pen it down

It's sometimes a mystery to me why there are so many problems I can ponder in my head that seem as unsurmountable conundrums, only to seem quite simple to resolve once I write them down(or more likely type them out). According to the extended Church-Turing hypothesis, all computable problems can be solved with a Turing machine. And a human brain is surely Turing complete, right? It can simulate a Turing machine by following the procedure step by step. But aha! The assumption of an infinite memory tape is not held! A normal human brain that doesn't write anything down can't store and retrieve arbitrarily long bit strings at will. So an unassisted human brain is not Turing complete. But armed with a recording device - aha! Then the human is Turing complete, and can solve all kinds of (computable) problems. So I guess when people argue that writing is the greatest human invention, I could supply another (not particularly intuitive) reason to support that argument.