PSYCH 4320 / COGST 4310 / BioNB 4330

Consciousness and Free Will

Theme V

  Week 10: levels and boundary problems

Week 10: levels and boundary problems

state-dependent and state-independent causal analysis

The cause coefficient describes to what extent a state is sufficient to specify its past causes.

The effect coefficient indicates how necessary a state is to specify its future effects. It is a function of two terms:

A state-independent informational measure of a system’s causal architecture can be obtained by taking the expected value of cause or effect information over all system states, a quantity called effective information (EI).
[EI can be expressed in two ways, via causes and via effects; these are identical, because the system is assumed to be time invariant.]

using IIT to define emergence, via causation

Cause and effect coefficients depend on causal architecture.

  1. The systems consist of two interconnected binary COPY gates with possible states 0 and 1.
  2. A causally perfect system, in which each state has one cause and one effect.
  3. A completely noisy (indeterministic) system.
  4. A completely degenerate (deterministic) system.

spatial causal emergence

Spatial causal emergence (counteracting indeterminism).

  1. The micro level Sm of system S is composed of identical noisy micro mechanisms.
  2. A macro causal level SM and its TPM are defined by the mapping M (shown for AB to α, CD to β is symmetric).
  3. The micro TPM.
  4. SM and its macro mechanisms.
  5. By reducing indeterminism and increasing effectiveness Eff, the macro beats the micro in terms of EI despite the reduced repertoire size (CE = 0.40 bits).

spatial causal emergence

Spatial causal emergence (counteracting degeneracy).

  1. A degenerate Sm with deterministic AND gates.
  2. The deterministic but degenerate micro TPM.
  3. The cycle of AND gates is mapped onto a cycle of COPY gates at the macro level.
  4. The deterministic macro TPM with zero degeneracy. By eliminating degeneracy and achieving perfect effectiveness, the macro beats the micro (CE = 0.57 bits).

temporal causal emergence

What is the "best" time step for describing causality in this system?

  1. Sm is composed of second-order Markov mechanisms A and B: at t0, each mechanism responds based on the inputs at t−2 and t−1, and outputs over t0 and t+1.
  2. Causal analysis over one micro time step gives an incomplete view of the system.
  3. A causal analysis over two micro time steps reveals the second-order Markov mechanisms.
  4. The optimal macro system SM groups two micro time steps into one macro time step for macro elements {α,β}.
  5. Each coarse grained macro mechanism effectively corresponds to a deterministic COPY gate.
  6. The macro one-time step TPM SM has Eff(SM) = 1, and the micro two-time step TPM has Eff(Sm) = 0.34; CE = 0.62 bits.

spatiotemporal causal emergence

Spatiotemporal causal emergence.

  1. A “neuronal” system merging the temporal characteristics of the system in the previous figure with a differentiated spatial structure. Regular and rounded arrows indicate intergroup and intragroup connections, respectively.
  2. Each macro element receives inputs from itself and the other macro element. The macro level beats the micro level, leading to spatiotemporal emergence [CE(S) = 2.92 bits].

regarding causation

A key question: does every event or phenomenon have a unique cause?

"Effectiveness/selectivity can be assessed at multiple spatiotemporal grains, and the particular spatiotemporal grain at which EI reaches a maximum is again an intrinsic property of the system. This in no way precludes an observer from profitably investigating the system’s properties at other macro levels, at the micro level, or at multiple levels at once (e.g., neuroscientists studying the brain at the level of ion channels, individual neurons, local field potentials, or functional magnetic resonance signals). However, causal emergence implies that the macro level with highest EI is the one that is optimal to characterize, predict, and retrodict the behavior of the system—the one that “carves nature at its joints” (26)."

regarding causation

A key question: does every event or phenomenon have a unique cause?

using IIT to define emergence, via causation

"Causal analysis as presented here endorses both supervenience (no extra causal ingredients at the macro level) and causal exclusion [for a given system at a given time, causation occurs at one level only, otherwise causes would be double counted (4)].

However, causal analysis also demonstrates that EI can actually be maximal at a macro level, depending on the system’s architecture. In such cases, causal exclusion turns the reductionist assumption on its head, because to avoid double-counting causes, optimal macro causation must exclude micro causation.

In other words, macro mechanisms can always be decomposed to their constituting micro mechanisms (supervenience); however, if there is emergence, macro causation does not reduce to micro causation, in which case the macro wins causally against the micro and takes its place (supersedence).

Thoughts? Questions?

My opinion: the exclusion principle is difficult to justify. What would be the implications of dropping it? What about integration/irreducibility?