### Theseus' Ship

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
-John von Neumann
This past week I've had a bit of a cold. My health is returning, and my brain is clearing up, but I figured I'd do a fun post for today. Something that I understand easily, in and out, because I've analyzed it so many times before. Not that I have an answer. After all, mathematics is simple next to this. Today we'll be looking at Theseus' Ship, and there will be more questions than answers. Today's topic is more about broadening the mind than it is about a specific point, or lesson to be learned.

For those of you who don't know of the Theseus' Ship debate, or need a refresher, I'll first describe the backstory. According to Greek mythology, there was a great hero named Theseus. As all heroes from Greek mythology, he went around slaying monsters, saving people, and that sort of thing. And, as many monster-slaying princess-savers did, he had a ship. This allowed him to get from place to place easily- especially if the damsel in distress was on an island.
Time passed, and eventually, so did Theseus. But his ship, being an inanimate object, stuck around for a bit longer. The people, grateful to Theseus for all his heroic deeds, decided to put his ship in a museum to honor him for all time. They also decided to preserve his ship and restore it as needed. And thus, the questions begin.

Over a period of time, the ship begins to rot and decay, and the people working at the museum replace the rotted boards one by one. They use the same type of wood, and keep everything as similar as possible. Eventually, every board in the original ship has rotted and been replaced. So, the first question is this: is it still the same ship? If so, how do you account for the fact that no piece of the original ship remains? If not, then at what point did it cease to be the same ship? When one board was replaced? When the last one was replaced? Why?

Now, the original wood wasn't burned or destroyed; it was simply replaced when it was no longer seaworthy. But the descendants of Theseus decide to take the original wood and rebuild Theseus' ship to honor him. So they rebuild the ship, each plank in the same place as it was originally, and although this ship isn't seaworthy, it's still, other than that, exactly the same as the ship that sits in the museum. Thus, the next question: is this the same ship? If so, what about the ship in the museum? Isn't that Theseus' ship, repaired bit by bit? And how can it be the same ship if it was entirely disassembled and reassembled? If it isn't the same ship, then where is Theseus' ship? After all, it was never dismantled. And aren't these the original pieces that were used?

Eventually, the museum decides to use a cheaper type of wood than the kind that was originally used. So, bit by bit as they repair the ship, the type of wood changes. Of course, it looks identical, and it's still wood, so no big deal, right?
But after a while, the museum starts to lose business. They aren't as popular as they were before. So, in an attempt to draw in a younger crowd, they decide to modernize and use metal to repair the ship instead. Of course, it's still replaced piece by piece, and it keeps the same shape. Eventually, the ship is made entirely of metal. Is this still the same ship? If not, then where is the original? After all, the original ship was never dismantled. And when did it cease to be the same ship? Was it when one new piece was put in, or two, or fifty? Was it the first plank of a different kind of wood, or the first piece of metal?