An Rodriguez and Anes Palma
July 2025
Living systems can be described as self-sustaining cause-effect loops (autopoiesis, “self-generation”). When such a loop forms an internal imprint of its own activity and later modifies its dynamics in response to that imprint, a minimal form of self-awareness appears. We formalise this idea, relate it to autopoiesis, Markov blankets, integrated information, and self-model theories, and sketch an empirical program for testing it. The framework defines consciousness, qualia, free-will, and self-awareness in purely causal terms that are, in principle, measurable.
Autonomous agents maintain themselves through closed causal cycles—a property called autopoiesis (Greek auto “self” + poiein “to make”). Some agents also construct internal models and let those models guide future states. We present a unified cause-effect account that quantifies the transition from self-maintenance to self-awareness and situates qualia and free-will within the same loop.
Autopoiesis (Maturana and Varela 1972) portrays life as a network that continually recreates itself. Strange-loop and self-model theories (Hofstadter 2007; Metzinger 2003) claim consciousness arises when feedback circuits represent the system itself. The free-energy principle with its Markov-blanket boundary (Friston 2013) shows how such networks hold internal and external causes apart while minimising prediction error. Integrated Information Theory, IIT (Tononi et al. 2014), attaches the scalar \(\Phi\) to measure irreducible internal causation. We integrate these strands into a single causal formalism.
Let \(x(t) \in \mathbb{R}^n\) be the internal state.
\[ x(t + \Delta t) = F\bigl(x(t), u(t)\bigr) + \eta(t) \]
where \(u(t)\) is exogenous input and \(\eta(t)\) is process noise.
Define the imprint:
\[ m(t) = f\bigl(x(t - \tau)\bigr) \]
where the lag \(\tau\) can range from milliseconds to years. The imprint is generated by the system itself and stored inside the causal loop.
The evolution of the system is described by the conditional density:
\[ P\bigl[x(t + \Delta t) = x' \mid x(t) = x,\; m(t) = m\bigr] \]
This is the probability that the state will take the value \(x'\) after a short interval \(\Delta t\), given present state \(x\) and imprint \(m\). We assume \(P\) is differentiable in \(m\). In a Gaussian-noise model, \(P\) is a Gaussian centered on \(F\bigl(x(t), u(t)\bigr)\).
Self-awareness is present if some measurable set \(A \subseteq \mathbb{R}^n\) satisfies:
\[ \frac{\partial}{\partial m} \int_A P\bigl[x(t + \Delta t) = x' \mid x(t), m\bigr]\,\mathrm{d}x' \neq 0 \quad (1) \]
and this dependence vanishes when \(m\) is replaced by an uncorrelated surrogate. Equation (1) formalises recognising itself.
\[ I(m; x') = I\bigl(m(t); x(t + \Delta t)\bigr) \]
measures how much the imprint reduces uncertainty about the future state.
Let \(X_{\text{past}}\) and \(X_{\text{fut}}\) be two copies of the system separated by \(\Delta t\):
\[ \Phi = \min_{\text{bipartitions}} \Bigl[I\bigl(X_{\text{past}}; X_{\text{fut}}\bigr) - I_{\text{partitioned}}\Bigr] \]
\(\Phi\) captures the irreducible causal power of the whole.
Qualia are recognised imprints tagged as originating outside the core loop. The experience of red, for instance, arises when the imprint produced by 700 nm light is later recognised as external to the self. Qualia can be removed (e.g. by sensory loss) while the primary autopoietic loop continues to run.
Free‑will is the capacity of internal imprints to bias future actions beyond what external inputs dictate. It has a measurable component:
\[ W = I\bigl(m(t); a(t + \Delta t) \mid u(t)\bigr) \]
but also encompasses higher‑order selection among action plans when multiple internally generated imprints compete.
Self‑awareness emerges when both conditions hold:
Free‑will is present when \(W > 0\) and at least two actionable alternatives exist whose probabilities shift as a function of \(m(t)\).
Autopoiesis supplies the loop; the Markov blanket supplies the boundary; free‑energy minimisation explains why storing \(m(t)\) reduces surprise; IIT supplies \(\Phi\) as a cross‑architecture yardstick. Our additions of \(I\), \(W\), and criterion (1) unify these elements.
The framework employs only loop, imprint, and reaction, yet accommodates consciousness, qualia, and free‑will in measurable terms. Modern neural recording, causal perturbation, and deep reinforcement learning sandboxes can estimate \(I\), \(\Phi\), and \(W\).
A deeper mystery remains: why a cause brings about an effect at all. The framework presupposes causal regularities but does not explain their ultimate origin; addressing that question may require new physics or metaphysical insight beyond present scope.
Self‑awareness, qualia, and free‑will emerge as quantifiable phases in a cause‑effect loop. Life is self‑causal; awareness is self‑modelled causality.
[1] H. Maturana and F. Varela, Autopoiesis and Cognition,
1972.
[2] K. Friston, Life as we know it, Journal of the Royal
Society Interface, 2013.
[3] D. Hofstadter, I Am a Strange Loop, 2007.
[4] T. Metzinger, Being No One, 2003.
[5] G. Tononi et al., Integrated information theory 3.0,
PLoS Computational Biology, 2014.