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And there is the real flaw: not the use of passwords, but the silly notion that average people should memorize them. WRITE THE DAMN THINGS DOWN!
Write them down, then what? It needs to be secure, you don't want someone else getting their hands on your password. It needs to be accessible, you may want to access that site on the go.
Beyond that, for the average user convenience will kill that idea quite quickly. After a few times of "I lost the damn paper" or "I left it in my other pants" etc... they will decide it's simply too much of a hassle and go back to their familiar memorized passwords.
The key elements in human thinking are not numbers but labels of fuzzy sets. -- L. Zadeh