The Ubiquity of Infinite Eternity

Sonny the robot sits in the corner with a blown fuse. Something, you might say, blew his mind. Innocently enough, several days ago, Bob, his friend, told him that he would receive an unexpected gift in the next two days, however Sonny reasoned that it wouldn't be unexpected if it showed up on the second day if it didn't show up on the first day, ergo, logically, it is impossible for him to receive an unexpected gift two days from now. Therefore it must show up one day from now, but it wouldn't then be unexpected then either. Therefore he reasoned that it is logically impossible to receive an unexpected gift from Bob in the next two days. Sonny told this to Bob, who merely laughed at him, which perplexed Sonny a bit. Sonny then received a gift two days after coming to his conclusion and was...surprised. He was surprised because it occurred when it was logically impossible for it to occur. He had witnessed a miracle it seems. At first, he considered that the term "unexpected" might be applied in an ambiguous manner, but no, upon reflection he realized that it did in fact apply to his reaction to having received the gift, exactly as was predicted. There was no ambiguity and so the paradox persisted. Sonny sat down in a corner to contemplate this, and ended up blowing a fuse. 'Poor fellow.

There is nothing wrong with Sonny's reasoning. And there was nothing wrong, it seems, with Bob's reasoning either, since he did indeed do what he said he would do...even if it was impossible for him to do it. Bob proved to be a miracle worker. As Will Smith's character Det. Spooner commented on in the movie I Robot, robots certainly are rational and logical...to a fault in Det. Spooner's opinion. So much so that he distrusted them. What is wrong in the above scenario is caused by the common incongruities of natural language and logic. Foretelling of an "unexpected" event in a future finite time frame poses logical problems, yet we usually deal with this type of thing by ignoring it. We're good at ignoring things.

A common example is when someone goes on and on about "eternity" and "infinity", usually in a metaphysical sense. We can point out that there is no actual eternity and there is no real infinity either, the former is merely hyperbole and the latter is similar hyperbole and also serves as a mathematical tool that is 'approached' by numbers but never actually achieved. As counter-intuitive as it may first seem, infinity is used in mathematics as a limit, which at first blush seems to be a contradiction in terms. (Which is very odd, but only if you think about it.) We can point out that there is no actual existing or real eternity or infinity 'till we're blue in the face, and STILL our metaphysical-minded friends will continue to speak of going to eternity (as if this is a destination and not a time frame) and experiencing infinity, or talking about infinite 'things', etc, which is impossible. ("Things" are said to exist by persisting over time, yet at any given instance, there is a finite number of any given things in the universe. At no 'time' can there be an infinite number of any real things. "Infinite" is either in reference to an open-ended set, or is a form of linguistic hyperbole).

The fact that infinity, which is by definition open-ended and limitless, can be used as an approachable limit, never to be achieved precisely because no real existing thing can be infinite, is, unfortunately something that most people will never be able to wrap their minds around.