google wave is a new type of web 2.0 hosted communication, presented at google's i/o conference a view days ago. http://wave.google.com . it is very early to tell what it really is, but it could be big. it is very open and also consists of an open protocol for communication, that can be used (basically) for everything - and that's where i started to think about sage. but first, i explain what i think it does and how sage could play a role in there!
a server (not necessarily google - it's more like jabber/xmpp where everybody could host a server and servers talk to each other if users use different servers) hosts the "communication", called "wave". that's a tree-like structure of data, replies, extensions, meta-info, etc. if someone modifies something or adds a reply, every other participant sees the modification in real-time.
there are also artificial participants, called robots. they can also do things just like a regular user. example: spellchecking! a spellchecker analyzes all text and if something is odd, it annotates/modifies the text.
okay, how works synchronization? basically, all operations happen on the server. i think it is an abelian group so that there are no "destructive" operations - only invertible - that cannot destroy the state-flow and the sum of all state changes is the current state. therefore, there is only one thread of communication for all participants. if something happens (lost connection), everything is re-synced fast.
the interesting point is, there are also gadgets: interactive elements for all participants (an example is a chess game) and that's where i think sage could be used. basically, my idea is to implement a button to create a cell from the notebook. then, you enter the url of a sage server + your credentials. now, input is sent to the server (also, autocomplete ....) and you get the answer back and a new cell is created. if i understand it correctly, the server is actually talking to sage, so it is possible that several users edit at the same time and the actual cell-data is saved inside this "wave".
what's missing is formatting the formulas - but there is also mathml which could do it.
i applied for an early developer sandbox access, once i know more about this i'll tell you more.
