contextual emergence of mental states from neurodynamics

Interlevel RelationsStatistical Mechanics and Thermodynamics

Neurodynamics and Mental StatesStable Partitions and Symbolic Dynamics

First Tests and Perspectives

Contextual Emergence of Mental Statesfrom Neurodynamics

Harald Atmanspacher, Robert Bishop, Peter beim Graben

Institute for Frontier Areas of Psychology, Freiburg, GermanyPhilosophy Department, Wheaton College, Wheaton IL, USA

School of Psychology, University of Reading, UK

Harald Atmanspacher, Robert Bishop, Peter beim Graben Contextual Emergence of Mental States from Neurodynamics

1 Interlevel Relations

2 Statistical Mechanics and Thermodynamics

3 Neurodynamics and Mental States

4 Stable Partitions and Symbolic Dynamics

5 First Tests and Perspectives

Hierarchical DescriptionsReduction and Emergence

social systems – collective behaviorembodied systems – behavior

mental systems – consciousnessneural systems – action potential

non-equilibrium systems – order parametersthermal systems – thermodynamic variables

many-particle systems – moments of distributionsquantum systems – canonical observables

social systems – collective behaviorembodied systems – behavior

mental systems – consciousnessneural systems – action potential

non-equilibrium systems – order parametersthermal systems – thermodynamic variables

many-particle systems – moments of distributionsquantum systems – canonical observables

L contains necessary L contains sufficientconditions for H conditions for H

strong reduction yes yes

supervenience no yes

contextual emergence yes no

radical emergence no no

Bishop and Atmanspacher 2006

SupervenienceContextual Emergence

Supervenience: L sufficient but not necessary for Hstatistical mechanics–thermodynamics

A thermodynamic system (H) can be multiply realized by amany-particle system (L) as long as the statistical distribution ofparticular particle properties in L satisfies particular conditions.

L: many configurationsof particles with qi , pi ,associated with < Ekin >

=⇒H: temperature Tcan be related to Lby T ∝< Ekin >

↑why correlation

for individual realizations ?

Contextual emergence: L necessary but not sufficient for Hstatistical mechanics–thermodynamics

L: canonical observables,equations of motion,statistical distributions

⇐=H: temperature Tcan be related to Lby T ∝< Ekin >

• select contexts in H: th. limit, th. equilibrium

• implement them due to stability criteria in L: KMS states

• identify proper coarse graining (topology change) in L• assign equivalence classes of L-states to single H-states with

same temperature Haag et al. 1974, Takesaki 1970

• identify proper coarse graining (topology change) in L

• assign equivalence classes of L-states to single H-states withsame temperature Haag et al. 1974, Takesaki 1970

Supervenience: L sufficient but not necessary for Hneurodynamics–mental states

A neural correlate of consciousness can be multiply realized byminimally sufficient neural subsystems (L) correlated with states ofconsciousness (H). Chalmers 2000

L: many configurationsof neurons withparticular properties

=⇒ H: one mental state(state of consciousness)

↑why correlation

for individual realizations ?

Contextual emergence: L necessary but not sufficient for Hneurodynamics–mental states

L: action potentials,firing rates, correlationsin neuronal ensembles

⇐=H: one mental state(state of consciousness)

• select contexts in H: “phenomenal families” details

• implement them due to stability criteria in L: SRB states

• identify proper coarse graining in L: “stable partitions”

• assign equivalence classes of L-states to single H-states withsame phenomenal properties Atmanspacher & beim Graben 2006

Partitions as Coarse GrainingsCyclic and Irreducible ShiftsSignificance of Generating (Markov) Partitions

Trajectories of a system in itsphase space X (L) are mappedonto strings of a finite set ofsymbols (H) by partitioning Xinto disjoint cells Ai .X is thereby mapped onto aset of symbol sequences s.If these sequences can begenerated by a finite transitiongraph, the symbolic dynamicsin H is a Markov shift.

Stable partitions can be constructed for cyclic or irreducible shifts.

cyclic shift irreducible shiftmultiple fixed points chaotic attractorbasins of attraction generating partition details

Generating Partitions (Markov Partitions)

• Well-defined mental states require coarse grainings in X thatare stable under the dynamics in X . Such partitions are:(i) basins of attraction for multiple fixed points,(ii) generating partitions for chaotic attractors.

• Generating partitions provide a rigorous theoretical constraintfor well-defined mental states, independent of their empiricalplausibility. Fell 2004

• Only generating partitions entail mutually compatible mentaldescriptions that are topologically equivalent with theunderlying neurodynamics. details

beim Graben & Atmanspacher 2006

Numerical TestsTests with Empirical DataPerspectives

Numerical TestsCollaboration with Carsten Allefeld & Jiri Wackermann, EAP/IGPP

• simulate 4 coexisting fixed point attractors with noise

• determine transition matrix based on 100 x 100 grid

• calculate eigenvalues and corresponding time scales

• look for gaps between successive time scales

• use first eigenvectors for identification of partition

0 2 4 6 8 10 12 14 16 18 200.96

1.04eigenvalues

0 2 4 6 8 10 12 14 16 18 200

4 timescales

0 2 4 6 8 10 12 14 16 18 200

8timescale separation factors

Tests with Empirical DataCollaboration with Carsten Allefeld & Jiri Wackermann, EAP/IGPP

• 20-channel EEG time series from petit-mal subjects

• 3 principal components: low-dimensional phase space

• 128 x 128 grid: (Markov) transition matrix

• eigenvalues: corresponding time scales

• gaps between time scales: number of relevant eigenvectors

• relevant eigenvectors: proper phase space partition

• partitioned data to be compared with original data

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 180.2

0.60.8 11.2

a) original data

← F(3) = 2.15

−2 −1.5 −1 −0.5 0 0.5

2055 2060 2065 2070 2075 2080

time [sec]

Can mental or behavioral states be derived from a properpartition provided by a suitable empirically registeredneurodynamics?

Potential examples for future work:

• “microstates” as proposed from topographical EEG analyses(Lehmann, Wackermann)

• behavioral states of spontaneously behaving animals frommultielectrode signals (Eschenko, Logothetis)

• studies in artificial intelligence, classification of vesicle behavior(Packard)

• compare Markov partitioning with partitions due to correlationanalyses (Amari)

Appended Material

Generating partitions P, which are stableunder the dynamics in X , implydescriptions that are topologicallyequivalent with descriptions based on X .(Then the intertwiner π : X → s isinvertible, π ◦ Φ = σ ◦ π.)

-s σ(s)

x Φ(x)

If partitions P,P ′ are notgenerating, observables based onP and P ′ are incompatible (oreven complementary).

Observables are incompatible(complementary) if they donot have all (have no)eigenstates in common.

return

Appended Material

Generating partitions P, which are stableunder the dynamics in X , implydescriptions that are topologicallyequivalent with descriptions based on X .(Then the intertwiner π : X → s isinvertible, π ◦ Φ = σ ◦ π.)

-s σ(s)

x Φ(x)

If partitions P,P ′ are notgenerating, observables based onP and P ′ are incompatible (oreven complementary).

Observables are incompatible(complementary) if they donot have all (have no)eigenstates in common.

return

Appended Material

Entropy of a partition P = (A1,A2, ...,Am) over phase space X :

H(P) = −m∑

µ(Ai ) log µ(Ai )

Dynamical entropy of an automorphism T : X → X with respect to P:

H(T ,P) = limn→∞

nH(P ∨ TP ∨ ... ∨ T n−1P)

The Kolmogorov-Sinai entropy pictures of T is H(T ,Pg ), iff Pg is generating.Otherwise, H(T ,P) < H(T ,Pg ), hence H(T ,Pg ) = supP H(T ,P).

• Pg minimizes correlations among partition cells Ai , so that they are stableunder T and only correlations due to T itself contribute to H(T ,Pg ).(Spurious correlations due to blurring cells are excluded).

• Pg allows the definition of symbolic states whose pre-images for n→ −∞are dispersion-free. (In simple cases: boundaries of Ai are mapped ontoone another.) return

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A phenomenal family is a set of mutually exclusivephenomenal states (with phenomenal properties)that jointly partition (some subset of) the space of mentalstates. Chalmers 2000

Increasingly refined levels of phenomenal families:

• creature consciousness: being conscious / not being consicous

• background consciousness: awake / hypnosis / dreaming / sleep

• sensual consciousness: visual / auditory / tactile / gustatory / olfactory

• visual consciousness: color / form / location / etc.

• color consciousness: red / yellow / green / blue / etc.

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contextual emergence of mental states from neurodynamics

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