I know that you can set up multiple virtual machines per physical computer. I'm wondering if it's possible to make multiple physical computers behave as one logical unit?
Fundamentally the way I imagine it working is that you can throw 10 computers into a facility one day. You've got one client that requires the equivalent of two computers worth, and 100 others that eat up the remaining 8. As demands change you're just reallocating logical resources, maybe the 2 computer client now requires a third physical system. You just add it to the cloud, and don't worry about sharding the database, or migrating data over to a new server.
Can it work this way?
If yes, why would anyone ever do things like partition their database servers anymore? Just add more computing resources. You scale horizontally with the hardware, but your server appears to scale vertically. There's no need to modify your application's infrastructure to support multiple databases etc.