Web 2^w

In a rather interesting article in Communications of the ACM, T.V. Raman describes the next Web revolution as a function applied to itself, resulting in an exponentially increasing web.
Web 2.0 [...] as the result of applying the Web function to itself, that is, Web 2.0 = Web2 (). Let W denote the set of all URL-addressableinformation.

[...] What is the size of this Web to come? Let W denote the set of all URL-addressable information. Each combination can in turn be deployed on the Web by making it URL-addressable and expressed mathematically as:

Note that a large portion of the impetus for the move from Web 1.0 to Web 2.0 and later to the predicted 2^
w is due to user needs; aggregations, projections, and mashups are all a direct consequence of the user’s need to consume information in a form that is most suited to a given task. Though the resulting set 2^w might be immense, most of these elements are relevant only when used by at least one user.

Very interesting read.