You don't present a particularly compelling definition of this thing you're calling the internet. It could be equally applied to a close knit society.
It wasn't my intent to give a compelling definition. I meant to highlight, which features of the internet I find important and novel as a concept.
J.C.R. Licklider seems to have understood most of its importance in the early 1960s, writing that it would become, "the main and essential medium of informational interaction for governments, institutions, corporations, and individuals."
Not only did he predict it and write about it, he was one of the most important factors in actualizing it: through his position in the management hierarchy of ARPA, he directed the funding of research into "packet switching", which is the main technical difference between the internet and, e.g., the telephone network, which in its early decades -- before it was subsumed into the internet in the 1990s and 2000s -- operated according to a contrasting principle called "circuit switching".
Licklider was a mentor to Lawrence Roberts, who through his position at ARPA directed additional funding to packet-switching research and to the actual creation in 1969 of the network (ARPAnet) that would become the internet.
Licklider's 1961 paper "Intergalactic Computer Network" would be a good place to look for information about what exactly Licklider was able to predict.
Although I know of no indications in their writings that he or Roberts understood the eventual importance of amateurs on the internet, someone in the chain of cause-and-effect between Licklider and Roberts and the actual implementation the internet understood some important things about contributors because the design of the internet made it easy for individuals to contribute -- and the only reason I am using the word "individuals" rather than "amateurs" is that before the early 1990s it was difficult for the average person to access the internet (or even to learn that it exists) without being employed by a large organization with a technological or scientific mission or employed or enrolled in an elite university.
I. J. Good wrote -- in the early 1960s IIRC -- that although artificial intelligence was the most potent long-term technological project he knew about, research into packet-switching was worth funding because it would probably bear fruit before AI would and because it would tend to amplify the "collective intelligence" of the human race.
When the ARPAnet consisted of only a handful (two?) machines, Doug Engelbart was already involved in some of the nut-and-bolts of getting it working. That fact, combined with Engelbart's prescience on other matters, combined with Engelbart's explicitly-stated career goal of increasing the "collective intelligence" of the human race, make him another author I would read if I were looking for early accurate predictions about the impact of what came to be called the internet.
Vannevar Bush's 1945 article "As We May Think" is generally considered the earliest published prediction of the societal importance of computer networking and computer-mediated communication.
Bush, Licklider, Roberts and perhaps also Good were "East Coast technocrats": people who alternated between being on the faculty of prestigious schools and management jobs in the U.S. Department of Defense.
I once knew a smart guy who was under the impression that the only basic research necessary for the creation of the internet was the research that led to sufficiently-fast computers and to the ability to communicate over fiber-optical cables, essentially ignoring the problems "higher up on the stack". A good antidote to that mistake is to read some seminal research papers, particularly the 1981 paper "End-to-end arguments in system design".
I don't know when the idea was first mentioned, but in conversations on the subject the essay As We May Think by Vannevar Bush is often referenced, from 1945.
http://www.theatlantic.com/magazine/archive/1945/07/as-we-may-think/303881/?single_page=true
The internet is quite a special invention. It had huge impact on the way we live in number of ways. And yet, it is mainly a conceptual breakthrough. While for most of history, humanity didn't have the technology needed for its creation, the internet wasn't even imagined shortly until its emergence. Many other technologies had no such problem (flight, audiovisual long-distance communication, audiovisual recording, death rays a.k.a. lasers or teleportation - as an example of a phenomenon we can easily conceive even though we're nowhere near the technology needed for it)
My question is when was the Internet predicted for the first time, when the idea of the Internet was uttered for the first time?
Let me clarify, what I mean by the Internet. I don't mean global communication. This is achieved by telephone networks, (was by) telegrams or by e-mails or Skype. But those are not the Internet, they are just part of it. Nor do I mean the global library - while this is closer to what I find essential about the Internet, it doesn't encompass the whole idea. Global library means one-way communication, analogous to a real library. It also emphasises the special status of authors, professionals, not ordinary folk. And even before the advent of Web 2.0, the internet was in great part created by amateurs. The internet is more of a form of huge advertising column, to which access is easy and which is not a curated repository of knowledge, but rather a mix of ads, telephone book, practical information about shops and services, information published by amateurs in a subject, personal diaries, a medium of exchange of goods, etc. - and on top of that, a tool for interpersonal communication. Eventually, it is a clearly a new form of communication, encompassing both two-way communication of casual chat and one-way communication between reader and author.
This is the idea I mean by the Internet. When was the first time this specific idea came to existence? When had people realised that global network of PCs and servers will result in that form of communication, creating its own space - cyberspace, rather than just a tool for communication and a form of a library?