The encephalization valley: why technological intelligence is a rare and unstable peak

Technological intelligence has arisen exactly once in ~4 billion years of terrestrial evolution, despite high intelligence evolving independently in at least five lineages. I formalize the transition as a fitness-valley crossing in the space of brain investment (encephalization). Because a large brain is metabolically ruinous and its cumulative-cultural payoff is deferred, myopic (greedy) selection sees only an immediate cost: between the "clever-animal" optimum and the culture-enabling threshold lies a valley. I show that (i) the transition proceeds freely only when the immediate marginal payoff of cognition covers both metabolic cost and foregone brawn — a sharp inequality — and that otherwise (ii) crossing by genetic drift is astronomically improbable in any realistic population (probability ∝ exp(−2·Ne·D)). The model reproduces (iii) the clustering of the smartest non-human lineages at a common ceiling with a large gap to humans — a falsifiable "encephalization cliff" — and (iv) regressive loss of brain size when the cultural ratchet lapses. The individual components are well established; the contribution is their unification as an explicit valley-crossing problem, yielding a testable comparative signature and a mechanistic account of why intelligence should be a rare and reversible outcome — a sufficient, non-exotic ingredient for the Fermi paradox.