Integrated Information (Φ): A Mind-Body Network Simulator

Coupling Between the Two Minds

Bridge strength (integration) 30%

Within-module strength 100%

Noise (temperature) 0.50

Update speed 4 / s

Integration (live, last 300 ticks)

Φ — integrated info

0.00 bit

H(whole)

0.00 bit

Mean activity

How it works

Six binary units split into two modules of three ("left mind", "right mind"). Every tick, each unit's next state is drawn from the activity of its neighbours:

a_i = w_in · (Σ own-module neighbours)/2
    + w_bridge · (Σ other-module neighbours)/3
θ   = (w_in + w_bridge) / 2
P(s_i → 1) = σ( (a_i − θ) / T )

That is a stochastic Boolean network — the same kind of coarse model used for cortical population dynamics. Φ is the network's integrated information, computed the way Integrated Information Theory (IIT, Giulio Tononi) defines it: over a sliding window of recent states it finds every way to split the 6 units into two groups A and B, and takes the minimum mutual information across all of them —

Φ = min over partitions {A,B} of
      H(A) + H(B) − H(A∪B)   [Shannon entropy, bits]

Bridge strength → 0: the two halves become statistically independent. The minimising partition is exactly the two modules, and Φ collapses toward 0 — informationally the system is two separate processes, not one.
Bridge strength → high: the modules co-vary, no split can be made without losing shared information, and Φ rises — the whole carries something the parts alone don't.
Noise (temperature): high noise decorrelates every unit regardless of wiring, driving Φ back down — coupling alone isn't enough, the coupling has to actually show up in behaviour.

This is IIT's proposed answer to the mind–body problem: it identifies subjective, unified experience with a system's irreducible integrated information rather than positing a separate mental substance — a physicalist stance in the philosophy of mind, opposed to dualism, and one live enough that the same Φ-style "perturbational complexity index" is used clinically to test for residual consciousness in anaesthetised or vegetative-state patients.

Within-module link Bridge link Active unit

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