We revisit the question (most famously) initiated by Turing: can human intelligence be completely modeled by a Turing machine? We show that the answer is \emph{no}, assuming a certain weak soundness hypothesis. More specifically we show that at least some meaningful thought processes of the brain cannot be Turing computable. In particular some physical processes are not Turing computable, which is not entirely expected. There are some similarities of our argument with the well known Lucas-Penrose argument, but we work purely on the level of Turing machines, and do not use G\"odel's incompleteness theorem or any direct analogue. Instead we construct directly and use a weak analogue of a G\"odel statement for a certain system which involves our human, this allows us to side-step some (possible) meta-logical issues with their argument.

中文翻译：

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人类智能的不可计算性

我们重新审视图灵发起的（最著名的）问题：人类智能能否完全由图灵机建模？我们证明答案是 \emph{no}，假设某个弱稳健性假设。更具体地说，我们表明，大脑中至少有一些有意义的思维过程是图灵可计算的。特别是一些物理过程不是图灵可计算的，这并不完全符合预期。我们的论证与著名的 Lucas-Penrose 论证有一些相似之处，但我们纯粹是在图灵机的层面上工作，不使用 G\"odel 不完备定理或任何直接类似物。相反，我们直接构造并使用弱类似于涉及我们人类的某个系统的 G\" 模型陈述，这使我们能够通过他们的论点回避一些（可能的）元逻辑问题。