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We endorse and expand upon Susan Schneider's critique of the linear model of AI progress and introduce two novel concepts: "familiar intelligence" and "strange intelligence". AI intelligence is likely to be strange intelligence, defying familiar patterns of ability and inability, combining superhuman capacities in some domains with subhuman performance in other domains, and even within domains sometimes combining superhuman insight with surprising errors that few humans would make. We develop and defend a nonlinear model of intelligence on which "general intelligence" is not a unified capacity but instead the ability to achieve a broad range of goals in a broad range of environments, in a manner that defies nonarbitrary reduction to a single linear quantity. We conclude with implications for adversarial testing approaches to evaluating AI capacities. If AI is strange intelligence, we should expect that even the most capable systems will sometimes fail in seemingly obvious tasks. On a nonlinear model of AI intelligence, such errors on their own do not demonstrate a system's lack of outstanding general intelligence. Conversely, excellent performance on one type of task, such as an IQ test, cannot warrant assumptions of broad capacities beyond that task domain.