Database Overlay

User interface
Database interface to files
Existing hierarchical filesystem
Storage media

The concept here is that you leave the existing 2-D hierarchical storage system in place. But you add a layer on top of it that behaves as a database, and presents you with a database interface to your files.

Because this concept uses existing stable technology as the foundation, it is not so difficult to “try out”. In fact, it has already been tried several times.

WinFS is a notable Microsoft project it implement a database overlay on NTFS. DBFS is an open source example that uses this approach.

How Does This Relate To Multiple Ways To Sort Files?

It’s not like you have to have a database to permit multiple ways to sort a files. And it’s not like a database file system would automatically give you a “multiple sort” interface. But applying the properties of a database to file management could potentially allow this kind of interface.