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For example, one that brains appear to be able to solve in polynomial time but computers can't, or one optimized for the brain's innate capabilities - like language learning, or different possibilities computed at once.

I've found some things about the brain's computational abilities, like a "predictive coding hierarchy" that helps it learn languages and Joe Z. Tsien's Theory of Connectivity in which neurons group into cliques and motifs to process complex concepts, but I haven't really found anything from an algorithmic perspective. My ultimate goal is to see if there's an encryption algorithm that can be done by a person with pencil and paper, but that can't be easily cracked by a computer.

Has any research been done on this? Thanks for any lead you may have.

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    $\begingroup$ You can find a lot of problems that human brains are better at than computers when looking for CAPTCHAs. $\endgroup$ Commented Nov 21, 2023 at 10:17
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    $\begingroup$ I don't see a formal -- or formalizable -- question here. Not appropriate for this forum. $\endgroup$
    – Aryeh
    Commented Nov 21, 2023 at 13:46
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    $\begingroup$ This is more a question about (meta)physics or biology. It turns out that most computing machines that exist in the physical universe are "roughly" like a finite-memory Turing machine. But actually, nature gives us a seemingly more powerful computational primitive, namely quantum computers. Of course, it is not proven that these are really more powerful than regular Turing Machines. So what you are asking is whether the universe gives us a primitive more powerful than quantum computers, or alternatively whether the brain is a quantum computer. Both are unknown despite centuries of research. $\endgroup$ Commented Nov 28, 2023 at 2:01
  • $\begingroup$ "one that brains appear to be able to solve in polynomial time" What makes you believe that? The brain seems to have quick solutions for some problems, but nothing is known about asymptotics. In fact, if a problem becomes large enough, I'd venture that a brain will give up. $\endgroup$
    – Turion
    Commented Dec 20, 2023 at 16:18
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    $\begingroup$ @Turion The brain would be like a specific type of a circuit without any (at least yet) known accurate way to scale it to larger sizes. One, however, in theory could compare it against non-uniform circuits of around the same size, but given the size, I don't see this happening at all. $\endgroup$
    – rus9384
    Commented Dec 21, 2023 at 8:39

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One example of such an "algorithm" is finding proofs for theorems. Regarding encryption — there's no inherent problem with a human using an SPN, for example, but it just requires a lot of computation, and if you remove too much you make it susceptible to bruteforcing. Generally humans wouldn't be that good at encryption, because it has to be deterministic and can't rely on creativity. For asymmetric encryption I can't think of anything practical for a human which isn't easily breakable, and looking at tables of runtime and keysize of known algorithms I don't imagine there is one.

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  • $\begingroup$ Do you have any proof that humans are better at finding proofs than machines? $\endgroup$ Commented Dec 22, 2023 at 16:02
  • $\begingroup$ @JoJoModding No, and I don't believe that is true – I believe that a machine could theoretically perfectly simulate a human, so it can't be worse at anything. However, that is clearly the case for currently known algorithms for that $\endgroup$ Commented Dec 22, 2023 at 16:07

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