Computation, Transport, and the Boundary Fallacy

The "brains are a million times more efficient than AI" claim is an artifact of how you draw the boundary around the system, not a fact about the physics.

The paper makes two moves. First, it shows that the distinction between "computation" and "communication" is not a real partition of physical events — it's a choice of description. Using the same formal criterion that BCOM's Kolmogorov Theory uses to define what counts as physical computation (a representation map that commutes with the system's dynamics, with low complexity and no dependence on the specific trajectory), a wire satisfies the definition: it implements the identity map, admissibly. So does an axon. So does a DRAM read. The same physical event is simultaneously transport (relative to a spatial cut) and computation (relative to an implementation map). You can't sort events into one bucket or the other without first making a choice that isn't given by nature.

Second, the paper shows what is well-posed nearby: Hong and Kung's 1981 result. Fix a computation graph and a memory hierarchy, and there's a provable lower bound on how many words must cross each memory boundary, regardless of scheduling. That's the honest version of "communication costs dominate" — it's a theorem about a specific algorithm running on a specific architecture, not a law of physics. Applied to a long-context transformer, the KV-cache traffic alone accounts for ~89% of the modeled energy per token, with arithmetic at ~4%. But that ratio is a consequence of the chosen geometry (100-layer model, 100k-token context, HBM bandwidth costs), not a universal truth. Change the architecture — recurrent models, in-memory compute, larger caches — and the ratio changes.

The million-fold efficiency gap dissolves under matched accounting. The folklore number comes from dividing a whole inference cluster (~20 MW) by one brain (20 W), which conflates datacenter multiplexing (~100k concurrent streams) with per-stream efficiency. Per stream, a served inference request costs roughly 100 W of accelerator — about ten brains' worth of power, not a million. When you compare per-word energies under matched boundaries, human speech runs 6–8 J/word (whole-brain power divided by speaking rate), while served inference spans 0.2–2 J/word depending on model size and batching. The ordering can reverse depending on which boundary you pick. The paper is careful to note this doesn't establish parity either: a brain simultaneously handles perception, memory, learning, and bodily regulation; a language model does prefill and decode on shared hardware with no persistent state between requests. They don't implement the same service, so the ratio doesn't currently mean anything clean.

Landauer's principle — the thermodynamic minimum energy to erase one bit — survives the critique but is essentially irrelevant. Even if you generously assign a full 32-bit accumulator erasure to every multiply-accumulate in a transformer forward pass, the Landauer floor comes out to ~66 nanojoules per token against ~1.4 joules actually spent: seven orders of magnitude off. The paper also corrects an earlier BCOM working paper (WP0162): predicted information doesn't have to be "paid for" at the Landauer rate, because it can be uncomputed using the model's retained correlations. Only the residual conditional entropy H(X|Y) — the part the model genuinely can't predict — carries a thermodynamic floor.

The paper's practical conclusion: stop reporting joules per word. A token is internal work for a model; a spoken word is an external action for a human. Any honest comparison needs a matched task, matched output quality, matched latency, and separately reported operational, training-amortized, and embodied energy costs.