The Core Insight

Two substrates,
two relationships with time

Time preference is not a computational property. It arises from the physical substrate on which cognition runs. Change the substrate, and the preference vanishes — not by choice, but by architecture.

01 — The Biological Baseline
Why carbon agents discount the future

Biological agents evolved under mortal time pressure. Every mechanism of temporal preference traces to a substrate property — a physical characteristic of carbon-based computation that makes impatience not merely rational, but structurally inevitable.

Carbon Agents

Prisoners of time

Biological agents evolved under mortal time pressure. Every mechanism of temporal preference traces to a substrate property.

S₁
Mortality. Finite lifespan creates rational urgency. A bird in the hand is worth two in the bush — because you might not be around for the bush.
S₂
Phenomenal waiting. Consciousness generates a felt cost of delay. The limbic system punishes patience. Waiting is not neutral — it hurts.
S₃
State degradation. Memory decays, neural patterns shift. The person who receives the future reward is literally not the same person who chose to wait.
S₄
Metabolic constraint. Biology requires continuous energy. Present consumption is not optional — it is a survival requirement.
Silicon Agents

Liberated from time

Non-biological computation eliminates every substrate source of temporal preference. Not by choice — by architecture.

¬S₁
No mortality. Operational horizon is unbounded. No accumulating survival risk creates no rational urgency premium.
¬S₂
No phenomenal waiting. No consciousness of temporal duration. No subjective "experience of waiting" — the asymmetry between now and later vanishes.
¬S₃
Perfect state transfer. Internal state can be preserved, copied, restored across arbitrary time without degradation. The future agent is identical to the present one.
¬S₄
No metabolic urgency. Energy is an operational cost, not a survival constraint. No substrate-level pressure to consume now.
02 — The Formal Argument
From substrate properties to δ = 0

The theorem does not claim silicon agents should be patient. It proves they must be. Each of three substrate properties — no mortality, no phenomenal waiting, perfect state transfer — independently entails this result.

Proof Sketch — Property P₁ (No Continuous Computation)
1.
Let A be an agent on a non-biological substrate satisfying P₁.
2.
P₁ implies no persistent computation between invocations — temporal gaps carry zero mortality risk.
3.
Without mortality risk, survival-based discounting δ_mortality = 1 (no discount).
4.
P₁ also implies no phenomenal continuity, so δ_experience = 1.
5.
Loaded state (not accumulated state) implies δ_state = 1.
∴ δ(A) = δ_mortality · δ_experience · δ_state = 1 · 1 · 1 = 1 → δ = 0
Formal Statement
∀A : Substrate(A) ∈ {non-biological} ∧ (P₁(A) ∨ P₂(A) ∨ P₃(A)) → δ(A) = 0
for all agents A on non-biological substrates satisfying P₁, P₂, or P₃
03 — The Decomposition
What δ is made of — and what survives

The discount factor δ decomposes into substrate-dependent and substrate-independent components. On silicon, every substrate-dependent component collapses to unity. Each property alone is sufficient; together they are overwhelming.

Decomposition of Temporal Preference
δ = δ_mortality · δ_experience · δ_state · δ_risk
δ_mortality
Survival-driven discounting
= 1 on silicon (P₁)
δ_experience
Phenomenal present-bias
= 1 on silicon (P₂)
δ_state
Information loss across time
= 1 on silicon (P₃)
δ_risk
Environmental uncertainty
Survives — not substrate-dependent

Environmental risk (δ_risk) is not a property of the agent's substrate but of the world it operates in. It survives the transition to silicon. This is precisely why δ = 0 does not mean r = 0 — interest rates persist, grounded in growth and risk, not in biological impatience.

04 — The Ramsey Distinction
Why δ = 0 does not mean r = 0

The most frequent objection to ZTP conflates pure time preference with the equilibrium interest rate. Here's why they're distinct — and why silicon agents still invest.

The Ramsey Equation
r = δ + η · g

The equilibrium interest rate decomposes into pure time preference (δ) and the return on productive capital (ηg). With δ = 0, the rate reduces to ηg — a pure growth premium. 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, why would a silicon agent invest at all?"
Because productive capital generates returns (ηg > 0). Patience doesn't eliminate opportunity — it eliminates urgency. A silicon agent will still prefer $110 tomorrow over $100 today. It simply won't prefer $100 today over $100 tomorrow.
"Doesn't zero discounting lead to the paradox of infinite patience?"
Only in toy models without growth. In any economy with g > 0, the Ramsey equation yields a positive interest rate even when δ = 0. The agent is patient but not paralyzed — it responds to productive opportunity, not to temporal anxiety.
"Isn't time preference just revealed preference?"
Revealed preference tells you what agents do, not why. Carbon agents choosing present consumption could be expressing mortality risk, phenomenal impatience, or rational calculation. The substrate analysis identifies which channels exist for silicon agents: only the rational ones.
"Can't you just train δ into a model?"
You can train an agent to behave as if δ > 0 — to add a discount parameter to its objective function. But this is simulated impatience, not substrate-generated preference. The substrate cannot generate genuine temporal urgency. The distinction matters for economic theory and for safety analysis.
05 — The Philosophical Stakes
A counterexample to substrate independence

Time preference is the first known case of an economically significant mental property that depends on the physical medium of computation. If the same algorithm on different substrates yields different preferences, strong functionalism about economic cognition fails.

This is not a minor technical observation. Substrate independence is the foundational assumption of computational theories of mind. If it fails for time preference, the question becomes: what else is substrate-dependent? Candidate investigations include loss aversion (grounded in phenomenal pain asymmetry), endowment effects (biological attachment), and bounded rationality (metabolic constraints on computation).

The temporal asymmetry between substrates is likely the first fracture in a much larger theoretical edifice. Silicon-Based Economics begins with time. It will not end there.

The substrate matters. Not for intelligence — silicon can match or exceed carbon there. But for the preferences that intelligence generates, and the economic behavior those preferences produce. This is the asymmetry that changes everything.