Manifold Mystery

After scouring YouTube for a certain video evidence, I came up short. However, as I was watching Dawson's Creek tonight, I instantly recognized something. The episode I was watching concerned the gang's trip to a Boston college. Joey was accidentally roomed with a boy, AJ. Anyway, long story short, as they are saying goodbye on the train platform, AJ goes into a speech about the math concept of manifolds. I RECOGNIZED EXACTLY WHAT HE WAS SAYING. No, it wasn't because I understood the concept or learned about it. I had read about manifolds in a book (A Beautiful Mind by Sylvia Nasar) and AJ very much said, word-for-word, a paragraph in the book.


Here is the quote from the book:

"In one dimension, a manifold may be a straight line, in two dimensions a plane, or the surface of a cube, a balloon, or a doughnut. The defining feature of a manifold is that, from the vantage point of any spot on such an object, the immediate vicinity looks like perfectly regular and normal Euclidean space. Think of yourself shrunk to the size of a pinpoint, sitting on the surface of a doughnut. Look around you, and it seems that you're sitting on a flat disk. Go down one dimension and sit on a curve, and the stretch nearby looks like a straight line. Should you be perched on a three-dimensional manifold, however esoteric, your immediate neighborhood would look like the interior of a ball. In other words. how the object appears from afar may be quite different from the way it appears to your nearsighted eye."


Here is the quote from the show:

A.J: Do you know what a manifold is?
(she shakes her head)
A.J: It's a math thing. It's hard to explain. But, imagine yourself shrunk to the size of a pin point sitting on the surface of a doughnut. Look around you and it looks like you're sitting on a- a flat disk, right? But go down one dimension and sit on a curve, and suddenly it looks like a- a straight line.
Joey: You kinda lost me somewhere around the doughnut.
A.J: In other words, the way something appears from afar might be quite different from the way it appears to your near-sighted eye.
Joey: So in order for me to figure things out, I should get myself some distance?


Coincidence? I think not! The book was published in 1998 and there is no reference to the quote in the back. The episode aired in 1999. So take it as you wish but I was really excited when I heard those lines. I ran up to my room to find the book. One mystery that I can't solve tonight. Good night!