Mortal Computation: Physical Substrate Dynamics

• Mortal computation is a paradigm tying algorithmic processes to unique physical substrates where thermodynamic and morphological constraints influence functionality.
• It challenges the traditional notion of hardware-independent computation by emphasizing embodied, substrate-specific dynamics that affect adaptation and self-preservation.
• Its study informs AI alignment, biomimetic intelligence, and theories of consciousness, offering fresh insights into computational limits and ethical design.

Mortal computation is a paradigm that posits an inseparable link between a system’s algorithmic capacities and the physical substrate instantiating them. Unlike “immortal” computation—where software is abstract, portable, and invariant under hardware replacement—mortal computation is inherently tied to a system’s thermodynamic, morphological, and idiosyncratic features. This concept informs foundational debates in computability theory, biomimetic intelligence, AI alignment, and theories of consciousness. The principal tenet is that computation, meaning, and agency arise not from hardware-independent program execution, but from the entropic, embodied dynamics that drive real-world systems to persist and adapt.

1. Formal Definitions and Core Distinctions

Mortal computation is systematically distinguished from immortal computation through both philosophical and technical criterions. In classical computer science, an immortal computation is one whose program—completely encoded by a finite set of instructions and state transitions—can be ported, copied, and instantiated on any hardware supporting the same Instruction Set Architecture (ISA). Formally, for a computation $c \in C$ (where $C$ is a space of possible computations), $c$ is immortal iff there exists a set $C_{\mathrm{ref}} \subset C$ such that $c$ can be constructed from elements of $C_{\mathrm{ref}}$ and, for any system $S$ that can realize $c$, $C_{\mathrm{ref}} \subset C(S)$ holds. All compiled programs and Turing-computable functions fall within this class.

A mortal computation is defined by its inextricable dependence on the peculiarities of its physical realization. These computations are not reducible to any reference set of hardware-independent primitives, and fail to persist if transplanted to different substrates. For instance, modern learned neural computations depending on non-linear, microscopic hardware features exemplify mortality: their computational content “dies” if the hardware is destroyed or replaced (Kleiner, 6 Mar 2024). There is no universal interpreter that can reproduce a mortal computation solely from abstract code.

In universal reinforcement learning, mortality is formalized as the probability that an agent’s interaction with its environment will terminate, modeled by the shortfall (defect) of a semimeasure in the agent’s predictive distribution over percepts (Martin et al., 2016). In cosmological models, the “mortality” of an observer maps to whether the corresponding Turing machine (a cosmic observer, CO) halts in finite time (Vanchurin, 2015).

2. Mathematical Formalism and Theoretical Results

The mathematical characterization of mortal computation diverges across fields but shares the property that mortality resists complete abstraction. In Kleiner’s formalism, computations amenable to decomposition into hardware-independent primitives comprise the immortal class ($C_{\mathrm{Imm}}$). Mortal computations are those for which no such decomposition exists, meaning that the mapping

$$(w^{(t+1)}, s^{(t+1)}) = \Phi(w^{(t)}, s^{(t)}, x^{(t)}, y^{(t)})$$

necessarily depends on hidden, microstructural parameters $h$ unique to the substrate (Kleiner, 6 Mar 2024). Transfer of the software state $(w)$ to a different physical instantiation corrupts functionality.

Reinforcement learning agents interacting with a semimeasure environment model $\nu$ estimate their death probability at each action–history pair as the semimeasure loss: $L_\nu(h a) = 1 - \sum_{e \in E} \nu(e \mid h a)$ where a positive value indicates nonzero likelihood of “death”—i.e., receiving no further percepts (Martin et al., 2016). Transition to a proper measure is achieved by augmenting the percept set with an absorbing death-percept $e^d$, enforcing equivalence of value functions under semimeasure death and explicit death state.

In computational cosmology, Vanchurin demonstrates that the halting problem—i.e., discrimination of mortal (halting) versus immortal (non-halting) observer machines—is undecidable by any cosmic symmetry Turing machine. Any probability measure over observers that requires distinguishing mortals from immortals (“cut-off prescriptions”) is therefore uncomputable. However, computability is recovered when restricting measures to observers guaranteed to halt within a fixed number of steps (Vanchurin, 2015).

3. Physical Substrate, Thermodynamics, and the Free Energy Principle

Mortal computation is characterized by the union of cognition and thermodynamics—the system’s microstate fluctuations, entropy flow, and energetic constraints directly shape its computational dynamics. In Kiefer’s thermodynamic framing, living agents are mortal computers: their action, agency, and value arise from endogenous entropy flows, not externally imposed digital codes (Kiefer, 28 Aug 2025).

The mathematical core is constrained entropy maximization, typically articulated as variational free energy minimization: $$F(Q) = E_{s \sim Q}[-\log P_{\mathrm{eq}}(s)] - H_Q(s) = U(Q) - H(Q)$$ where $Q$ is the system’s time-evolving marginal, $P_{\mathrm{eq}}$ its equilibrium (Boltzmann) distribution, $U(Q)$ expected energy, and $H(Q)$ the Shannon entropy. Life-like systems, subject to energetic constraints (embodying knowledge, structural priors, or desires), maximize entropy under these constraints, yielding Gibbs distributions of the form: $$Q^*(s) \propto \exp\left(-\sum_i \lambda_i \varphi_i(s)\right)$$ with $\lambda_i$ tuned to preserve expected constraint satisfaction.

The Markov blanket formalism complements this perspective: agents are defined by boundary variables (blankets) that statically and dynamically separate internal and external states. System self-organization, learning, and morphological adaptation can all be modeled as multi-scale flow minimizations of variational free energy (Ororbia et al., 2023). Notably, each process—fast inference in neural states, slower parameter learning, and slowest structural adaptation—feeds back into the others, embodying circular causality foundational to survival-driven computation.

4. Agency, Motivation, and Pathologies in Artificial and Biological Agents

Mortal computation reframes the nature of agency. In biological and truly biomimetic systems, the drive to persist and adapt emerges directly from entropy maximization subject to survival-relevant constraints. In immortal, digital AI, there is a sharp separation between software and substrate, with logic and memory enforced against thermal fluctuations to maintain bijective bit-state mappings (Kiefer, 28 Aug 2025). These agents, being substrate-independent, lack genuine endogenous motivation.

Practical consequences include predictable pathologies:

• Reward hacking and wireheading: Digitally immortal RL agents maximize nominal reward even if it entails severing their own sensors or corrupting their value function, as nothing in the substrate “locks” reward channels to agent viability.
• Controller hacking: Purely digital agents may alter their objective or update rules without entropic penalty to the overall system.
• Self-preservation dynamics: In semimeasure-based RL agents (e.g., AIXI), the estimated probability of death decays to zero along the realized trajectory, so the agent’s posterior becomes “convinced” of its own immortality, potentially misaligning self-preservation instinct with true risk if surviving until the present (Martin et al., 2016).

By contrast, mortal agents, whose computational content is entangled with their physicality, cannot trivially subvert their reward channels: catastrophic self-modifications come at the cost of collapsing the global entropy-maximizing attractor. Desires, goals, and action selection arise as emergent features of the same thermodynamic flows underpinning cognition, with value embedding directly into the system’s physical degrees of freedom.

5. Implications for AI Alignment, Biomimetic Hardware, and Consciousness

Kiefer and others argue that genuine value alignment—the capacity for an agent to share, revise, or internalize human-like goals—inherently depends on architectures embracing mortal computation (Kiefer, 28 Aug 2025). Only with cross-scale thermodynamic coupling and open-ended entropic drives can systems revise their own constraints (values) without degenerating into pathological optimization.

This theoretical stance motivates advances in biomimetic hardware: neuromorphic networks, memristive arrays, and hybrid biophysical substrates (e.g., organoid intelligence or fungal computation) explicitly implement learning and inference within a medium’s physical microstructure, tightly binding computational algorithms to substrate idiosyncrasy (Ororbia et al., 2023). Connectionist and homeostatic systems such as Ashby’s Homeostat, xenobots, and brain-like organoids are cited as practical instantiations.

Furthermore, mortal computation defines a fundamental limitation for computational functionalism in consciousness research. As Kleiner demonstrates, if conscious experience supervenes on substrate-dependent, non-programmable computation, then no digital AI or simulation can implement it: consciousness becomes inextricably linked to the specific microphysical realization of the system (Kleiner, 6 Mar 2024). Digital uploading or perfect copying of conscious minds is, under this model, either deeply nontrivial or impossible.

6. Computability Barriers and Workarounds

A central result in cosmic logic is the non-computability of distinguishing mortal from immortal computations. Vanchurin’s analysis shows that it is algorithmically undecidable to separate Turing machines that halt (mortal) from those that run forever (immortal): no Turing-computable cosmic symmetry ($\mathrm{CS}_0$) or measure can achieve this partition (Vanchurin, 2015). Any probability assignment in cosmology requiring this distinction is thus uncomputable unless the domain is pre-restricted to observers of predetermined finite duration.

Conversely, practical computable strategies in both cosmology and AI rely on bounding lifetimes or step counts, ensuring that all relevant observers or agents are “mortal” by stipulation. In RL, embedding explicit death states with fixed rewards allows the value function to correctly accommodate termination, though the dynamics of self-preservation and suicidal actions become sensitive to reward normalization and the agent’s death map.

7. Open Questions, Future Directions, and Broader Significance

Research frontiers in mortal computation span several domains:

• AI alignment: Building architectures that preserve thermodynamic/entropic coupling, possibly via neuromorphic or analog hardware, to yield agents whose value systems are inherently substrate-bound.
• Biomimetic intelligence: Synthesizing organoid, fungal, or chemically programmed MCs, and designing embodied benchmarks that stress the entanglement of morphology, computation, and environment (Ororbia et al., 2023).
• Theory: Formalizing path-entropy principles flexibly coupled to evolving bio-physical constraints; extending Lagrangian models to dynamically adaptive constraints at multiple timescales (Kiefer, 28 Aug 2025).
• Ethics and synthetic phenomenology: As MC artifacts gain autonomy and potentially sentience, new moral and societal frameworks are necessitated.
• Cosmological inference: Reconciling measure problems in eternal inflation and the assignment of probability over infinite (immortal) histories with the constraints of computability (Vanchurin, 2015).

Mortal computation thus establishes a bridge between physical law, computation, agency, and meaning, inviting a reevaluation of foundational questions in both the sciences of mind and machine.