That's not strictly true. If you're careful and imaginative, with moderate effort you can commit a fair amount of highly random data to memory. You just can't expect to change it every month.
This may be oversimplified, but it's the correct horse battery staple.
Eh, it depends, a random fragment of a very long poem for instance can be quite easy to memorize but at 80-90 words/300-400 characters long is pretty damn secure, doesn't even need to be written down then.
What the? If you write it down, it's a bad password. Make it a pass phrase, make it long. And possibly store it in an encrypted password database, protected by a master pass phrase.
This may be oversimplified, but it's the correct horse battery staple.