Here's your interesting thought for the day. Shamir's Secret Sharing. This topic of secret sharing I believe holds immense value for the future of passwords and encrypted data on the decentralized web. Consider this approach in an applied environment akin to the P2P file-sharing of yesterday. In this new ideal system you could have a decentralized fully encrypted setup where private data could be stored securely in a public blockchain or other distributed, decentralized format.
Shamir's Secret Sharing is an algorithm in cryptography created by Adi Shamir. It is a form of secret sharing, where a secret is divided into parts, giving each participant its own unique part, where some of the parts or all of them are needed in order to reconstruct the secret.
If you're interested in learning more you can see the mathematical algorithm on the associated Wikipedia page.