***Warning! An English prof is about to engage in unsupervised math-y and science-y talk!***
I love fantasy and sci-fi fiction of all kinds (books, television, movies, and comics), but I am a little frustrated at the way in which many of the stories I love address the idea of infinite universes. If someone who is better informed than I am about science and mathematics can show me why I’m mistaken in the argument that I’m about to make, please let me know in the comments. I’d be happy to be wrong.
Before I go on, let me make a distinction: I’m not talking about the idea of a multiverse (that is, the belief that there is more than one universe). I’m talking about the idea that there is an infinite number of these universes. It’s an idea that shows up in a lot of good stories: The Dark Tower, the CW superhero shows (notably The Flash and Legends of Tomorrow), and Jonathan Hickman’s run on Avengers and New Avengers that culminated last year in Secret Wars.
The problem with the theory of infinite universes is that it is mathematically impossible. As David Hilbert illustrated by his Grand Hotel thought experiment, if there actually were any infinite number of anything, this would lead to various logical contradictions and absurdities.
I sometimes illustrate the problem to my students this way: if I have in my possession an infinite number of items––say, apples––and someone comes along and steals half of my apples, how many do I have left? I still have an infinite number of apples. So no problem! Steal as many apples as you want! Since I have an infinite number of them, it’s not possible for you to reduce the number of apples that I have.
As much as I admire Jonathan Hickman’s run on Avengers and New Avengers––and I do admire his work a lot––he runs into the problem I’ve just illustrated in his depiction of the multiverse and the concept of incursions.
The story that Hickman tells beginning with Avengers #1 (2012) and running all the way to the end of Secret Wars (2015) centers on the notion that a catastrophic event in one of an infinite number of universes has caused the untimely death of that universe. It has also caused a chain reaction that is leading to the deaths of other universes through so-called incursions––points in space-time where two universes “smash together at the incursion point of the initial event” (New Avengers #2).
In short, the multiverse is dying––first two universes at a time, but the number increases exponentially. Each universe-death decreases the number of universes, meaning that the Avengers are witnessing a countdown to the death of the entire multiverse. If they don’t find a way to stop it, all of existence will be wiped out.
But there’s a problem. As Reed Richards says in New Avengers #2 (2013), the Marvel-verse consists of an infinite number of universes. This means that, no matter how many universes get destroyed, no matter how long the countdown of universe-deaths goes on, there will always be an infinite number of universes. By definition, infinity is a number that cannot be reduced by subtraction.
So how do we get from that infinite number of universes to the Time Runs Out storyline––which ends with the threat of the last incursion, the last two universes, whose collision is the basis for Secret Wars? The answer, as far as I can tell, is that we mathematically can’t––at least, we shouldn’t be able to.
I hate to slight a series of books as great as Hickman’s run on the Avengers titles––especially since it is far from the only work of fiction that posits the existence of an infinite multiverse. If you love comics and haven’t read it, then I recommend that you get a Marvel Unlimited subscription or read it in the trades because it’s really good. But it also inadvertently exposes the logical problem with the whole notion of an infinite multiverse.