In our book Why machines will never rule the world [13, 14] we argue that arti- ficial general intelligence is mathematically impossible. This is because the human beings and the processes which exhibit intelligence are complex systems whose be- haviour cannot be captured by the kinds of models that we can generate with or without computers. Proponents of contemporary machine intelligence respond with two lines of argument: a theoretical one, grounded in the universal approximation theorems for neural networks and the Church-Turing-Deutsch principle; and an em- pirical one, grounded in rapidly rising scores on standardized benchmarks. In this communication we examine and reject both responses. First, we show serious issues in the physicalist counter-argument based on the Church-Turing-Deutsch principle. Second, we review recent evidence to the effect that prominent benchmarks are compromised by training-data contamination, flawed test construction, and strate- gic optimization. Our central argument remains: That models required to perform cognitive behaviour in open-ended, thermodynamically complex and non-ergodic environments are not and will not become achievable.

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