Edward Kmett and Dr. Yoneda are debating about the role of Kan extensions in category theory.
Edward: I use them because they have computational content, but you believe they express a deeper insight?
-- End Prompt
Dr. Yoneda: Yes, and that is why I am convinced that they are not just useful tools for computer scientists. They can be used to make new discoveries in mathematics! You see, we do not know everything there is to know about any given subject. We only learn more as our knowledge grows. And so it goes with mathematics! The more we discover, the richer it gets. But what if we could find something even better than that? What if we found an infinite set of all possible mathematical objects? That would be like finding an infinity of stars in the sky! There are more out there than anyone could ever count!
You hang up the phone. The car drives up to the front door of the mansion and stops.
Driver: Okay, we're here. Good luck, Mr. Kmett!
Driver gets out of the car and opens your door. You get out of the car and grab your bag.
Driver: (looking up at the mansion) Man, that's a big house!
You look up at the mansion and feel a shiver of fear run through you. You are unsure why, but it just feels like something bad is waiting for you in there.
You walk up to the front door and ring the doorbell.
Soon, the door opens and you see a young girl with long blond hair and a blue dress. She looks about 5 or 6 years old.
Girl: Hello. My name is Eliza.
Edward: Um... hi. I'm looking for Dr. Yoneda.
Eliza: Come on in. He's been expecting you.
Eliza opens the door and you walk in. She walks a few feet ahead of you, but every now and then she looks back to make sure you're still there.
Soon, you find yourself in a study area. There are two couches and a desk in the middle of the room. Dr. Yoneda is sitting at his desk doing some work.
Dr. Yoneda: Hello, Edward. I've been expecting you.
You drop your bag on the floor and sit down in one of the chairs in front of the desk. Eliza sits in the other chair.
Dr. Yoneda puts down his pen and looks up at the two of you.
Dr. Yoneda: So, what do you think?
You look around the room and try to form an opinion, but you're too confused to do so.
Dr. Yoneda: You look confused. Is the house a bit much? I know it's a lot to take in, but I think it's important to live in an environment that stimulates the mind. Now, why don't you tell me a little about yourself and what brings you here.
Eliza: He's here about the ad, isn't he, Dr. Yoneda?
Dr. Yoneda: (smiling) Perhaps.
You decide to go along with the conversation and tell Dr. Yoneda everything he wants to know.
After you are done, Dr. Yoneda looks at Eliza and nods.
Eliza gets up from her chair and walks over to the desk. She takes out a notepad and writes something down. Then she turns to you.
Eliza: I just need to ask you one question.
Eliza looks at you with her big blue eyes.
Eliza: Do you want to learn?
You look into her eyes and feel your will slipping away. You want so badly to say "yes." Just tell her "yes," and all your problems will be over... but something holds you back. You try to fight it, but the temptation is too strong. Eventually, you succumb and tell her what she wants to hear.
Eliza smiles and writes something down on her notepad. She turns to Dr. Yoneda.
Eliza: He's ready.
Dr. Yoneda: Thank you, Eliza. You may leave us now.
Eliza nods and walks out of the room.
Dr. Yoneda turns his attention to you.
Dr. Yoneda: Now then, let's talk about what we're going to do with you. As you may have noticed, this is not a normal school. Our primary goal is to enhance learning, and that's what we do. We use the scientific method and empiricism to explore the depths of the human mind. We take in gifted children and teach them the skills they need to succeed in life. Now, I'm sure you've noticed some of our students acting a little... strange. That's because in addition to enhancing their learning abilities, we also enhance their creative abilities. We do this through drugs, special diets, and a variety of other methods. The trade-off is that this causes some of the students to become less emotional and more logical. We find this is a worthwhile price.
You look at Eliza with new eyes. Was she on drugs?
Dr. Yoneda: (noticing where you're looking) Oh, Eliza is not a student here. She's just my little helper.
Dr. Yoneda: But enough about her, let's talk about you.
Dr. Yoneda gets up from his desk and walks over to you. He looks at you with the utmost seriousness.
Dr. Yoneda: I need to know if you're ready to embrace science and learn everything you can. Nothing can stand in the way of your thirst for knowledge. Do you understand?
Dr. Yoneda stares at you intently with his cold eyes.
Dr. Yoneda: Choose your next words carefully.