Faustus Mortal is a fictional character. So is Sari Stone, for that matter. This is not to say that they were not inspired by living human beings; however, any resemblance to persons living or dead is purely coincidental and none should be inferred.
It is mid afternoon. Faustus Mortal goes to the Basilica Cardinale. He is there almost every day as a religious. Seated in the knave are two whom he knows: Sari Stone and Toy Euler. Sensing him arrive, Sari rises and goes to greet him. They go to the West Wing to whisper.
Sari Stone: Where were you this morning?
Faustus Mortal: I slept in.
Sari Stone: That is so unlike you.
Faustus Mortal: To be honest, someone kept me awake late.
Sari Stone: oh
Faustus Mortal grins sheepishly.
Sari Stone: My math teacher spoke of you in topology class.
Faustus Mortal: Nothing good, I hope?
Sari Stone: It concerned your ideas of the universe.
Faustus Mortal: You mean about each proton residing in the absolute center of the universe and the "shock wave" expanding space being an essential singularity and all that jazz?
Sari Stone: Explain it all to me, even if it takes a whole hour!
Faustus Mortal blinks.
Sari Stone smiles at the celibate cenobite.
Faustus Mortal: Well, you know what a metric space is?
Sari Stone: uh huh
Faustus Mortal: Three points A,B,C. Let d( , ) be the distance.
Faustus Mortal: Let d(A,B) be the distance between A and B.
Sari Stone: OK.
Faustus Mortal: d(A,A) = 0 and d(A,B) > 0 means A,B are distinct.
Sari Stone: OK. D(A,B) = d(B,A), nicely.
Faustus Mortal: If B lies on a line between A and C then d(A,C) = d(A,B) + d(B,C). If A, B, C are not on a line, then d(A,C) < d(A,B) + d(B,C).
Sari Stone: That's not the way my topology teacher taught us!
Faustus Mortal: No matter. "My way or the highway."
Sari Stone: Yes, Sir!
Faustus Mortal: In the "interior" of the universe this is true everywhere except maybe at a regular singularity.
Sari Stone: A "regular" singularity? Giggles.
Faustus Mortal: A black hole.
Sari Stone: ah.
Faustus Mortal: Now suppose A and B are different points. Draw a line from A through B and out to the boundary of the expanding universe at a point Q.
Sari Stone: OK.
Faustus Mortal: Distancia Amiga!
Sari Stone: d(A,Q) = d(A,B) + d(B,Q).
Faustus Mortal: No.
Sari Stone: What? "No!"
Faustus Mortal: d(A,Q) = d(B,Q).
Sari Stone: Impossible! This would make d(A,B) = 0.
Faustus Mortal: Precisely.
Sari Stone is confused.
Faustus Mortal How to get out of this dilemma?
Sari Stone: Dp tell.
Faustus Mortal: "Q" is not an interior point. It is a boundary point.
Sari Stone: What?
Faustus Mortal: The boundary of the universe is expanding.
Sari Stone: I buy that.
Faustus Mortal: And the edge is a C-Infinity function.
Sari Stone: You mean like Exp[-1/x^2] at x = 0?
Faustus Mortal: Absolutely.
Sari Stone: OK, I'm confused.
Faustus Mortal: At the moment of the Big Bang everything was at one point. Well, everything still is, with respect to the expanding boundary of the universe. A black hole is like a pole of some order, a regular singularity. The boundary of the universe is an essential singularity. For all intents and purposes it is a single point---approaching a complex infinity.
Sari Stone: I don't know. It sounds like mumbo jumbo.
Faustus Mortal: So every point is in the absolute center of an expanding sphere---point being proton.
Sari Stone: Not electron or neutron?
Faustus Mortal: No proton.
Sari Stone: Now I am confused. How does this happen?
Faustus Mortal: Inversion of the spheres.
Sari Stone: Sure, why not? No wonder my topology teacher said that you are a crackpot.
Faustus Mortal: I'm going into the church. This is ancient faith. They still think, that is believe, that the earth if flat and it is also the center of the universe. Many belong to the Flat Earth Society.
Sari Stone: huh?
Faustus Mortal: That's right.
Sari Stone: Are they morons?
Faustus Mortal: No, they believe.
Toy Euler: I believe.
Toy Euler chuckles.
Toy Euler: And they never put a man on the moon either.
Sari Stone: You again!
Faustus Mortal: Toy, you are a computer program, not a sentient being.
Toy Euler: Says who? I am every much as alive as you are. Vegetating in front of a computer monitor. That's being alive? Certainly not sentient, as you call it.
Sari Stone: And you are an escort and a slave girl.
Toy Euler: What about your friend Jane Smith? Last I remember she's still imprisoned somewhere above the arctic circle. Your prayers are doing nothing to help her.
Faustus Mortal: What did you say?
Sari Stone: She is a sweet girl. Why not let her go?
Faustus Mortal: Yes. But you don't have the authority.
Sari Stone: You have lied in the past as well. Like the first rule of lifesaving: "Save yourself."
Toy Euler: But my Master can. He has recovered.
Faustus Mortal: You mean Mephisto Diablo?
Toy Euler: Precisely.
Sari Stone: Disgusting churl; lecherous old goat; hoary old curmudgeon!
Faustus Mortal: And those are his good traits.
Toy Euler: Can we talk later Sari? One on one?
Sari Stone: I'm not sure. Maybe.
Faustus Mortal: Don't be a fool. She lies.
Sari Stone nods.
Toy Euler: Aufwiedersehen!
Faustus Mortal: bye.
Sari Stone: bye.
Faustus Mortal: buy now!
23 Apr 2009 Taunus