Can we build a system that functions like a general-purpose computer (with its own processor, state, etc.), with no owner or operator, that effectively "runs in the sky," in plain view, as a public good? A computer that is impossible to shut down or tamper with, on which anyone can deploy new programs or use existing ones?
If so, what would we do with it? One answer is digitally provable ownership. Digital signatures enable individuals to "own" public keys, with ownership asserted through demonstration of knowledge of the corresponding private key (e.g., by exhibiting a suitable digital signature). The guarantees of a digital signature scheme loosely correspond to certain property rights we're accustomed to in the physical realm (like the right to use and right to exclude). Programs running on the computer in the sky (either its OS, or programs managed by the OS) can then create pairs (x,pk), with the interpretation that the owner of data x = the owner of the public key pk. The computer in the sky can attest to ownership by verifying a signature. The benefits of "owning x" may stem from on-chain rights (e.g., the right to transfer) and/or off-chain utility (e.g., access to a "superfans-only" communication channel with a famous musician).
Digitally provable ownership is functionality that we haven't historically had, which is part of the reason why so many of today's platforms have exclusive access to data that, conceptually, should be platform-independent. With this new functionality, one can imagine a new generation of platforms in which user-generated data (follower lists in social media, reviews for products or services, etc.) is decoupled from the platform in which it happened to be generated.