Our brains are Turing complete. Anything that is computable/ understandable, can be understood by humans.
Our brains are fallible, and so only approximately equivalent to Turing machines; and even ignoring that can only compute every computable thing given both infinite error-free storage capacity (which they don't have internally or externally) and sufficient time to execute the necessary steps of the computation.
Realistically, there are computable functions which no human brain will be ever be capable of computing.
Whether being able to compute a thing is sufficient, necessary, or tangential to understanding it is also a question.
So are actual computers. They're just "less fallible" and closer to a Universal Turing Machine than human brains in certain ways. A Commodore 64 is also incapable, in practice, of computing certain computable functions, due to memory limitations and what have you, but nobody would really claim a Commodore 64 is not Turing complete.
Sure, but no one was making claims about actual computers other than the human brain that requires pointing that out.
> but nobody would really claim a Commodore 64 is not Turing complete.
Actually, it's a rather common observation that real-world computers are not Turing complete (languages, considered independent of the limitations of concrete machines, may be) and particularly that concrete machines with limited storage space and operating with finite time constraints may not be able to compute all computable results, even though the abstract model they approximate, without those limitations, can.
I'm not sure a human can compute any algorithm beyond a certain complexity. But maybe if that human never aged or got bored and had an endless supply of paper. But then you're not dealing with a real human being anymore. Even if you had a super patient, super long lived human, what's to say they wouldn't get indefinitely stuck with really involved calculations?
i) Tell a person how a Turing machine works,
ii) Give her reams of paper
iii) Make her miserable by running some instruction.
iv) ?
v) Profit!
Seriously though. I don't think Turing completeness means anything at all; we're increasingly beginning to understand how important representations are. As hackers I'm sure we understand what this means in terms of PLs, but this is no coincidence IMO.
But given enough time and memory, shouldn't it be possible?
Although maybe that would require more than the universe has available, in which case I suppose it would be impossible in that sense I guess.