I thoroughly enjoyed the recent Spider-man: Across the Spider-verse movie. If you haven’t seen it, be sure to watch the first movie Spider-Man: Into the Spider-verse and then see this one — I’m not a comic book geek at all, but they are excellent movie- and some of the artwork in the latest is absolutely astonishing. I kept oscillating between appreciating the story and being transfixed by the composition of characters and background construction. It’s a good story, and it’s beautiful.
BUT … I got distracted by a math problem. Throughout the movie (this text isn’t a story-spoiler but I do talk about the different Spider-folk seen!) you are introduced to different universes’ Spider-folk, and many of them are numbered — and they are all finite numbers. What does that mean? Well, numbers like 7, 13532 and 91234818183481 “end” and you don’t get 8213481234… where the ellipses says the numbers continues on (perhaps infinitely?) and so doesn’t (couldn’t) fit on the screen.
This interrupted the movie for me — because this is a classic math topic : The German Tank Problem (link). During World War II, the Allies noticed that the German tanks were numbered sequentially (1, 2, 3, … n) and so they could roughly determine how many tanks (the n) the Germans had produced. The mathematically determined estimate was far closer to the actual number (found out by German records after the war) than the number that Allied Intelligence had thought (because the Germans were otherwise trying to obfuscate the situation).
So how does this work? Well let’s say you had tanks (or Spider-folks) numbered 2, 28, 73, 111 and 205. You know, then that there are at least 205 tanks produced. But likely (remember this is stats, so it’s all a probability-game) there are tanks numbered more than 205. So what we do is look at the gap between the numbers that we do know, and extrapolate that gap to where the maximum number should be. I’m not going to get to into the weeds (and there are LOTS of weeds to go through… and this is only one perspective on those statistical weeds. For a deeper analysis, start with Wikipedia link ) so we’re going to short-circuit to a formula. If you’re into Stats (I am not) then enjoy! Now, back to my calculation…
N is the suspected total number of tanks (or Spider-folks)
m is the highest number from your collection of captured tanks (observed Spider-folk)
n is the count of the captured tanks (or observed Spider-folk)
This calculation is known to underestimate the value of N but should be close (the Allies calculated the correct number of tanks within 5% after a year’s observations).
I then turn to folks who have catalogued those Spider-folks labelled in the film (Cineplex would not agree to pausing the film for me to note the numbers down!):
|Peter B. Parker||616|
|Web Slinger (& Horse)||31913|
|Margo Kess (Spider Byte)||22191|
|Spider that bit Miles Morales||42|
|Peter Porker (SpiderPig!)||8311|
So what do we get? Our m = 312500 and our n = 20 so with our handy calculator we get…
and so N = 328, 125.
Now, the more Spiderfolks you know, the closer you’ll get to an estimate of the total number of Spiderfolk. There were A LOT of Spiderfolk not numbered in the movie… crowds of them! But you work with what you’ve got.
My underlying struggle is that this is a MultiVerse … so there should be an infinite number of possible Earths. All Sony had to do was to put ONE Spider-folk with a universe number that was displayed as infinite (like 572156… ) and I would be happy!
The underlying mathematics of this problem is covered in AP Statistics but of course, you can play with the formula any time!
A London-based investor named Tommo_UK used this method on phone’s IMEI numbers to determine how many iPhones Apple had produced (link). Amusingly, Apple switched to random IMEI numbers to avoid this.
Caveat : There is some controversy (in the Comic-book world! Really!?) because some call the MCU universe Earth-199999 instead of Earth-616. So perhaps N = 209,522?