The author doesn't seem to be very familiar with the Church side of the Church-Turing thesis. That is where the "limits of computation" notion comes from.
For a long while I've had the opinion that the major conceit about Turing machines is, yes they can do things that humans suck at. However it's likely they are a pretty hackneyed way to accomplish what neuron based systems are really good at.
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[ 3.3 ms ] story [ 19.5 ms ] thread"All total functions are recursively enumerable"