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The Church-Turing thesis comes to mind. It would at least suggest that humans aren’t capable of doing anything computationally beyond what can be instantiated in software and hardware.

But sure, instantiating these capabilities in hardware and software are beyond our current abilities. It seems likely that it is possible though, even if we don’t know how to do it yet.

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The church turing thesis is about following well-defined rules. It is not about the system that creates or decides to follow or not follow such rules. Such a system (the human mind) must exist for rules to be followed, yet that system must be outside mere rule-following since it embodies a function which does not exist in rule-following itself, e.g., the faculty of deciding what rules are to be followed.
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We can keep our discussion about church turing here if you want.

I will argue that the following capacities: 1. creating rules and 2. deciding to follow rules (or not) are themselves controlled by rules.

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That humans come in various degrees of competence at this rather than an, ahem, boolean have/don't have; plus how we can already do a bad approximation of it, in a field whose rapid improvements hint that there is still a lot of low-hanging fruit, is a reason for techno-optimism.
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Thousands of years?

We've only had the tech to be able to research this in some technical depth for a few decades (both scale of computation and genetics / imaging techniques).

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And then we discover that DNA in (not only brain) cells are ideal quantum computers, DNA's reactions generate coherent light (as in lasers) used to communicate between cells and single dendrite of cerebral cortex' neuron can compute at the very least a XOR function which requires at least 9 coefficients and one hidden layer. Neurons have from one-two to dozens of thousands of dendrites.

Even skin cells exchange information in neuron-like manner, including using light, albeit thousands times slower.

This switches complexity of human brain to "86 billions quantum computers operating thousands of small neural networks, exchanging information by lasers-based optical channels."

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