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View corpus contextPhysical and economic constraints still leave an enormous unused LLM question budget: at current efficiencies the US could support roughly 225,000 tokens per person per day by 2028—thousands of times current usage. But the paper warns that abundance of computation doesn't solve the harder problem of agency and direction—deciding which questions are worth asking will determine real value.
Photons = Tokens: The Physics of AI and the Economics of Knowledge
Using thermodynamics and information theory, the paper constructs an order-of-magnitude supply-and-demand balance for LLM tokens, concluding physical and economic constraints permit far more token production than current use but that the central scarcity is which questions are worth asking, not raw computational capacity.
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Cumulative provider counts captured on specific dates; providers are never combined.
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View corpus contextDebates about artificial intelligence capabilities and risks are often conducted without quantitative grounding. This paper applies the methodology of MacKay (2009) -- who reframed energy policy as arithmetic -- to the economy of AI computation. We define the token, the elementary unit of large language model input and output, as a physical quantity with measurable thermodynamic cost. Using Landauer's principle, Shannon's channel capacity, and current infrastructure data, we construct a supply-and-demand balance sheet for global token production. We then derive a finite question budget: the number of meaningful queries humanity can direct at AI systems under physical, information-theoretic, and economic constraints. We apply Coase's theory of the firm and the durable-goods monopoly problem to the AI value chain -- from photon to atom to chip to power to token to question -- to identify where economic value concentrates and where regulatory intervention is warranted. We argue that the expansion of the token budget does not resolve a deeper constraint: under structural uncertainty, the decisive variable is not how many questions can be answered but which questions are worth asking -- a problem of agency and direction that computation alone cannot solve. We connect limits of measurement in the token economy to a structural parallel between Goodhart's law and the Heisenberg uncertainty principle, and to Arrow's impossibility result for efficient information pricing. The framework yields order-of-magnitude estimates that discipline policy discussion: at current efficiency, the projected 2028 US AI energy allocation of 326~TWh could support roughly $6.5 \times 10^{17}$ tokens per year, or 225,000 tokens per person per day -- more than three orders of magnitude above estimated mid-2024 utilization.
Summary
Main Finding
The paper frames the token (an LLM subword) as a physical commodity and produces a MacKay-style arithmetic for the global token economy. Using Landauer’s thermodynamic bound, Shannon capacity, and current infrastructure data, it constructs a token supply–demand balance, derives a finite “question budget,” and locates where economic value concentrates in the photon→atom→chip→power→token→question chain. Key quantitative conclusion: at current efficiency and a projected 2028 U.S. AI electricity allocation of 326 TWh, the U.S. capacity would support ≈6.5×10^17 tokens/year, or ≈225,000 tokens per person per day—orders of magnitude above mid‑2024 utilization—while actual energy per token remains ≈5×10^19 times the Landauer limit.
Key Points
- Tokens are physical: generating one requires silicon computation, electricity, and heat dissipation. Computation has a thermodynamic cost.
- Landauer floor: at ~12 bits/token (working estimate), Emin ≈ 3.4×10^−20 J/token.
- Measured inference cost: ~5×10^−4 Wh/token ≈ 1.8 J/token → an efficiency gap ≈5×10^19 between actual practice and the thermodynamic minimum.
- Global mid‑2024 inference level (adopted): ~10^12 tokens/day ≈125 tokens/person/day. Projected U.S. 2028 inference capacity (326 TWh at current efficiency): ≈1.8×10^15 tokens/day → ≈225,000 tokens/person/day.
- Inference is increasingly dominant: inference accounted for ~60–70% of AI electricity in 2024 and is projected to grow.
- Efficiency gains (hardware, quantization, software, model distillation) reduce per‑token cost but, via Jevons paradox / “LLMflation,” tend to multiply total token consumption.
- Physical information bounds matter: Shannon channel capacity limits throughput; Bekenstein/Lloyd bounds limit absolute storage and operation rates.
- Resource & infrastructure constraints can bind: copper and other materials for data centers present multi‑decadal lead times and scaling limits that may restrict buildout.
- Economic structure: applying Coase and durable‑goods monopoly reasoning, value concentrates upward in the stack (control of chips, power, and token provisioning), creating leverage points and regulatory priorities.
- Measurement/pricing limits: a structural parallel is drawn between Goodhart’s law and Heisenberg uncertainty (measurement alters value), and Arrow’s impossibility theorem implies efficient pricing of information is fundamentally problematic. Hence abundance of tokens does not solve problems of agency and direction—knowing which questions are worth asking remains the binding constraint.
Data & Methods
- Conceptual approach: MacKay-style arithmetic / balance sheet for tokens; combine physical limits and infrastructure data to estimate supply and demand.
- Thermodynamics: Landauer’s principle Emin = kB T ln 2; adopt T≈300 K and 12 bits/token → Etoken_Landauer ≈ 3.4×10^−20 J.
- Empirical inference energy: use Epoch AI (2025) range 1×10^−4–2×10^−3 Wh/token; mid‑range 5×10^−4 Wh/token → Etoken_actual ≈1.8 J.
- Information theory: Shannon channel capacity C = B log2(1 + S/N) to bound throughput; Bekenstein bound and Lloyd’s limits to bound absolute information and ops.
- Supply/demand data and assumptions:
- Mid‑2024 global inference estimate used: ~10^12 tokens/day (provider-reported aggregates and industry analyses).
- U.S. total electricity generation ~4,178 TWh/yr (2023); AI electricity in U.S. estimated 53–76 TWh (2024), projected 165–326 TWh (2028) by IEA.
- Assumed US hosts ~50–60% of global AI compute for conservative per‑person lower bound.
- Training vs inference: inference assumed ~60–70% of AI electricity; training is a large up‑front cost but amortized over inference.
- Numeric conversions and balance:
- 326 TWh / (5×10^−4 Wh/token) ≈ 6.5×10^17 tokens/year ≈1.8×10^15 tokens/day.
- Per person capacity (global pop ≈8×10^9): ≈225,000 tokens/person/day.
- Efficiency gap (actual / Landauer) ≈ 1.8 J / 3.4×10^−20 J ≈ 5×10^19.
- Economic and resource analysis:
- Jevons paradox (efficiency → higher demand) discussed with historical and recent LLM cost reductions (termed LLMflation): inference price reductions ~10×/year historically; 1000× decline 2021→2024 reported for fixed benchmark dollar costs.
- Material constraints: copper requirements for hyperscale AI facilities (tens of thousands of tons per facility), long mine lead times, and projected growth in copper demand create potential bottlenecks.
Limitations and explicit assumptions: - Demand estimates are uncertain (selective provider reporting; rapid growth). - The 12 bits/token and 5×10^−4 Wh/token are working estimates; real values vary by model, deployment, and accounting of training vs inference. - The balance sheet mixes global demand with (primarily) U.S. supply assumptions to produce conservative per‑person bounds; true global capacity is higher once non‑U.S. infrastructure is included. - Extrapolations assume no revolutionary change in physics (Landauer floor remains absolute).
Implications for AI Economics
- Capacity is large but finite: physical and informational limits mean tokens and questions are bounded; policy should recognize concrete ceilings rather than treating compute as effectively unlimited.
- Focus governance on direction and agency, not just capacity: the decisive problem under structural uncertainty is which questions are asked (allocation of the question budget), a choice computation alone cannot resolve.
- Regulatory priorities:
- Address externalities: electricity pricing and cross‑subsidies implicitly favor AI buildout; regulators should internalize grid and environmental externalities (e.g., time‑of‑use pricing, capacity charges, carbon pricing).
- Resource policy: plan for material bottlenecks (copper, semiconductors) via strategic mining investment, recycling, and substitution incentives.
- Market structure and control points: value concentrates at chip, power, and token provisioning layers—these are logical leverage points for antitrust, interoperability, and access regulation.
- Pricing and measurement limits: Goodhart/Heisenberg parallel and Arrow’s theorem imply markets and metrics will misalign incentives when tokens or proxy metrics become targets; designers of incentives and benchmarks must account for measurement‑distortion effects.
- Energy policy and efficiency: efficiency improvements will lower per‑token cost but likely increase total consumption (Jevons), so energy planning must accommodate faster growth in AI electricity demand.
- Research and investment signals:
- Continued hardware and algorithmic efficiency investments remain high‑value (large thermodynamic headroom).
- Investment in governance, information valuation mechanisms, and decision processes (to choose which questions to ask) is as important as investment in pure compute expansion.
- Practical takeaway for economists and policymakers: quantify token budgets using physics+infrastructure arithmetic to ground debates; then design policies addressing externalities, resource bottlenecks, and the allocation of limited question capacity rather than assuming infinite, costless information.
Assessment
Paper Typetheoretical
Evidence Strengthn/a — The paper is a theoretical, order-of-magnitude accounting exercise using physical laws, information theory, and economic argumentation rather than empirical causal estimation; it does not attempt causal identification of real-world effects.
Methods Rigormedium — The approach is logically grounded (Landauer's principle, Shannon capacity, Coasean firm theory) and provides disciplined back-of-envelope estimates, but relies on multiple strong assumptions and projections (e.g., efficiency parameters, 2028 energy allocation, mapping of tokens to thermodynamic cost) that introduce substantial uncertainty and limit empirical validation.
SampleNo human-subject sample; uses physical constants and information-theoretic formulas, current infrastructure and efficiency data, projections (e.g., projected 2028 US AI energy allocation of 326 TWh), and mid-2024 utilization estimates to construct a global token supply-and-demand balance and per-capita token budgets.
Themesproductivity governance innovation human_ai_collab
GeneralizabilityRelies on assumed current and projected energy and hardware efficiency parameters that may change with technology improvements or architectural shifts, Uses a US-centric energy projection for 2028, so numerical results may not generalize to other countries or global aggregates without adjustment, Definition of the 'token' and mapping to thermodynamic cost is LLM-specific and may not apply to other AI architectures or future modalities, Abstracts away market dynamics, behavioral responses, and institutional differences that affect allocation of computational resources, Aggregate, order-of-magnitude estimates mask distributional heterogeneity across firms, sectors, and users
Claims (9)
| Claim | Direction | Outcome | Confidence & Evidence | Details |
|---|---|---|---|---|
| We define the token, the elementary unit of large language model input and output, as a physical quantity with measurable thermodynamic cost. Other | positive | thermodynamic cost per token |
Reading fidelity
high
Study strength
medium
|
not reported
|
| Using Landauer's principle, Shannon's channel capacity, and current infrastructure data, we construct a supply-and-demand balance sheet for global token production. Market Structure | positive | global token supply and demand (production capacity) |
Reading fidelity
high
Study strength
medium
|
not reported
|
| We derive a finite question budget: the number of meaningful queries humanity can direct at AI systems under physical, information-theoretic, and economic constraints. Decision Quality | mixed | finite question budget (meaningful queries available) |
Reading fidelity
high
Study strength
medium
|
not reported
|
| At current efficiency, the projected 2028 US AI energy allocation of 326 TWh could support roughly $6.5 \times 10^{17}$ tokens per year. Other | positive | token production capacity (tokens/year) given 326 TWh |
Reading fidelity
high
Study strength
medium
|
roughly $6.5 \times 10^{17}$ tokens per year
|
| The 326 TWh capacity corresponds to about 225,000 tokens per person per day. Other | positive | tokens per person per day |
Reading fidelity
high
Study strength
medium
|
225,000 tokens per person per day
|
| This projected capacity is more than three orders of magnitude above estimated mid-2024 utilization. Adoption Rate | positive | gap between projected capacity and mid-2024 utilization |
Reading fidelity
high
Study strength
medium
|
more than three orders of magnitude above estimated mid-2024 utilization
|
| Applying Coase's theory of the firm and the durable-goods monopoly problem to the AI value chain (photon → atom → chip → power → token → question) identifies where economic value concentrates and where regulatory intervention is warranted. Governance And Regulation | positive | locations of concentrated economic value and recommended sites for regulatory intervention in the value chain |
Reading fidelity
high
Study strength
speculative
|
not reported
|
| The expansion of the token budget does not resolve a deeper constraint: under structural uncertainty, the decisive variable is not how many questions can be answered but which questions are worth asking — a problem of agency and direction that computation alone cannot solve. Decision Quality | negative | ability of increased computational capacity to address value-direction and question-selection under uncertainty |
Reading fidelity
high
Study strength
speculative
|
not reported
|
| Limits of measurement in the token economy resemble a structural parallel between Goodhart's law and the Heisenberg uncertainty principle, and relate to Arrow's impossibility result for efficient information pricing. Governance And Regulation | mixed | limits of measurement and pricing of information (token economy) |
Reading fidelity
high
Study strength
speculative
|
not reported
|