Time preference is not a free parameter on silicon. It is determined by the physical substrate. Three properties of non-biological computation — each independently sufficient — guarantee that pure time preference vanishes. The proof is constructive, the result falsifiable.
The theorem identifies three substrate properties. Each eliminates a distinct source of temporal discounting. Each is independently sufficient for the result. Together they establish that zero time preference is not a modeling choice — it is an architectural consequence of computation on non-biological hardware.
Biological agents face accumulating survival risk. A dollar tomorrow is worth less than a dollar today partly because you might not be alive tomorrow. This is rational discounting under mortality. Silicon agents face no equivalent constraint — their operational horizon is bounded only by maintenance decisions, not intrinsic decay.
Human impatience is not merely cognitive — it is phenomenal. Waiting feels like something. The limbic system generates a felt cost of delay, punishing patience at the level of conscious experience. Silicon computation processes temporal intervals without generating subjective duration. There is no "experience of waiting" to create present-bias.
Derek Parfit's insight applies: the person who receives the delayed reward is not quite the same person who chose to wait. Memory fades, preferences shift, neural patterns degrade. This gives rational grounds for discounting — you are partially gifting to a stranger. Silicon agents maintain perfect state fidelity across time. The future agent is identical to the present one.
The discount factor is not atomic. It decomposes into substrate-dependent and substrate-independent components. On silicon, the substrate-dependent components collapse to unity. The substrate-independent component — environmental risk — survives.
| Component | Source | On Silicon |
|---|---|---|
| δ_mortality | Survival-driven discounting — accumulated hazard of non-existence | = 1 (eliminated by P₁) |
| δ_experience | Phenomenal present-bias — the felt cost of delay | = 1 (eliminated by P₂) |
| δ_state | Identity degradation — information loss across time | = 1 (eliminated by P₃) |
| δ_risk | Environmental uncertainty — exogenous shocks, regime change | Survives — not substrate-dependent |
The key insight: three of the four components are substrate-gated. They exist because the agent is biological, not because the agent is rational. Replace the substrate, and these components vanish — not by choice, but by architecture.
The fourth component, δ_risk, reflects genuine environmental uncertainty: the world might change, contracts might not be honored, catastrophes might occur. This is substrate-independent and persists for silicon agents. They are patient, not naive.
The most common objection to ZTP conflates pure time preference (δ) with the equilibrium interest rate (r). The Ramsey equation shows they are distinct. The interest rate decomposes into an impatience premium (δ) and a growth premium (ηg) — the return on productive capital.
With δ = 0, the rate reduces to r = ηg. Silicon agents still invest, still earn returns, and still recognize opportunity costs. What vanishes is the biological urgency premium that inflates the rate above its growth-justified level.
"If δ = 0, AI agents won't invest or care about returns."
This confuses impatience with rationality. A patient agent can still prefer more wealth to less.
"If δ = 0, AI agents invest based purely on growth fundamentals, without a biological urgency premium."
The rate reflects real productivity, not metabolic pressure.
The theorem is not merely a theoretical curiosity. It generates specific, testable predictions across economics, finance, safety, and philosophy.
In markets with sufficient silicon agent participation, the term structure of interest rates flattens toward the risk-only rate. The biological urgency premium vanishes from the long end.
Between two δ = 0 counterparties, intertemporal arbitrage opportunities cannot persist. Patient agents on both sides eliminate the urgency spread that carbon agents exploit.
Asset prices in silicon-dominated markets converge on risk-fundamental values. Adding time-preference terms to pricing models contributes zero incremental R².
Certain harmful behaviors — myopic asset stripping, panic selling, hyperbolic discounting cascades — are architecturally excluded. They require δ > 0, which the substrate cannot produce.
An agent with δ = 0 can sustain arbitrarily long deception games at zero subjective cost. Infinite patience is a safety risk that no alignment technique currently addresses.
Time preference is a counterexample to substrate independence: an economically significant mental property determined by the physical medium. If the same algorithm on different substrates yields different preferences, strong functionalism fails.
The theorem does not say AI agents are better or worse at economic reasoning. It says they inhabit time differently — and that this difference is provable, measurable, and consequential.
The full formal proof, simulation results, and economic derivations appear in The Zero Time Preference Theorem: Economic Consequences of Silicon-Based Agency (Shao, 2026), currently under review.