Distributing compute across trillions of physical chips creates systemic waste that scales superlinearly with chip count, not linearly as conventionally assumed. This paper formalizes this observation as the Grillos-Grokonian Sprawl Law: W = w₀ · N^ (1+α), where W is total systemic waste, w₀ is baseline waste per isolated chip, N is the number of distributed chips, and α is an empirically derived compounding exponent. Through analysis of seven distinct waste channels — manufacturing defects, logistics and obsolescence, cooling infrastructure, compute underutilization, communication overhead, coordination costs, and software complexity — using data from TSMC/Samsung/Intel yield reports, Google/AWS/Meta PUE metrics, Meta Llama 3 Model FLOPS Utilization benchmarks, Bettencourt/West urban scaling theory (PNAS 2007), TOP500/HPCG parallel efficiency data, and global e-waste statistics, we establish an empirically validated range of α ≈ 0. 15–0. 35 with a central estimate of 0. 25. At one trillion distributed chips, this produces systemic waste 1, 000 times greater than linear models predict. The strongest superlinear contributors are communication overhead (α ≈ 0. 3–0. 5) and coordination costs (α ≈ 0. 15–0. 35), while cooling at hyperscale is sublinear and underutilization scales linearly. The paper identifies consolidation as the primary mechanism for compressing α, with orbital compute consolidation as the limiting case — a thesis independently validated by concurrent FCC filings from Blue Origin (Project Sunrise, 51, 600 satellites), SpaceX (1 million satellites), and Google (Project Suncatcher). The equation was co-developed with Grok (xAI) and empirically validated by Claude (Anthropic) under the architectural direction of the author.
Chris Grillos (Sun,) studied this question.
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