Achilles, the Tortoise, and the Story of the Three Clockworks

Achilles returns from an exhausting morning chucking the javelin with his mates to see his friend the Tortoise rubbing his shell against a rock. Achilles tosses the half-drunk wineskin he is holding to the ground and sits down next to a tree.

Achilles: Ah, Torty. Done flossing, I see.

Tortoise: Why yes, I am polishing my shell.

Achilles: Big date tonight?

Tortoise: You might say that. My dear Mrs. Tortoise has informed me that our eggs are due to be hatching this evening, and I would prefer that my progeny’s first glimpse of their aged father be as impressive as can be managed.

Achilles: Congratulations! A proud papa.

Tortoise: Yes, yes. I do hope that my limited wisdom will be sufficient to steer the young tortoises from the strawberry fields of dalliance, and keep them to the straight and narrow path of virtue.

Achilles: Definitely. Virtue and all that. But surely, young tortoises are guided by instinct to some degree? I mean, I would think that, with your and Mrs. Tortoise’s genes, little could go wrong.  You are, I should say, the wisest Tortoise I know.

Tortoise: It is not my contribution as father to my own young Tortoises that most concerns me, it is true. It is my contribution as father…to the society of Tortoises writ large.

Achilles: I don’t follow.

Tortoise: Have I ever told you the story of Daedelus and the Three Clockworks?

Achilles: Hold on a sec. [Takes a swig from the wineskin.] Okay, go ahead.

Tortoise: Daedelus, as you know, was the marvelous inventor and mechanician who created the Labyrinth wherein the Minotaur prowled–

Achilles: Yeah, yeah, I know. My first cousin took care of old Miney-taur.

Tortoise: [slightly annoyed] WHEREIN the Minotaur prowled. Before building the Labyrinth, however, he created a series of models that could fit on a tabletop, to test out which designs would be most difficult to solve.

Achilles: What’d he do, have mice try to run through the maze?

Tortoise: He did try mice at first, and he could train them to solve the maze using a piece of cheese and their sense of smell. But he wanted to know how a human could solve a maze the very first time, with the Minotaur inside the maze somewhere waiting to kill them. Daedelus also wanted to know whether there were rules that you could use to solve a maze that you had never seen before. Lastly, he was bored without having anything new to invent. So he created three small clockwork men, one orange, one green, and one blue.

Achilles: So could they all solve the maze?

Tortoise: In the first clockwork, he arranged the gears such that whenever it encountered a wall, it would turn to the left. When he tried it in his first model maze, it turned once, twice, and then got caught in a room, going around and around until its clockwork wound down and it stopped. It looked like this. [The Tortoise grabs a piece of stick in his beak and uses it to draw in the dirt.] These are the walls, and this is the path of the first clockwork:



Achilles: So going left didn’t work. What about the next one?

Tortoise: The second clockwork had gears arranged to always turn right when it hit a wall. It turned right, then turned right again, then ended up in another room from which it could not leave, and went round and round until its clockwork wound down and it stopped. Its path looked like this:


Achilles: And the third clockwork?

Tortoise: Its gears were arranged so that it would go left, then right, then left, then right, and so on.


Achilles: It got out! It escaped! Good job, little blue guy.


Tortoise: Yes, yes. So my question for you is: was the third clockwork better at solving mazes than the other two?

Achilles: Well, it was better at solving this maze. If you’d given it a mirror-image maze, or something else, it would have gotten just as stuck as the others.

Tortoise: Precisely. And now you know why I am polishing my shell.

Achilles: Because your shell is…the little tortoises’ maze?

Tortoise: [sighs] Something like that.  But now I must be going down to the beach.

Achilles [looks up at sky]: It’s only noon, and the beach is right over there- I could throw a javelin that far, if I wasn’t so tired. I thought the eggs weren’t hatching until tonight?

Tortoise: We Tortoises must begin journeys well in advance.

Achilles: I was thinking of going down with you but [yawns] I think I’ll stay here, and just [looks at wineskin, lifts it to confirm it is empty] think of another maze [yawns] or maybe just take a nap.

Tortoise: Well, as they say, catch me if you can.

Achilles: Catch “us!” You’re a family Tortoise, now.

Tortoise: Indeed.

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