI Communications archive. Volume 15 , Issue 4 •Milner, R., 1993. Elements of interaction: Turing award lecture. ACM, pp. 78-89.•Wegner, P., 1997. Why interaction is more powerful than algorithms. ACM, pp. 80-91.•Wiedermann, J. and Leeuwen, J., 2002. The emergent computational potential of evolving artificial living systems. IOS Press, pp. 205-215.
References
•Boschetti, Causality, emergence, computation and unreasonable expectations, Synthese, in print.
•Prokopenko, Boschetti & Ryan, 2009, An Information-Theoretic Primer On Complexity, Self-Organisation And Emergence, Complexity, DOI: 10.1002/cplx.20249.
•Batten, Salthe & Boschetti, 2008, Visions of Evolution: Self-organization proposes what natural selection disposes, Biological Theory, Vol. 3, No. 1, Pages 17-29
•Boschetti, McDonald & Gray, 2008, Complexity of a modelling exercise: a discussion of the role of computer simulation in Complex System Science, Complexity, 13, 6, pp 21-28
•Boschetti & Gray. 2007, A Turing test for Emergence, in M. Prokopenko (ed.), Advances in Applied Self-organizing Systems, Springer-Verlag, London, UK, 2007 , pp 349-364
•Boschetti & Gray, 2007, Emergence and Computability, Emergence: Complexity and Organization, Volume 9 Issues 1-2, 120-130
