The Thanos Paradox
Thanos. The Ragnarok humanoid. The man to end all men. Also a big, bald man with an unfathomable amount of scars. Jokes aside, we all know the significance of Thanos. In Avengers: Infinity War, Thanos had a gauntlet that contained all the infinity stones. Although, as he possessed all the infinity stones, he could have willed them to do whatever he desired, the algorithm he set for the gauntlet was — 1 snap = 50% total elimination.
While we watched the movie, captivated by the exhilarating climax, we failed to latch onto the mathematical inconsistency in Thanos’s ultimatum to terra firma. We dreaded a future with Thanos, absent of all living things. But wait. How can that be possible? Setting 50% as an infinitely iterative mechanism would result in pretty much nothing, but there would still be an extremely infinitesimal fraction of living matter, probably like 0.000000000000000001. You get the point. Let me show you (mathematically) the Thanos paradox.
After watching Endgame, I, and other members of the Internet community noticed the fatal flaw in Thanos’s ‘snapping’. We all realized that total elimination is, to put it simply, mathematically impossible. If any of you recall, in school you probably learned about sequences, specifically geometric sequences (I’m a high schooler so this is fresh in my memory yippee!). In a geometric sequence, there are two important parameters to formulate a sequence.
First, we have a, or the initial term in a sequence. Second, we have r or the common ratio that increments a term. The form of a geometric sequence is ar^n-1. N refers to the number of iterations in a sequence.
Now we can formulate Thanos’s sequence.
According to Thanos, 50% of all living things are eradicated. This leads to a=0.5. Next, we also define r as 0.5 as 50% of whatever remains is eradicated when Thanos snaps — 50% of 50% is 25%, so after the second snap, 75% of biotic things will be eliminated. So on and so forth.
This eventually gives as the nth term, or the common form of the sequence — 0.5*(0.5^n-1). If we want total elimination, we have to equate this equation to 0 to find n. Let’s just throw this into symbolab.com, the savior of all burgeoning math students.
Woah. Although common sense and basic math should’ve told you that Thanos flunked 2nd-grade arithmetic, we now have solid proof. Essentially, n can’t be a real number and satisfy the equation we postulated. And we obviously need n to be a real number for total elimination!
Now you’re probably thinking, but Anay, we’d only have like a millionth of a person left. Yes, folks. That is true. Thanos would only have a fingernail to engage in intellectual discourse with. But still. Particles of living matter do remain. In this world of political correctness, statistics, and perennial accuracy, we must abide by the status quo, put our foot down, and say Thanos didn’t really eliminate every living thing. If you’re curious, you can find the almost-eliminated value of n on Quora, Reddit, etc. He’d have to snap his fingers around 32–33 times. But that’s too boring. We want the math and the stats we deserve.
Well, that’s the Thanos paradox. The big, blue man with a gnarly physiognomy thought he’d eliminate everyone but his math failed him. The total elimination impossibility theorem, eh. I’d be pretty pissed if math caused the downfall of my lifelong dreams and ambitions. That’s the reality of life. It sucks.
