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"Indefinite does not mean infinite" is a common refrain in Wikipedia discussions, particularly when considering indefinite blocks. The purpose of this brief essay is to explain what that means in practice.
Common use cases for indefinite blocks edit
The most obvious and common uses of indefinite blocks are for vandalism-only accounts, as well as trolls, sockpuppets, spammers, and other people whose purpose in being here is clearly at odds with Wikipedia's purpose. In these cases, indefinite usually does mean infinite. As a general rule, we don't want these people back, though I'm a big believer in second chances (within reason) and I like to think that anyone can change.
Long-term editors edit
The phrase "indefinite is not infinite" is most commonly used when discussing blocks of long-term editors rather than throwaway accounts. While there are (or should be) no vested contributors, indefinite blocks of established editors who have put a lot of time and effort into Wikipedia, and are "here to write an encyclopaedia" should be rare. These blocks are always to be lamented, but sometimes the issues with an editor's conduct are such that an admin feels they have no choice. In these cases, the block usually does not need to be infinite (as in forever) even if it is indefinite (as in having no fixed duration).
Admins usually make this choice because the blocked editor's conduct is disruptive enough that a fixed-term block (which the blocked editor can wait out) would not be appropriate. An indefinite block does not expire automatically and can only be lifted by affirmative action. This means that, to be unblocked, the blocked editor must convince the blocking admin or the community that they will change their editing in some way that means that they will not repeat the conduct which led to the block. Sometimes this may take hours or days, and sometimes it may take longer, possibly considerably longer. The timing is largely up to the blocked editor, who must make a commitment to change in order to be unblocked.
For example, an editor blocked for copyright violations will need to demonstrate a better understanding of Wikipedia's copyright policies; an editor blocked chronic edit warring may need to a agree to a revert restriction; somebody blocked for battleground behaviour will need to show that they have made progress in not personalising disputes. In some cases, mentorship may be appropriate.
In others, admins or the community may not be comfortable unblocking for quite some time, especially if the conduct was egregiously disruptive or the blocked editor has a long history of sanctions. Even these blocks are not necessarily infinite, and may well be lifted once enough time has passed and if the blocked editor can make a convincing request.