Brain is Turing-equivalent?


A Turing-equivalent system can compute the same set of functions that an idealized Turing machine can.

Uncomputable functions cannot be evaluated on a Turing machine.

The terms super-Turing computation and hypercomputation are used interchangeably to refer to computing uncomputable functions.

Turing machines ⊆ brains

Claim: the brain is at least as computationally powerful as a Turing machine.

Brains ⊆ Turing machines

Claim: the brain is no more computationally powerful than a Turing machine. *Be skeptical!

To summarize:

The second set inclusion is unsatisfying. Unfortunately, I can’t see any way to directly prove this hypothesis without tackling the physical Church-Turing thesis, so we’ll have to be satisfied with a conjecture backed by considerable evidence. If the brain is in fact super-Turing, and the super-Turing facilities are instrumental in the mechanism of intelligence, then AGI is impossible on modern computers. That said, I don’t see any reason that evolutionary fitness would benefit from the computation of uncomputable functions, considering how exotic they are. To use classical computers as a substrate, we must make the relatively safe assumption that the brain is exactly as capable as a Turing machine.

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  1. Copeland, B. Jack, The Church-Turing Thesis, The Stanford Encyclopedia of Philosophy (Summer 2020 Edition), Edward N. Zalta (ed.). ↩︎

  2. Broersma, Hajo, Susan Stepney, and Göran Wendin. Computability and complexity of unconventional computing devices. Computational Matter. Springer, Cham, 2018. 185-229. ↩︎

  3. Piccinini, Gualtiero, Computation in Physical Systems, The Stanford Encyclopedia of Philosophy (Summer 2017 Edition), Edward N. Zalta (ed.). ↩︎