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?
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)
Understanding → Prediction
Outline
1.
2.
3.
4.
not all behaviours are ‘causal’
it is useful for us to discriminate between entailment and causation
it is useful to identify causation with intervention
there is a strong relation between causation and emergence
5. not all emergent processes are causal
6. all causal processes are emergent
Consequence
7. it is very hard to make sense of this picture only in terms of behaviours
8. 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)
1. not all behaviours are ‘causal’
2. it is useful for us to discriminate between entailment and causation
3. it is useful to identify causation with intervention
Entailment: logical necessity or physical inevitability
P╞ 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)
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
Causation as asymmetry: asymmetry in correlation, asymmetry in agency/control,
Principle of Independence (Hausman, 1998)
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)
Emergence
4. there is a strong relation between causation and emergence
5. not all emergent processes are causal
6. all causal processes are emergent
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
Pattern Formation
5. not all emergent processes are causal
6. all causal processes are emergent
Human
Causal power
Model
Experimental
Economics
Input + Rules
Human decision making
Enter
Rules ←
Behaviour of
Economically
Rational Agent
Event
a
Human action
Event
b
Human action
Event
c
Human action
??
….
Reminder of
moral values
…….
Event z
Human action
Output
Observation
Model
Input + Rules
Enter
Event
a
Event
b
Event
•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?
Two alternatives:
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)
….
Event z
Output
•If I can interact with the run
•I need to preconceive all possible
interventions, since they need to be written in
the code
Model
Input + Rules
Enter
Event
a
Event
b
Event
c
??
….
Event z
Output
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)
Logic
entailment
Model
Input + Rules
Human decision making
Enter
Event
a
Human action
Event
b
Human action
Event
c
Human action
….
…….
Event z
Human action
Output
Observation
Experimental
Economics
Effective
control /
causation
Logic
entailment
Input + Rules
Human decision making
Enter
Event
Event
Event
Human action
a
b
c
….
“Useful causation requires control.
Clearly it is valuable to know that
malaria …results from mosquitoes. ..
Effective
…while it is true that mosquitoes
control /
follow the laws of physics, we do not
causation
usually say that malaria is caused by
Human action
…….
the laws of physics (the universal
cause).
Human action
Event z
Output
Human action
That is because we can hope to
control mosquitoes, but not the laws
of physics” Patte, 1997
Observation
Logic
entailment
Input + Rules
Enter
Event
Event
Event
a
b
c
….
“Useful causation requires control.
Clearly it is valuable to know that
malaria …results from mosquitoes. ..
Effective
…while it is true that mosquitoes
control /
follow the laws of physics, we do not
causation
usually say that malaria is caused by
the laws of physics (the universal
cause).
Event z
Output
That is because we can hope to
control mosquitoes, but not the laws
of physics” Patte, 1997
Logic
entailment
Input + Rules
Human decision making
Enter
Event
a
Event
b
Event
c
….
Event z
Output
Convert effective control
into logic necessity
Human action
Human action
Project processes into
‘rule subspace’
Effective
control /
causation
Human action
…….
Convert Causal Emergence
into Pattern Formation
Human action
Observation
Logic
entailment
Input + Rules
Neo Classical economic theory
Rational Economic Agent
Enter
Event
a
Event
b
Event
c
….
Convert effective control
into logic necessity
Project processes into
‘rule subspace’
Event z
Output
Nash ‘optimal’ equilibrium
Invisible Hand
Logic
entailment
Input + Rules
Distributed sensors
Features detection algorithm
Enter
Event
a
Event
b
Event
c
….
Convert effective control
into logic necessity
Project processes into
‘rule subspace’
Event z
Output
New discoveries
New scientific laws
Logic
entailment
Input + Rules
AI Rules
Enter
Event
a
Event
b
Event
c
….
Convert effective control
into logic necessity
Project processes into
‘rule subspace’
Event z
Output
Intelligence
Machine 1
Statistical Complexity = C1
Words = {00, 01, 10, 11}
Transition = {00→01, 01→10, 10 →11, 11 →00}
00011011000110110001101100011011..
Unit of Interaction
Interactive identity machines
P = in(message).out(message).P
Wegner, P.Why Interaction is More Powerful than Algorithm.
Comm. ACM 40(5), 89–. 91 (1997).
01101100011011000110110001101100..
Machine 2
Words = {00, 01, 10, 11}
Transition = {00→10, 01→11, 10 →01, 11 →00}
Statistical Complexity = C2
Machine 1
Statistical Complexity = C1→C1’
Words = {00, 01, 10, 11}
Transition = {00→01, 01→10, 10 →11, 11 →00}
..00011011000110110001101100011011 1011..
Change in statistical complexity
..non stationarity..
..0110110001101100011011000110 11 00..
Machine 2
Words = {00, 01, 10, 11}
Transition = {00→10, 01→11, 10 →01, 11 →00}
Statistical Complexity = C2 →C2’
Machine 1
Words = {00, 01, 10, 11}
Transition = {00→01, 01→10, 10 →11, 11 →00}
00011011000110110001101100011011..
Unit of Interaction
Interactive identity machines
P = in(message).out(message).P
Wegner, P.Why Interaction is More Powerful than Algorithm.
Comm. ACM 40(5), 89–. 91 (1997).
22233233222332332223323322233233..
Machine 2
Words = {22, 23, 32, 33}
Transition = {22→23, 23→32, 32 →33, 33 →22}
Machine 1
Words = {00, 01, 10, 11}
Transition = {00→01, 01→10, 10 →11, 11 →00}
00011011000110110001101100011011 22 halt
22233233222332332223323322233233 00 halt
Machine 2
Words = {22, 23, 32, 33}
Transition = {22→23, 23→32, 32 →33, 33 →22}
Machine 1
Words = {00, 01, 10, 11}
Transition = {access memory 3 steps back and copy two consecutive symbols}
0100100101000110110001101100011 33 13..
What happened
22233233222332332223323322233233 01 halt
• ’13’ is not a possible word for
either Machine 1 or Machine 2
• It is not a wff (well-formedformula) for either systems
• It is genuinely novel
Machine 2
Words = {22, 23, 32, 33}
Transition = {22→23, 23→32, 32 →33, 33 →22}
Machine 1
Words = {00, 01, 10, 11}
Transition = {access memory 3 steps back and copy two consecutive symbols}
0100100101000110110001101100011 33 13..
Ingredients
• Some behaviour
• Some basic interaction
• Some ability to handle novel input
22233233222332332223323322233233 01 halt
Machine 2
Words = {22, 23, 32, 33}
Transition = {22→23, 23→32, 32 →33, 33 →22}
Machine 1
Words = {00, 01, 10, 11}
Transition = {access memory 3 steps back and copy two consecutive symbols}
01001001010001101100011011000113313..
Types of behaviours
•
•
•
•
Entailments
Relations
Generation of higher level unit
Causation
2223323322233233222332332223323310 halt
Machine 2
Words = {22, 23, 32, 33}
Transition = {22→23, 23→32, 32 →33, 33 →22}
1.
2.
3.
4.
Outline
not all behaviours are ‘causal’
it is useful for us to discriminate between entailment and causation
it is useful to identify causation with intervention
there is a strong relation between causation and emergence
5. not all emergent processes are causal
6. all causal processes are emergent
Consequence
7. it is very hard to make sense of this picture only in terms of behaviours
8. 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)
What are the minimum ingredients I need to generate both
causation and emergence?
Summary
1) 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 systems
Closed systems, No novelty, Uncomputability, Chaos
Interaction
Causation as a relation between
entities/processes
Agency theory, Menzies and Price, Pattee..
Importance of organisation
to generate new behaviours
Self-organisation, Prigogine, Laughing..
Causal asymmetries
Hausman (1998)
Statistically novel
non-causal behaviours
Statistically novel
causal behaviours
Ability to handle novel situations
Genuinely novel
non-causal behaviours
Genuinely novel
causal behaviours
Closed | Complex Systems | Open
Far from equilibrium, energy & information flows, Novelty
Things to check
•Mathematical / formal tools to describe changes in context and structure (group theory and
beyond)
Shadelength = Poleheight * F [Sunangle ]
Shadelength ← Poleheight * F [Sunangle ]
F [Sunangle ] = Poleheight / Shadelength
F [Sunangle ] ← Poleheight / Shadelength
Group = {A, Property, Property, …, .. } → Closed to interaction
Things to check
•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..
Ultimate test
“You really understand an algorithm when you've programmed it” (Chaitin, 1997)
Ultimate question
Logic
entailment
Input + Rules
Human decision making
Enter
Event
a
Event
b
Event
c
….
Event z
Output
Convert effective control
into logic necessity
Human action
Human action
Project processes into
‘rule subspace’
Effective
control /
causation
Human action
…….
Convert Causal Emergence
into Pattern Formation
Human action
Observation
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
For more information
[email protected]
http://www.per.marine.csiro.au/staff/Fabio.Boschetti/