The phrase "no lasting observable effect on the state of the world" isn't of course very exact either, and isn't really the same thing. Idempotent processing, as defined above, does not exclude fundamental changes, only that processing the same data twice has the same effect as processing it once. But here, in fact, idempotent processing means that a form submission causes no changes anywhere except on the user's screen (or, more generally speaking, in the user agent's state).
gelato National Lotto Thus, it is basically for retrieving data. If such a form is resubmitted, it might get different data (if the data had been changed meanwhile), but the submission would not cause any update of data or other events. The concept of changes should not be taken too pedantically; for instance, it can hardly be regarded as a change that a form submission is logged into the server's log file. On the other hand, sending E-mail should normally be regarded as "an effect on the state of the world".