Photons = Tokens: The Physics of AI and the Economics of Knowledge

TL;DR

This paper quantifies the physical and economic limits of AI token processing using thermodynamics and information theory, highlighting constraints on AI question capacity and implications for policy and regulation.

Contribution

It introduces a physical and economic framework for understanding AI token costs and limits, applying thermodynamics and information theory to quantify AI's computational and economic boundaries.

Findings

Current US AI energy use could support 225,000 tokens per person per day by 2028.

The token economy is constrained by physical and informational limits, not just technological capacity.

Economic value in AI concentrates at specific points in the value chain, influencing regulation.

Abstract

Debates 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.