The argument about a runaway intelligence explosion is a claim about equations. An Oxford philosopher just worked them out.
Toby Ord posted a preprint titled 'The Dynamics of Intelligence Explosions' to arXiv on 14 August. It models the feedback loop in which AI systems are used to improve AI systems, and concludes that singular growth — capability rising to infinity within a finite stretch of time — is harder to reach than recent economics-inspired models suggest. Ord identifies a class of growth in between: faster than exponential, yet never hitting that vertical wall. The factor he argues has been overlooked is generation time, the length of one round of the improvement cycle; for singular growth to happen, generation time has to fall towards zero. The paper is a preprint and has not yet been peer reviewed.
Why it mattersBoth camps in the AI argument lean on the same mental picture — a system improving itself faster and faster until nobody can follow — and mostly treat it as intuition. Ord's contribution is to insist it is an equation with parameters, and that one of those parameters is how long each round of improvement actually takes: designing, training, testing, deploying a better model. That is something you can measure in the real world rather than assert. It moves a debate usually conducted in adjectives onto ground where evidence can eventually settle it.
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