Here is a ship.

It belonged to Theseus, the hero who — according to Greek myth — sailed to Crete, killed the Minotaur and came home to Athens. The Athenians were so proud of the ship that they kept it in the harbour for centuries as a monument.

But wood rots. So whenever a plank decayed, they took it out and put in a new one.

Eventually, every single original plank had been replaced.

Is it still the Ship of Theseus?

This question was recorded by the Greek writer Plutarch nearly two thousand years ago. He noted that philosophers used the ship as a standard example of a puzzle about things that grow and change, "some declaring that it remained the same, others that it was not the same."

They still haven't agreed.

The obvious answer is wrong. Both of them.

Most people's first instinct is: of course it's the same ship. It was repaired gradually. Nobody ever stopped and built a new one. It has the same name, same shape, same history, same place in the harbour.

Fine. Now try this.

Replace one plank. Same ship? Obviously.

Replace half the planks. Same ship? Probably.

Replace all but one. Same ship? Hmm.

Replace the last one. If it's still the same ship now, then the ship's identity apparently has nothing to do with what it's made of. Which is a strange thing to believe about a physical object.

And if it's not the same ship anymore — at which plank did it stop being the Ship of Theseus? The 50th? The 312th? The last? Any answer you choose seems arbitrary.

Then Hobbes made it worse

In 1655, the English philosopher Thomas Hobbes added a devastating twist.

Imagine that someone has been following the repair crew around. Every time they throw an old plank away, this person picks it up and keeps it. When the last plank is replaced, they take all the original planks and carefully reassemble them, exactly as they were.

Now there are two ships.

One sits in the harbour, made of entirely new wood, but continuously maintained since the time of Theseus. The other is made of every single original plank, in the original arrangement.

Which one is the Ship of Theseus? They can't both be. Can they?

If you said the repaired ship is the real one because of continuity, Hobbes's reassembled ship has a powerful claim: it's literally made of the ship Theseus sailed. If you say the reassembled ship is the real one, then you have to explain where the Ship of Theseus was while it was a pile of planks in a shed.

This was never about boats

Here's where the puzzle stops being a parlour game.

In 2005, a team led by Jonas Frisén found a clever way to measure how old human cells really are. Above-ground nuclear tests in the 1950s and 1960s briefly spiked the amount of carbon-14 in the atmosphere, and that spike got locked into the DNA of every cell created at the time. By measuring it, the researchers could date cells, a bit like tree rings. They found that the average cell in an adult body is roughly seven to ten years old — but with enormous variation between tissues.

So you're not a completely new ship. But you're not the old one either. You're something in between: a pattern that persists while the material flows through it.

The river you can't step into twice

Plutarch wasn't the first Greek to worry about this.

Around 500 BC, the philosopher Heraclitus wrote a line that has been quoted ever since, usually paraphrased as "you cannot step into the same river twice". The water flowing past your ankles today is not the water that flowed past them yesterday. And yet we happily call it the same river, give it a name, and draw it on maps.

What surviving fragments of Heraclitus actually say is subtler — something closer to "on those who step into the same rivers, different and different waters flow". The river stays the same because the water keeps changing. A river that stopped flowing wouldn't be a river at all; it would be a lake, or a ditch.

That's a beautiful idea, and a slightly unsettling one. It suggests that for some things, change isn't a threat to identity. It is identity.

Ships of Theseus everywhere

Once you know the puzzle, you start to see it all over the place.

The warship that's still in service. USS Constitution, launched in Boston in 1797, is the oldest commissioned warship still afloat. Over more than two centuries it has been repaired and restored many times, and only a small part of its original timber survives. The US Navy still regards it as the same ship — with the same name, crew, and duties.

The broom. In a much-loved 1996 episode of the British sitcom Only Fools and Horses, the road sweeper Trigger proudly announces that he has had the same broom for twenty years. It has had, he explains, seventeen new heads and fourteen new handles. Philosophers occasionally cite this as "Trigger's broom".

The band with no original members. By 2009, the British pop group Sugababes no longer contained any of the three women who founded it. Meanwhile, those three original members got back together and started performing under a different name. Hobbes would have recognised the situation instantly: one group with the name and continuity, another with all the original parts.

The company. A business can replace every employee, every office and every product — and still be legally the same company, with the same debts.

Your own body, a river, a navy ship and a pop group are all asking the same question: is it the parts, or the pattern?

Ways out of the puzzle

Philosophers have proposed several escapes. None is perfect.

"Same" means two things. There's qualitative identity (looking exactly alike) and numerical identity (being one and the same thing). Two identical teacups are qualitatively identical but numerically distinct. Some argue that the ship puzzle is just us confusing these two meanings.

Identity is a convention. Maybe there's no deep fact of the matter at all. "Same ship" is a label we apply for practical reasons — legal ownership, museum signs, insurance. The answer depends on what you need the word for.

Objects are stretched through time. Some philosophers argue that objects aren't fully present at each moment but are four-dimensional, with "temporal parts", the way a road has parts in different places. The Ship of Theseus is the whole worm-like shape stretching across the centuries, and the two ships in Hobbes's version simply share some early stages.

Only the original atoms count. Others bite the bullet: change a single part and, strictly speaking, you have a new object. It's logically clean — and it means you are not, strictly speaking, the person who started reading this article.

The version that keeps philosophers up at night

The British philosopher Derek Parfit took the puzzle to its logical extreme with a thought experiment about a teleporter.

You step into a machine on Earth. It scans every atom of your body, destroys it, and transmits the information to Mars, where a perfect copy is built from local materials. The person on Mars has your memories, your personality, your fondness for terrible puns. They feel exactly like you.

Did you travel to Mars? Or did you die, and a stranger with your memories wake up on another planet?

Now suppose the machine malfunctions and fails to destroy the original. There are two of you. Which one is you?

Parfit's own unsettling conclusion was that personal identity might not be what matters. What matters, he suggested, is the continuity of memories, character and connections — and that might come in degrees.

He said he found this liberating. Most readers find it terrifying.

So, is it the same ship?

Here's one honest answer: the question doesn't have a hidden correct answer waiting to be discovered. It shows us that our ordinary word "same" is doing several jobs at once, and usually we never notice because they all point in the same direction.

The Ship of Theseus is a situation where they point in different directions.

You, reading this, have been rebuilt in parts more times than you know. Your memories have been edited. Your opinions have been swapped out plank by plank. And yet when you wake up tomorrow, you'll feel absolutely certain that you're the same person.

Maybe that certainty is the most interesting part of the puzzle.