This is based on MIRI's FDT paper, available here
Eve, Carl, and Fiona are all about to have a very strange few days. They don't know each other, or even live in the same city, but they're about to have similar adventures.
Eve heads to work at the usual time. As she walks down her front steps, her neighbor calls out to her.
"I heard a rumor that your house has termites," says the neighbor.
My dear reader: you and I know that Eve's house doesn't have termites, but she doesn't know that.
"I'll have to look into it," responds Eve, "but right now I'm late for work." And she hurries off.
As she's walking to work, Eve happens to meet a shadowy stranger on the street. That shadowy stranger is carrying a large box and a small box, which are soon placed on the ground.
"Inside the small box is $1000," says the stranger. "Inside the big box, there may be $1 million, or there may be nothing. I have made a perfect prediction about what you're about to do, but I won't tell you. If I have predicted you will take only the big box, it will have $1 million in it. If I have predicted that you will take both boxes, then I left the big box empty. You can do what you want."
Then the stranger walks off, ignoring Eve's questions.
Eve considers the boxes. The mysterious stranger seemed trustworthy, so she believes everything that she was told.
Eve thinks to herself: if I was told later that I took only the big box, then I'd know I'd have $1 million. If I were told I had taken both boxes, then I'd know that I only had $1000. So I'd prefer to have only taken the big box.
She takes the big box. When she gets to work, she opens it to find that it is indeed full of ten thousand hundred dollar bills. She is now a millionaire.
Eve goes straight to the bank to deposit the money. Then she returns home, where she has a strange letter.
The letter is from the notorious termite extortionist. The termite extortionist has been in the news a few times recently, so Eve knows that the villain is for real.
The letter reads:
I heard a rumor that your house might have termites. I have investigated, and I now know for certain whether your house has termites. I have sent you this letter if and only if only one of the following is true:
a) Your house does not have termites, and you send me $1000.
b) Your house does have termites.
The Notorious Termite Extortionist
If her house has termites, it will take much more than $1000 to fix. Eve thinks about the situation.
If she were to find out later that she had paid the extortionist, then that would mean that her house did not have termites. She prefers that to finding out that she hadn't paid the extortionist and had to fix her house.
Eve sends the Extortionist the money that was asked for. When she checks her house, she finds that it doesn't have termites, and is pleased.
Eve decides to take the bus to work the next day. She's so distracted thinking about everything that's happened recently that she gets on the wrong bus. Before she knows it, she's been dropped off in the great Parfit Desert.
The Parfit Desert is a terrible wasteland, and there won't be another bus coming along for over a week. Eve curses her carelessness. She can't even call for help, because there's no cell signal.
Eve spends two days there before a taxi comes by. By this point, she is dying of thirst. It seemed she would do anything to get out of the desert, which is what she says to the taxi driver.
"It's a thousand dollars for a ride into town," says the Taxi driver.
"I left my money at home, but I'll pay you when we get there," says Eve.
The taxi driver considers this. It turns out that the taxi driver is a perfect predictor, just like the mysterious stranger and the termite extortionist.
The taxi driver considers Eve. The driver won't be able to compel her to pay once they're in town. And when they get to town, Eve will think to herself:
If I later found out that I'd paid the driver, then I'd have lost $1000. And if I later found out that I hadn't paid the driver, then I'd have lost no money. I'd rather not pay the driver.
The taxi driver knows that Eve won't pay, so the driver goes off without her. Eve dies of thirst in the desert.
Eve has $999,000, her house does not have termites, and she is dead.
As he heads to work, Carl's neighbor mentions a rumor about termites in Carl's house. Carl, also late for work, hurries on.
A mysterious stranger approaches him, and offers him two boxes. The larger box, Carl understands, will only have $1 million in it if the stranger predicts that Carl will leave the smaller box behind.
As Carl considers his options, he knows that the stranger has either already put the money in the box, or not. If Carl takes the small box, then he'll have an extra $1000 either way. So he takes both boxes.
When he looks inside them, he finds that the larger box is empty. Carl grumbles about this for the rest of the day. When he gets home he finds that he has no mail.
Now dear reader, let's consider the notorious termite extortioner. The termite extortioner had learned that Carl's house might have termites. Just as with Eve's house, the extortioner investigated and found that the house did not, in fact, have termites.
The extortioner considered Carl, and knew that if Carl received a letter he wouldn't pay. The extortioner knew this because he knew that Carl would say "Either I have termites or not, but paying won't change that now". So the extortioner doesn't bother to waste a stamp sending the letter.
So there is Carl, with no mail to occupy his afternoon. He decides to catch a bus downtown to see a movie. Unfortunately, he gets on the wrong bus and gets off in the Parfit Desert. When he realizes that the next bus won't come for another week, he curses his luck and starts walking.
Two days later, he's on the edge of death from dehydration. A taxi, the first car he's seen since he got off the bus, pulls up to him.
"It's a thousand dollars for a ride into town," says the Taxi driver.
"I left my money at home, but I'll pay you when we get there," says Carl.
The taxi driver considers Carl. The driver won't be able to compell him to pay once they're in town. And when they get to town, Carl will think to himself:
Now that I'm in town, paying the driver doesn't change anything for me. Either I give the driver $1000, or I save the money for myself.
The taxi driver knows that Carl won't pay when the time comes to do it, so the driver goes off without him. Carl dies of thirst in the desert.
Carl has $1000, his house does not have termites, and he is dead.
As Fiona leaves home for work, her neighbor says to her "I heard a rumor that your house has termites."
"I'll have to look into that," Fiona replies before walking down the street.
Partway to work, a mysterious stranger confronts her.
"Yes, yes, I know all about your perfect predictions and how you decide what's in the big box," says Fiona as the stranger places a large box and a small box in front of her.
The stranger slinks off, dejected at not being about give the trademarked speech.
Fiona considers the boxes.
If I'm the kind of person who decides to only take the one large box, then the stranger will have predicted that and put $1 million in it. If I'm the kind of person that decides to take both boxes, the stranger would have predicted that and left the big box empty. I'd rather be the kind of person that the stranger predicts as deciding to take only one box, so I'll decide to take one box.
Fiona takes her one large box straight to the bank, and is unsurprised to find that it contains $1 million. She deposits her money, then goes to work.
When she gets home, she finds that she has no mail.
Dear reader, consider with me why the termite extortionist didn't send a letter to Fiona.
When the termite extortionist learned of the rumor about Fiona's house, the resulting investigation revealed that there were no termites. The extortionist would predict Fiona's response being this:
If I'm the kind of person who would decide to send money to the extortionist, then the extortionist would know this about me and send me an extortion letter. If I were the kind of person who decided not to give money to the extortionist, then the extortionist wouldn't send me a letter. Either way, the cost due to termites is the same. So I'd prefer to decide not to pay the extortionist.
The extortionist knows that Fiona won't pay, so the letter is never sent.
Fiona also decides to see a movie. In a fit of distraction, she takes the wrong bus and ends up in the Parfit Desert. When she realizes that the next bus won't be along for a week, she starts walking.
Two days later, Fiona is on the edge of death when a taxi pulls up.
"Please, how much to get back to the city? I can't pay now, but I'll pay once you get me back," says Fiona.
"It's $1000," says the taxi driver.
The taxi driver considers Fiona's decision-making process.
When Fiona is safely in the city and deciding whether to pay the taxi driver, she'll think to herself: If I were the kind of person who decided to pay the driver, then the driver would know that and take me here. If were the kind of person who decided not to pay the driver, then the driver wouldn't give me a ride. I'd rather be the kind of person who decided to pay the driver.
The taxi driver takes Fiona back to the city, and she pays him.
Fiona has $999,000, her house doesn't have termites, and she is alive.
Dear reader, the one question I want to ask you is: who is spreading all those rumors about termites?