Precomputed result
A three-unit feedforward chain has φs = 0
| Substrate | Three binary units in a feedforward chain A → B → C. A has no inputs and is maximally noisy (P(ON) = 1/2 regardless of the past); B copies A; C copies B. |
| State | (0, 0, 0) — all units OFF |
| φs | 0.0 |
| Minimum partition | The substrate is not strongly connected, so φs = 0 by construction: a directional partition cutting in the feedback direction severs no causal connections and makes no difference. PyPhi reports the null cut over (A, B, C), zero connections severed. |
| Formalism | iit-4.0-2026 |
| PyPhi | 2.1.dev1610+g0581dae8c.d20260807 |
| Script | feedforward-3node.py |
The result is structural, not numerical: integrated information is defined so that φs = 0 whenever the system is not strongly connected in the graph-theoretic sense, because there is then necessarily a system partition that loses no information — cutting the connections that run in the feedback direction, of which a feedforward system has none. No choice of units, state, or noise changes this; the chain above is the smallest non-trivial witness.
Because φs = 0, the substrate does not exist as one whole for itself: it supports no cause–effect structure and cannot be conscious, whatever function it computes. This is the feedforward half of the dissociation that the unfolding argument turns on (see the ledger).
To reproduce, run the script with any install of PyPhi 2.0+:
uv run python canon/feedforward-3node.py
Sources
- Albantakis et al. (2023). Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms. PLOS Computational Biology. https://doi.org/10.1371/journal.pcbi.1011465 — "Integration: Determining the irreducibility of a candidate system" (iit:ref/albantakis-2023b)